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Light in the Local Universe
i
LIGHT IN THE LOCAL UNIVERSE
My thesis is that light, and other forms of radiant energy, are
transferred from emitting atoms to absorbing atoms instantaneously,
without traversing the space, or the time, between the two. In a pair
of earlier books I have tried to explain how this is possible, and what
difference it makes in the interpretation of experimental results.
All of the observations which have been made by physicists have
been based on what they could see, in what I have called the local
universe, unique to each observer. But, they have generally been used
as though they were made in a universe where time is the same
everywhere. In this universe light would appear to have a finite
speed. I call this model of the real world the galactic universe.
While we no doubt live in this galactic universe, what we actually see or
experience is all contained in our local universe, where we define the
present time by what we can see right now. Einstein’s theory of
Special Relativity is the preeminent example of the use of data
obtained in the local universe as though it represented measurements
made in the galactic universe.
The difference between the two models is trivial in the everyday
world, but in astronomy, nuclear physics, and in particular, where
physicists are accelerating atomic particles to unimaginably high
velocities, it makes a big difference.
Or, I could be completely wrong.
Les Hardison
Les Hardison
ii
Light in the Local Universe
Copyright 2013
All rights reserved
Written and Published by
Les Hardison
Arinsco, Inc.
1682 Edith Esplanade
Cape Coral, FL 33904
ISBN 978-1 -4507-6373 -8
Light in the Local Universe
iii
CONTENTS
Chapter 1 Introduction .......................................................................... 1 Chapter 2 The Two Universes .............................................................. 5
The Galactic Universe .................................................................... 7 The Local Universe ...................................................................... 12 The Choice between the Two Models ...................................... 22
Chapter 3 Relativity in the Galactic Universe ................................ 25 Use of Galactic Space-Tme ......................................................... 26 Size and Distance .......................................................................... 29 Measurement of Distance and Length ...................................... 30 Time, AND its Measurement ..................................................... 33 Velocity Measurements ................................................................ 38 Relativistic Mass ............................................................................ 41 Energy Considerations ................................................................. 42
Chapter 4 Relativity in the Local Universe ...................................... 45 Distance Measurement in the Local Universe ......................... 48 Time in the Local universe .......................................................... 52 Velocity in the Local Universe .................................................... 59 Why Light Appears to Move at 300,000 km/sec .................... 71 Mass in the Local Universe ......................................................... 78 Energy in the Local Universe ..................................................... 80 Summary ......................................................................................... 85
Chapter 5 Velocities of Objcets Moving Away ............................. 89 Speculations on the Possibility of having two Ts .................... 98 Conclusion ..................................................................................... 99
Chapter 6 Time in the Two Universes .......................................... 100 Where the Two Times Agree .................................................... 100 Where the Times Disagree ........................................................ 104 Agreement about the Speed of Clocks .................................... 110 The Influence of Time Measurement on c ............................. 123 The Significance of c .................................................................. 124 The Uniformity of Time Throughout Galactic Space .......... 126 Accomodting the Invariant Speed of Light ............................ 129
Chapter 7 Comparison of The Two Systems ................................ 132 Measurement of Time ................................................................ 136 Measurement of Distance .......................................................... 144
Les Hardison
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Velocity in the Two Systems ..................................................... 147 Energy Consideration................................................................. 155 Comparison of Relativistic and Local Values ......................... 156 Why the Square Root Factors? ................................................. 160 A Credible Mistake ..................................................................... 163 The F correction explained ....................................................... 166
Chapter 8 Critique of Special Relativity ......................................... 172 Construction of the Basic Diagram ......................................... 172 The Meaning of t ........................................................................ 177 Which Way Does Light Travel? ............................................... 179 Seeds of Doubt ........................................................................... 182 The Speed of Light ..................................................................... 184 Transverse Motion Not Considered ........................................ 187 Pure Translation .......................................................................... 191 Summary ....................................................................................... 195
Chapter 9 Orbital Motion .................................................................. 200 Orbital Motion Around the Observer ..................................... 200 Orbital Motion Adjacent to the Observer .............................. 207 A Final Observation ................................................................... 212
Chapter 10 The Large Hadron Collider ......................................... 216 General description of the LHC at CERN ............................. 219 The Experiments at CERN ..................................................... 226 How are Mass and Velocity Measured at CERN? ................. 229 The CERN Results in Local Terms ......................................... 238 How Does the CERN LHC Funcition?.................................. 243
Chapter 11 Do Neutrinos Move Faster than Light? .................... 255 The Faster Than Light Neutrino Error ................................... 256 Are Neutrinos a Form of High Energy Radiation? ............... 259 The Opera Experiment Paper .................................................. 260
Chapter 12 Conclusions .................................................................. 301
Light in the Local Universe
1
CHAPTER 1 INTRODUCTION
The first book, A New Light on the Expanding Universe, was an
attempt to explain a different concept of how the Universe we live
in is put together and functions. It was based on the assumption that
light really does not travel at 300,000 Km per second, but instead
goes from one place to another in no time at all. That is, the emission
of radiant energy from one atom, and the reception of that energy
by another atom, are simultaneous events. They happen at the same
time, judging from the standpoint of the local time at the observer’s
location. This is equally true for two observers moving with respect
to each other in our three dimensional world.
To make this happen requires five dimensions --- the three we
observe when we look around us, and a fourth, which is the direction
the entire Universe is moving as it expands, at the apparent speed of
light 1 , plus a fifth dimension, around which our entire four
dimensional super-universe is wound, like a vast number of strings
representing our lines of sight..
The Universe described is pretty bizarre, but not as strange in many
ways as the one espoused by current theoretical physicists.
Allowing light to move at essentially infinite speed makes many of
Albert Einstein’s deductions untenable. For example, he deduced,
and I think firmly believed, that as objects accelerated (with respect
to an arbitrarily located observer) their time passed more slowly. The
1 The apparent speed of light is italicized here, as it is a phrase used in a special
sense. In this case it denotes the velocity, approximately 300,000 Km/sec,
which is usually defined as the speed of light in a vacuum, but is, in my
view, the speed at which the universe is expanding into the fourth
dimension.
Les Hardison
2
mass of the object increased and the linear dimensions got smaller
as the speed became significant relative to the apparent speed of light,.
My world is a little bit easier to believe, because sizes and masses
don’t change with velocity. They really can’t because all velocities
have to be measured with respect to something, and one reference
point is as good as another. So, simply shifting one’s coordinate
system to the moon should make our dimensions smaller and our
mass greater (at least as seen from the moon). But, how can one see
our mass from the moon?
Other changes in outlook follow from this simple change in
viewpoint. For example, the whole concept of energy changes. There
is no longer any need for “potential energy” as a concept. Things do
not acquire potential energy as they are lifted from the earth. If they
did, they would have a maximum potential energy with respect to
the earth when they are so far away from it that there would be no
way to even tell if the earth existed.
Instead, part of the inherent energy all matter has due to its velocity
in the fourth dimensional direction is apparent to an observer when
its direction of motion through four dimensional space isn’t parallel
his own. Every observer has his own private direction, and all
observers would judge the velocity and kinetic energy of each mass
they observe differently from all others who aren’t “stationary” by
their own standards.
The way the hydrogen atom is constructed has to change from the
accepted picture based on Bohr’s model, in order for light to be
transferred instantaneously. The concept proposed by Bohr back in
the early part of the 20th century, does not appear to be applicable to
hydrogen molecules, but only to hydrogen atoms, and is impossible
to apply to elements heavier than helium. The picture which does fit
with the theory of light presented here is applicable to all atoms,
regardless of size.
Many of these subjects were covered in the first book, and a few
additional ones were dealt with in the second book. However, a vast
Light in the Local Universe
3
array of experimental data has been collected by physicists and
carefully fitted into the present accepted concept of the way matter
is composed, and how it behaves.
This picture, usually called The Standard Model, is based on
quantum mechanical concepts, and quantum mechanics is, in turn
based on the presumption that light consists of waves/particles
(photons) which move through a vacuum at 300,000 Km/sec. I
think the basis is wrong, and therefore much of the substance of
quantum mechanics is wrong. I don’t believe photons exist; they are
simply made up by physicists to account for some of the properties
of light they can’t explain otherwise. Likewise, the other “transfer
particles”, muons, gluons and gravitons are, to my way of thinking,
mythical.
There are innumerable measurements made by experimental
physicists which have integrated into the Standard Model, and which
must fit just as well into my model of the Universe, and a lot of
pieces and parts that aren’t necessary in my model.
Most of these I am only vaguely aware of, having not much
education in physics beyond the fundamentals. However, all of the
measurements need to fit into my picture at least as well as they do
into the Standard Model for it to be a good theory. I am not sure
they do, because I haven’t had time to learn about all of them.
I won’t pretend to cover the whole of physics in this book either,
because I don’t know the tiniest fraction of all of the experimental
results which have been produced by the thousands of physicists,
living and dead, who have made significant contributions to the
literature. But, in this book, I will try to examine some of the
additional experimental work I have become aware of. Of course, I
will do so from the view point of someone who has something to
sell (my ideas about how the Universe works), so let the reader
beware.
Even more importantly, I believe that there are two distinct ways of
looking at the physical universe, which I have called the galactic
universe and the local universe. Modern physics operates in the former,
Les Hardison
4
yet all of the observations are of necessity, made in the latter. My
rules apply strictly in the local universe, and the main disagreements lie
in the translation from one system to the other.
I will present a description of the two universes, and work out the
conversions necessary to represent time, distance and velocity in the
galactic universe, when the measurements are made in the local
universe. In doing so, I hope to explain why the Einsteinian
corrections to measured physical constants are unnecessary when
they are ascribed to the local universe in which they were measured.
In particular, there is a lot being done (at great expense) to explore
the internals of the fundamental particles the world is made of,
mainly protons, neutrons and electrons. The premier experimental
apparatus in this field, and possibly in any field these days, is the
Large Hadron Collider at CERN in Geneva, Switzerland. This very
impressive machine accelerates bunches of protons (which are a kind
of hadron) to 99.9999999 per cent of the apparent speed of light, and
smacks them into other bunches going the opposite direction,
producing unbelievable temperatures, and every kind of nuclear
particle known to man. I don’t presume to understand what they are
doing in detail or how they evaluate the results. I do believe that the
protons in the accelerator are going many times the apparent speed of
light, when looked at as taking place in the local universe of the
experimenters. How this could be the case will take some explaining,
and I will try to furnish the explanation.
Finally, it has been difficult for me to define an experiment which
might produce acceptable results according to my theory, and
untenable results according to conventional physics. The Einsteinian
approach has worked pretty well. However, I may have found an
experiment or two which would be effective in supporting my
picture of the Universe as contrasted with conventional physics. I
will include a description of the proposed experiments.
Light in the Local Universe
5
CHAPTER 2 THE TWO UNIVERSES
In a previous Book2 A New Light on the Expanding Universe,
I presented the case that light is transmitted instantaneously from
the source to the receptor, without waves or particles transiting the
intervening space,
I was able to reconcile this concept with the generally accepted laws
of physics. However, there was one problem which was not
resolved. The energy which seems to be inherent in matter, in my
view, is
2E mc , EQUATION 1
regardless of the velocity of the mass with respect to the reference
system in question. This is based on the presumption that all of the
matter in the universe is moving in a fourth dimensional direction,
the direction in which the expanding universe is expanding, and that
the velocity we see in our three dimensional world is just a
component of the total velocity, c.
Conventional physics says the equation should be
22
2
mvE mc . EQUATION 2
In the previous book, I argued for the first case because it is simpler,
although it makes no provision for physical bodies moving faster
than c, presumably because there is no way for them to be
2 Hardison, Les, A New Light on the Expanding Universe, 2010, Self
Published ISBN978-0-615=37746-9
Les Hardison
6
accelerated past c by gaining energy from other physical bodies, as
all have exactly the same absolute energy and therefore the same
absolute velocity.
After careful consideration, I believe that E=mc2 represents the
total energy of electrons and protons when they are considered to
be moving as observed in the local universe in which all of our
measurements are made. When these measurements are imputed to
the galactic universe, the illusion of the added component appears.
This chapter considers the proposition that perhaps both equations
are correct, but that they apply to different ways of looking at the
universe. Equation 2, when one looks at the world from the godlike
viewpoint, which I have called galactic space-time or the galactic
universe, and that Equation 1 is the correct representation of the
energy of moving bodies when the Universe is considered to be a
local universe, which can actually be seen by an observer at his own
local “present time”.
I will do my best to describe the two alternative ways of viewing
space and time. Throughout the discussion it is important to keep in
mind that the universe viewed by physicists is largely consistent with
what I have called the galactic universe, on which the Special Theory of
Relativity and most of the subsequent developments in physics is
based. The concept of the local time is my description of an
alternative way of looking at the things, and one which I believe is
simpler, and helps explain a number of the conundrums in modern
physics.
Light in the Local Universe
7
THE GALACTIC UNIVERSE
The galactic universe is most simply explained by reference to an
analogy, in which the real, 3D space is represented by the two
dimensional surface of a balloon. The balloon is expanding, as our
3D space is expanding, and it must have another dimension to
expand into. This third dimension in the analogy I have called T,
defined as
,T ct EQUATION 3
where:
T= a fourth spatial dimension
c= the apparent speed of light (about
300,000 Km/sec)
t =time.
Time is measured from some arbitrary time, which could be the time
of the Big Bang, or any subsequent time.
The galactic universe is defined as the space contained in the entire
volume of the universe where time is everywhere the same at any
given moment. If it is, right now, January 1, 2013 at precisely 12:00
noon Central Standard Time in the US, it is also exactly the same
time on the far side of the moon, or on a far distant planet in a
different galaxy. We choose to use different time zones for
convenience, but the essential concept of the present time is
presumed to apply uniformly throughout the galactic universe.
This is very difficult to visualize because the expansion of the three
dimensional volume requires a fourth dimension for it to expand
into, just as the two dimensional surface of a surface of the balloon
could not expand if it did not exist in a three dimensional world.
It is possible to picture a two dimensional analog of the universe,
where the expansion is taking place with the diameter of the balloon
increasing in a direction perpendicular to the surface. I have called
this the T direction, and the assumption that the velocity of
Les Hardison
8
expansion is c, the presumed speed of light, fits very well with the
estimated age of the universe and preset size of the universe.
In this analog, time is galactic time and is everywhere (on the surface
of the balloon) the same as it is at the point representing our location
in space and time as the observer at the origin of our own coordinate
system. This should not be difficult to grasp, as a balloon being
blown up obviously has all of the elements comprising the surface at
the same diameter, at the same time.
The surface of the balloon represents all of the points in the galactic
universe at the present galactic time.
FIGURE 1
INSTALLING A COORDINATE SYSTEM FOR THE GALACTIC
UNIVERSE
On the two dimensional surface resenting our three dimensional
universe, I have set up an arbitrary coordinate system, with the
observer, who is studying the universe at the origin. This origin could
be placed at any point on the balloon’s surface without altering the
geometry of the situation
Light in the Local Universe
9
In the local area close by the origin, the universe appears flat, and we
can make calculations and draw figures on a simple rectangular grid
without any particular problems. Because the diameter of the
Universe is very great, on the order of 27 billion light years, the
curvature is not likely to be a problem when we are dealing with
things within a few million light years of our reference system origin.
There should be no problem treating it as a nice orthogonal square
grid on the surface of the balloon, and 3D space as a similarly square,
well-behaved grid system. So, for the rest of this discussion, the two
dimensional analog surface and the 3D real world coordinate system
will be shown like this
.
FIGURE 2
THE 2D ANALOG OF THE 3D GALACTIC UNIVERSE
We can define time very simply in this snapshot of the universe. It
is, in every point in x – y portion of the universe, the same time as it
is at the origin. The time at the origin can be taken as a parameter
that is increasing at a constant rate, so time is independent of the
placement of the origin. Distance, presuming distance could be
Les Hardison
10
measured by the placement of measuring rods between any two
points, would be independent of the particular time the
measurement was made, for stationary objects, and would depend
on the time for moving objects, where the movement is measured
with respect to the observer at the origin.
One must bear in mind that our observations of real objects and
events does not permit us to use this galactic grid system, for the
simple reason that the Universe is expanding, and things which we
would define as distant objects cannot be observed as they exist at
the instant we make the observation. This is because, in this space
time arrangement, light appears to move at a constant, limited
velocity, c which is approximately 300,000 km/second. Because this
is enormously fast in comparison to our everyday observations, it
seems to be instantaneous. However on the scale of interstellar
space, it is slow enough that it may take years, or millions of years,
to reach us.
The conclusion must be reached that any observation of a distant
body or event involves, not the “present” galactic time, but a “past”
galactic time, at which time the body may have been different than it
is “now” and at a different location in three dimensional space. How
different depends on how far away the event or body is from us and
on how fast it is moving relative to our present location.
In the galactic universe, it appears that light and other forms of radiant
energy transfer move through space at a constant velocity c,
regardless of the choice of coordinates, or the relative motion of the
observer with respect to the “path” of the light. In this galactic universe,
E=.mc 2 for objects at rest with respect to our three dimensional
coordinate system, and seem to have an additional velocity and
kinetic energy (velocity energy) when moving with respect to the
coordinate system we are using.
Because the expansion of the universe is in a dimension of which we
have no sensation at all, it is difficult to conceive of it as anything
but a sort of abstract construct which complicates the straight-
forward three dimensional space we experience daily. Yet the
Light in the Local Universe
11
evidence is pretty strong that the universe is, in fact, expanding. It
appears to have been doing so for a long time, on the order of 14
billion years, and to have grown in size from something very small
near the beginning of time, as we know it, to something on the order
of 14 billion light years in radius, or 28 billion light years in diameter.
There is more on the geometry of the galactic universe as I see it in the
appendix to this chapter.
Les Hardison
12
THE LOCAL UNIVERSE
Our own, local universe3, comprised of the totality of all that can see
or sense in any way at any given instant in time, differs considerably
from the galactic universe described in the previous chapter.
Generally speaking, modern physics models the world along lines I
have called the galactic universe model, where the entire 3D universe
as we know it exists at any given moment in time as a sphere where
every object, and all the space surrounding the objects, exists at the
same instant of time.
The shape of this space is not hard to imagine, if one leaves out the
fourth dimension into which the universe is expanding. It is simply
a sphere, with the observer at the center.
However, it is considerably more difficult to imagine this sphere with
a fourth direction, basically at right angles to the normal three
directions (forward and backward, left and right, and up and down,
or x, y and z) but it is analogous to the surface of a balloon, which
has a two dimensional surface curved in a third dimension, and
expanding continuously into that same third dimension. Every point
on the surface of the balloon has a common time. Every observer
located on the surface would have exactly the same time on his local
clock, but every observer at a different location than ours would see
a different picture of the universe. His local universe would be
different from ours.
3 Note: I have not italicized the words referencing local and galactic space
or time for the remainder of the book. These terms always reference the
special meanings I have defined for them.
Light in the Local Universe
13
The galactic universe is a very useful analog, but there is one striking
problem with it. That is, if the balloon surface represents the entire
universe, the parts that are far away from us cannot be seen from
any observation point on the surface. Because light appears to move
slowly (in comparison with the vast size of the balloon), by the time
light from a distant star gets to us, it will only give us information
about where the star was and what was going on there at some time
in the far distant past.
The same problem exists for observations of objects and events
which are much closer to us. As observers, we see nothing of the
surface of the balloon as it is now, but rather only things as they were
at some time in the past (the very, very near past for objects close
by, and the far distant past for objects far away.) Still, what we are
observing is not the universe the way it exists at the time we as local
observers define as right now, but rather the universe at it existed at
various times in the past by galactic standards.
On the other hand, the universe which we actually see, the
composite of objects reaching back in galactic time millions of years
for distant galaxies, comprises our local universe, which is entirely at
our present local time. So, what we see, at the present moment,
comprises our local universe at our local present time. We have no
access whatever to information from other points in the galactic
universe, or on the surface of the balloon at other locations.
Again, it is convenient to use a two dimensional analog to represent
the nearby relatively orthogonal portion of the expanding universe,
but instead of a two dimensional plane as our mapping surface, we
have an inverted conical surface with a 90 degree cone which
contains the x and y coordinate system with the origin, and the local
observer, located at the apex of the cone.
The one point at which the galactic universe and the local universe
share location and time is at the origin. The apex of the cone
representing the local universe is placed at the origin of the galactic
universe, so it appears to extend into the galactic past. All of the rays
extending out from the origin of the local present cone represent the
Les Hardison
14
pathways by which light or other forms of radiation could reach the
observer at the origin from any point in the local universe.
FIGURE 3
THE SHAPE OF THE LOCAL UNIVERSE
The shape of the local present is depicted in Figure 3.
In this picture, the entire universe that is visible from the origin lies
along the surface of the cone, and it is all presumed to exist in the
local present. As the galactic universe expands in the fourth
dimensional T direction, the local universe cone moves right along
with it, but the methods of keeping time and measuring distances
and velocity must be altered radically.
Whereas the nearby part of the galactic universe appears to be a flat
plane (actually a tiny segment of a vast sphere) when viewed as a two
dimensional analog of our three dimensional Universe, the local
universe appears as the surface of a cone. The x and y axes are bent
downward at a 45 degree angle, if our vertical, or T scale, is chosen
with units consistent with the units of the x and y axes. That is, all
of the units are given in length units, such as Km, or all of them are
given in time-like units, such as years and light years.
Light in the Local Universe
15
Figure 4 illustrates, in a cross sectional view of the local universe
cone, the relationship between galactic past, present and future, and
the past, present and future of the local universe. In the local
universe, everything lying along the 45 degree lines of sight
represents things which we can see at the moment, and which
comprises our local present. The local past is all of the area lying
inside the cone, which may have been seen in the past, but can never,
under any circumstances, be seen again from our position at the
origin. And outside the cone lies the future, which we may be able
to see at a later time.
FIGURE 4
THE LOCAL UNIVERSE PAST, PRESENT AND FUTURE
In Figures 3 and 4, the lines of sight are plotted as lines where
x = T, so they are at 45 degrees relative to the x Axis in the galactic
universe, and to the T Axis. If they are lines of sight, it is apparent
that things are receding into the past of an observer permanently
affixed to the origin at a velocity V, which represents the speed at
which the three dimensional universe is moving in the fourth
dimensional direction, T. So, there would be no quarrel with us
writing that T=Vt.
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16
However it is also apparent that, from the standpoint of the galactic
universe, T=ct. Therefore we can presume that in the local universe,
V = c, where c is the apparent speed of light. Thus the lines of sight are
along lines where x=ct and x=-ct. In Chapter 3, we shall make the
case that the relationship between these variables makes a
compelling case that the velocity of light, as seen by a real (i. e., local)
observer is infinite, and the velocity of the universe in the fourth
dimensional direction is c, the apparent speed of light. There is, however,
a missing piece to this story which needs to be filled in later.
We make all of our observations from our present location in the
local universe, where what we see at any given time is what we know
to exist. Yet, the historical practice in the physical sciences, dating
back to Newton and earlier, is to presume that reality is represented
by the galactic universe, where the time scale is independent of the
location. This has led to all sorts of corrections, and many
unexplained observations of physical phenomena. For example, the
presumption that light has a finite velocity which is the same for all
observers, regardless of their speed relative to each other.
The invariance of the speed of light is possible only under two
circumstances. One is where the velocity of light is infinite, which
would, of course be measured the same way by any two observers
whether moving relative to one another or not, and the other is that
described by the Theory of Special Relativity, which suggests that
time moves at a different pace for systems moving relative to one
another, and somehow modifies the properties of matter moving
with respect to the observer.
Science has accepted the latter case, wherein the time contraction
calculated for objects moving relative to us is presumed to be real,
and with it all of the consequential results. The dimensions of objects
shrink and their masses increases with velocity relative to any
arbitrary reference system. These are, of necessity, illusions of some
sort, because two observers moving relative to each other would
assign two totally different masses to the same object, and would
believe it had two different lengths.
Light in the Local Universe
17
So, there is some reason to consider the other possible solution to
the problem of the invariance of the speed of light; that is, that light
moves instantaneously from place to place. This would eliminate
many of the problems with relativistic physics, but would raise the
question, “what is c, the apparent speed of light, if it is not actually the
speed of light?” I will try to answer this in subsequent Chapters. But
for now, let us presume that the local universe is a coordinate system
superimposed on the galactic system of space and time coordinates
described previously, and that the local universe consists of
everything one can see at any given moment.
Whether one accepts the idea that the speed of light is infinite or
not, there is no choice but to accept that the local universe, which
one sees from his present location at the present time, is shaped like
the inverted cone in Figure 3, where everything he can see is lies
within the surface of the cone. This is true whether one accepts that
the light moves instantaneously from the various points along the
surface to his eyes at the apex of the cone instantaneously, or rather
gets there by moving through the intervening space as the apparent
speed of light, as though swimming through space like a fish swims
through water. Most of the following is true in either case.
The observer, at the apex of the cone is at the single point where the
local universe and the galactic universe are at exactly the same time.
As one moves away from the apex in any direction, the distance
increases, and one moves backward through galactic time, into the
galactic past. In the local universe, I have chosen to take the surface
of the cone as the local present, where one’s universe consists of what
one can see at the present moment. This involves the implicit
assumption that the light from distant objects is transferred
instantaneously, at least in term of the local time, which is the same
for all the point on the cone, so far as we, at the apex, are concerned.
We might presume that an object, such as another laboratory
containing another observer were located some distance away, but
close enough that we could see him from our position at the apex.
Were we to possess extraordinary eyesight, and a marvelous
telescope, we might be able to make out the clock on his work table.
Les Hardison
18
Because we would have assigned the time on our clock to the entire
cone, we might presume that the clock on his work table will read
the same as ours, but this is not true. He is, in terms of galactic time, in
the past, and his clock will, at some future time (from our point of
view) read the same as ours does now, when his balloon surface
reaches the same T value as our balloon surface is at now. But right
now, by our standards, he is in the galactic past, and his clock runs
on galactic time, as does ours. We would make out his time as being
earlier than ours by exactly the distance between us divided by the
speed at which the universe is expanding. That is, his clock will read
slow by (Δx/c)Δt.
This second observer, if he is not moving with respect to our
position, would see us at an even earlier time; and think our clock
was reading too early by the same amount we thought his clock was
reading too early a time.
During this discussion, it must be borne in mind that the local
universe, like the galactic universe, is simply a reference system for
depicting a particular instant in time, during which what we perceive
as the real world exists. The 4D universe seems to be quite
independent of time, and is unchangeable and immutable. The
galactic universe represents the point in time (in the fourth
dimensional direction (T=ct), at which we are right now. It is a cross
section of the 4D world at the present moment in time, and we can
picture what it looked like at past moments in time, and predict some
things about how it will look at future moments, but we can only see
the local universe.
The local universe is the part of the 4D universe we can actually see
at that time, because radiant energy transfer takes place at intervals
along relatively straight diagonal lines in 4D space. (Yes, space is
curved by the presence of matter and electric charge, but these
weren’t dealt with in Special Relativity, and we will simply consider
the surface of the balloon undistorted for most of this book.)
All of this discussion pertains to a 2 dimensional analog universe
with x and y as the coordinates, and z presumed to be equal to zero.
Light in the Local Universe
19
The third dimension in this analog universe is T, where T = ct. T is
a dimension measured in length units, such as micrometers or light
years, c is the speed of expansion of the universe in the T direction,
and t is time, measured in units of microseconds or years, or other
time units consistent with the measurement of the spatial
dimensions.
In the analog models, the galactic universe is the nearby, relatively
flat surface of a huge sphere. The observer’s local universe, on the
other hand, is a cone with its apex on the surface of the galactic
universe, and the time throughout the cone is the same. So, at the
observer’s location, galactic time and local time are the same.
However, at any other point, local time differs from galactic time by
the ratio of the distance away from the origin to the apparent speed of
light, c.
FIGURE 5
THE LOCAL UNIVERSE CONE BENEATH THE GALACTIC
UNIVERSE PLANE
In Figure 5, the cone representing the local universe coordinate
system is shown just touching the plane representing the galactic
universe with the apex of the cone at the origin of the galactic
coordinate system.
Les Hardison
20
For the most part, physicists have treated the two systems for
measurement of time, distance and velocity as though they were the
same. From my point of view, this has led to some very great errors
in perception of how things “really are”. This concept works quite
well in explaining many phenomena, and making useful predictions.
However, I believe the concept of the local universe offers a more
reasonable representation of reality, and certainly a simpler one.
In the local universe we must assume that, if we see something, it
actually exists in the local present time. This involves assuming that
the light, or other electromagnetic radiation used to detect an object,
reached our eye at essentially the same time it was emitted by the
source of the radiation. In other words, the speed of light is infinite
in the local universe.
It is not too different from the space Dr. Einstein was hinting at with
Special Relativity. He defined simultaneous events as those which an
observer could see happening at the same time. If I see two stars at
the same time, even though they may be light years apart, it implies
that the emission of light from each of them and the reception of
the light at my eyeball are simultaneous events. I know that I am
seeing them at the same local time I am experiencing, as though that
the light took no time to get from each of them to me, the observer.
I can understand that, from my observations I may be able to
calculate what things might be like in the galactic universe at this
point in galactic time, but there is no way to verify my predictions
until some later time.
So, I have two times I can use in making predictions. The local time
I assign to an object, which is the same time as my own galactic clock
reads, or the galactic time, which is still in my future. I have to keep
these two times straight, or I will get some misleading results.
An analogy that one may experience in ordinary life involves
traveling from one country to another, possibly by cruise ship. If one
carries a smart phone, it keeps track of time in two ways. Because it
contains a GPS receiver and computer, it always knows precisely
where you are at the moment, and adjusts the time on your clock
Light in the Local Universe
21
automatically to the time zone you are in. So, when you cross the
border from one time zone to the next, the clock jumps an hour
forward or backward, depending on which direction you are moving.
This is very much like my concept of local time, where the important
element is where your clock is located at the moment.
However, concurrently, you may also keep track of Universal Mean
Time, which used to be called Greenwich Mean Time. This is the
reading of the clock in the observatory in Greenwich. England.
UMT is exactly the same everywhere in the world. It changes
continuously, but, like galactic time, if you will, as it presumes the
time is the same no matter where you are on the surface of the earth.
The two clocks only agree when you are in the Greenwich, England
time zone.
In the following chapters, I will try to establish the rules for relating
time, location or distance, velocity and energy as measured in the
local universe of the observer, and how it would appear if a godlike
observer were able to make the measurements in the galactic
universe. I will try to point out where modern physics uses the
attributes of each, and how much simpler life would be if we stuck
to the local world as the place to do our calculations.
While I do not doubt that there is an element of reality in the galactic
universe model, it is a model of a reality which we can never
experience directly, while the local model is a true representation of
the world the way we see it.
Les Hardison
22
THE CHOICE BETWEEN THE TWO MODELS
So, when one wishes to represent the world as it really is, he has a
choice of using the galactic model or the local model I have
proposed, or some other model of his own choosing.
In the galactic model, the universe is analogous to a vast balloon,
expanding into a fourth dimension at a rate which appears to be
constant with time, where all of the points on the surface of the
balloon at any instant are presumed to be at the same time, and it is
presumed that observers at a distance from our own position would
have clocks which read essentially the same time as our own clock.
In the local model, it is presumed that the local time is the same for
everything we can see at the moment. Because those things we can
see are all at some distance from us, they would be in the past by
galactic standards, and the clocks of distant observers we could see
or communicate with would all read earlier times than our own. The
farther away they were, the earlier their clocks would read.
Although the two universes appear to be identical to the ordinary
observer, dealing with ordinary objects which are not moving very
fast (relative to the rate at which the universe is expanding) or not
very far away (relative to the amount of change in the size of the
universe in a time period a person can experience - a second, a year,
or even a lifetime), the difference becomes important when dealing
with fast moving objects, or those which are far away from us.
These are the things which Albert Einstein dealt with when working
on his Special Theory of relativity. At the time he did his work, there
had not been enough data collected by astronomers to lead them to
believe that the universe was, in fact, expanding, or to speculate on
what it was expanding into if it were. So, Einstein used the same
presumption that all his predecessor physicists had used, and that
was that time was everywhere the same within the universe.
Still, he was faced with the seemingly irrefutable observation that the
speed of light was finite and constant throughout the universe,
Light in the Local Universe
23
without regard to the velocity of the observer who was measuring it.
This was anomalous because all physical objects which move
through space, or through a medium such as air or water, are
observed to have different speeds when measured by different
observers who are moving relative to one another. Light or
electromagnetic radiation in general, seems to be an exception to this
rule.
This anomaly led to his development of the Special Theory of
Relativity, which provides a picture of the universe in which it is
possible for observed velocities which are close to the apparent speed
of light to appear to be moving at the same speed regardless of the
velocity of the observer.
However, the Special Theory of Relativity contains within it some
anomalies which sow seeds of doubt as to either the input data, the
interpretation of the model of the universe, or the derivation of the
equations. The relationships between the measurement of distances,
time, velocity and energy when viewed by a “stationary” observer,
and one moving at a significant velocity relative to the stationary
observer, all involve complex correction factors and seem to lead to
analogous conclusions when observers are presumed to be moving
relative to each other. For example, they will assign different masses
to any given object.
The local universe model is not an alternative to the galactic
universe, but is rather a part of it. However, it represents the part
which an observer can actually see, rather than simply imagine.
Thus, it is possible to assert that all of the measurements of
scientists of whatever type are made, essentially according to the local
model of the universe. However, it appears that they are often
attributed to the galactic reference system, as though the
measurements were made without taking into account the time
differences between the observer and the things being observed.
Einstein used the galactic system for the development of Special
Relativity, without defining it as such.
Les Hardison
24
This conclusion is based on his implicit use of the idea that time is
the same everywhere along his x Axis, which is a one dimensional
analog of our three dimensional space. I believe some of the
translations of data from the local universe observations to galactic
universe representations are faulty, and should be replaced by
equations which are based on my interpretation of the nature of the
local universe.
Light in the Local Universe
25
CHAPTER 3 RELATIVITY IN THE
GALACTIC UNIVERSE
Einstein correctly pointed out with his Special Theory of Relativity4
that time, when measured in a reference system moving with respect
to our own, must appear to run slower by an amount which becomes
significant when the relative velocity approaches the apparent speed of
light.
In order to make the speed of light invariant when measured by
observers moving relative to one another, he derived equations
relating to space and time that limits the velocity of all objects to the
apparent speed of light. Such objects appear to become smaller as they
move relative to the observer, and masses become greater.
The effects are not noticeable under ordinary, every-day conditions.
If they were, it would be easier to say that it is absurd that the
physical properties of matter change with velocity relative to any
arbitrary coordinate system.
A real observer looking for information about the present state of
the galactic universe must take what he sees at the moment, and
make presumptions about what will happen during the future, so he
may guess a position and state of the object in his present galactic
time. This is true of everything in the galactic universe. Nothing can
be known of it for certain, as it is not, at present, what we can see.
The fictitious observer at the origin of a coordinate system lying
wholly within the confines of galactic space would have to have
4 Einstein, Albert. Relativity, the Special and General Theory, Translated by
Robert W. Lawson, University of Sheffield, Crown Publishers. New York,
NY, Third Edition, 1918.
Les Hardison
26
some supernatural, god-like power to see what was happening
instantaneously in the space represented by the surface of the
balloon, or in the real world. Such an observer does not exist, but it
is be handy, from time to time, to imagine what he might see, if he
did exist.
USE OF GALACTIC SPACE-TME
In the following pages, I will try to walk you through Einstein’s
derivation of the equations of Special Relativity, and try to
demonstrate that they are presumed to apply to the galactic universe,
as I have defined it.
We can begin by looking at the expressions for length, time and
velocity in the galactic system. Einstein accounted for light from all
observers by starting with the assumption that light moved through
the space between the emitter of the light and the receptor much as
a fish swims through water, just a lot faster. Except that, no matter
whether you were moving relative to any arbitrary reference system
or standing still, the measurement would come out the same. Based
on this assumption, he deduced that time had to be different for
observers moving relative to the stationary coordinate system, and
he derived the equations of Special Relativity, which are still, after
over 100 years, taken to be essentially correct.
Light in the Local Universe
27
FIGURE 6
EINSTEIN’S DIAGRAM OF THE GALACTIC UNIVERSE
In this relatively simple diagram, he showed the path of light leaving
the origin in the diagram, and moving either to the left or the right
with a velocity c, which is what had been measured quite accurately
at the time Einstein did his work on Special relativity. Also, it had
been determined that, as close as measurements could be made, the
speed was constant, regardless of the motion of the observer relative
to anything else.
So, his simple plot shows the plot of the distance light shining out
from the origin moves to the left or right at the velocity c, if it is
going to the right, and – c if it is going to the left. These are not
unreasonable assumptions; although one would have to point out
that there is no way for an observer to determine what happens to a
beam of light which moves away from his present location.
Everything we see in the real world is the result of light moving from
somewhere else toward the observer, who is in the center of his own
observable universe.
He then postulated a second observer’s with his own coordinate
system, moving relative to the stationary observer, at a velocity v
relative to the stationary observer.
Les Hardison
28
He said that the second observers measurements of the path of the
light leaving the stationary origin would have to be exactly the same
path as that seen by the stationary observer, which means he would
have to agree that the velocity c was the same for him as it would be
for the stationary observer. This would not be true if they were both
observing a fish swimming through water, or a space ship moving
through space. Both would appear to be moving at velocities that
were different for the moving and stationary observers.
In order to make the arithmetic come out right, he used the Lorentz
transformation, which involved allowing the rate of passage of time
to be different for the moving and stationary observers. This not
only meant that, while the speed of light was measured the same by
all observers regardless of their motion relative to each other, all
other velocities had to come out the same also. Both the distance
and the time had to be “corrected” when the velocity of the object
or system was significant compared to the presumed speed of light.
These corrections are at the heart of the Special Theory of Relativity,
and have been treated as essentially holy writ since shortly after their
introduction.
Light in the Local Universe
29
SIZE AND DISTANCE
Essentially all of the equations derived as a part of the Special Theory
of Relativity are based on the assumption that light moves at a finite
speed, c, through empty space and that the velocity of light is
invariant. That is, two observers moving relative to one another will
both measure the same velocity for light. This was presumed to be a
special characteristic of light, or other forms of electromagnetic
radiation, although the prior experimental work was all done with
visible light.
The basic methodology involved using the Lorentz transformation,
relating special coordinates with a time coordinate and translating
them so that a single velocity, in this case c, would be measured the
same by each of two observers moving relative to each other at any
arbitrarily chosen fixed velocity.
The step by step application of the Lorentz transformation is, for
the reader’s convenience, appended to this chapter, so only the
resulting equations, which comprise the core of the Special Theory
are repeated and discussed here.
Les Hardison
30
MEASUREMENT OF DISTANCE AND LENGTH
The relationship he derived for distance measurement is
2
2
'
1
x vtx
v
c
EQUATION 4
where:
x’ = distance to the fixed object at x
observed by the moving observer
x = distance to the object from the origin
of the stationary coordinate system
t = time, measured in terms of a clock that
is stationary with respect to the
coordinate system
v = velocity of the object referred to the
stationary coordinate system.
This should apply equally well when we are talking about observing
objects which are moving relative to our coordinate system (and are,
presumably, stationary with respect to a coordinate system moving
with the object.)
In short, objects seem to be farther from us when they are moving
away from us at a velocity which is significant with respect to the
apparent speed of light, where x-vt is the distance we would ordinarily
agree upon if the velocity were small in terms of the apparent speed of
light.
Also, the implication here is that the distance to objects which are
moving away from us will appear to be smaller than someone
moving along with them would think them to be, and the lengths’
shorter, because for x =0,
Light in the Local Universe
31
2
2
'
1
v tx
v
c
, EQUATION 5
where v t represents the uncorrected distance of the moving
object.
Were an object originally at the origin considered to be moving,
relative to a stationary system, x in the above equation would be
equal to 0, and the velocity would be in the positive direction, rather
than subtractive. So, the coordinate of the object moving at velocity
v relative to the fixed coordinate system would be
2
2
'
1
vtx
v
c
. EQUATION 6
The time experienced by anyone moving along with the moving
object would have been taken by Isaac Newton to be t, just as a
godlike observer living in the galactic universe would presume it to
be, uniform throughout the galactic universe.
The notion that objects are shorter when moving away from the
observer is somewhat mystical, in that it should be apparent to
anyone that all of the objects surrounding him are, by his standards,
quite normal in size, and do not seem to be changing from day to
day, even though out velocity relative to some of the heavenly bodies
is quite high, and our velocity relative to the sun is changing rapidly
in direction, and also, to a lesser extent, in orbital velocity as the earth
approaches and recedes from the sun.
Therefore, the meaning of the shrinkage of length must apply only
to the observations of others, moving rapidly compared with c, the
apparent velocity of light, relative to our own position in space. The
method of measurement of the length of an object moving away
from us with a velocity significant with respect to c is tricky, in that
any sort of measuring stick used to measure the length would, of
Les Hardison
32
course, also show the same degree of shrinkage as the object being
measured.
This suggests to me that there is more to the story than is revealed
by the equations of Special Relativity. This is a point I will make
repeatedly.
Light in the Local Universe
33
TIME, AND ITS MEASUREMENT
The most significant departure from conventional physics contained
in Special Relativity involves the concept that time does not appear
to pass at the same rate for systems or objects moving at velocities
significant with respect to c, the apparent velocity of light. This was a
complete game changer for physics, which had previously regarded
time as a given, inflexible subjective experience which always passed
at a measured rate, whether the measurement was made by
astronomical observations or a mechanical clock.
In order to account for the invariance of the apparent velocity of
light, Einstein had to presume that the clocks of observers moving
relative to one another (in our three dimensional space) ran at
different speeds.
Einstein calculated that time would pass more slowly for the moving
observer, and the rate of passage of time would be such that
2
2
2
'
1
vxt
ctv
c
. EQUATION 7.
In this equation, x is the coordinate of a stationary point relative to
the stationary coordinate system. So, it is a constant in the equation,
as is the velocity. So, in comparing time intervals, as opposed to
absolute times,
2
2
'
1
tt
v
c
. EQUATION 8
Les Hardison
34
Generally speaking, for objects which are not very far away, the
numeric value of vx is much, much less than c, and the revised time
can be written as
2
2
'
1
tt
v
c
, EQUATION 9
or
2
2
' 1 1
1
t
t Fv
c
, EQUATION 10
for vx very small when compared with c2.
This gives the impression that the rate of change of time is slower in
the moving system than in the stationary one.
This is, of course, untrue. Otherwise, our clocks, which seem to run
at a very ordinary and reproducible pace, would change speed
whenever some arbitrarily chosen secondary reference system
changed speed. I will try to demonstrate, in a later chapter, that the
correction factor F is not a real characteristic of the physical
universe, but the correction of an error by making observations
made in the local universe and incorrectly attributing them to the
galactic universe.
I maintain that all clocks (accurate ones, at least) run at the same
speed, and do not change rates at all. However, when you observe a
clock attached to a body that is moving with respect to your position,
you will see it taking longer between ticks than yours because each
successive tick is farther away from you than the previous one, and
therefore farther in the galactic past. The frequency of the ticks will
vary just as the frequency of sound varies when the source is moving
relative to you. You are acutely aware of the apparent change in
Light in the Local Universe
35
pitch, but you know that the frequency of the fire siren does not
change as it goes past.
Here again, subjective experience is such that time usually appears
much the same for one observer as another, because little within our
direct experience attains a velocity high enough relative to our own
to produce measureable differences. However, astronomers deal
routinely with distant stars and galaxies which are moving at
velocities high enough to suppose that they would experience
significant difference in time, were we able to communicate with
observers on them.
And, closer to home, but just as inaccessible to most of us, are the
electrons orbiting the nuclei of atoms, which move at substantial
velocities relative to the apparent speed of light, and are subject to
relativistic correction factors.
The velocity of an object stationary with respect to the stationary
coordinate system would appear to be moving with respect to the
moving coordinate system at a velocity equal to that attributed to the
moving coordinate system by the stationary observer. That is to say
that either system could be chosen to represent a stationary observer
and the other the moving one, and the results should come out the
same, except for the sign of the velocity being changed.
So, in Special Relativity, the relative velocity of two systems is
accurately perceived by observers in each, as the rate of change of
distance with respect to time in their own system. However, Einstein
has used his basic supposition, that light moves at the fastest possible
velocity, v=c, to draw a further conclusion. That is that time, and
space, and physical objects within space, actually get smaller when
they are moving relative to you, the “stationary observer”.
Still, there is some disquieting aspect to the shrinkage of time. Again,
time seems pretty normal and regular to us in our everyday lives.
While subjectively, it appears to pass quickly sometimes and slowly
at other times, the clocks, the seasons, and the decay of radioactive
materials seem to agree pretty well, as though we were like the
Les Hardison
36
stationary observer in Einstein’s derivation, and the time shrinkage
applies only to somebody else.
This is as far as Special Relativity went in relating the properties of
space and time to the velocities assigned to them relative to a system
considered to be stationary. However, in General Relativity, he dealt
with accelerations, and found gravitational effects to be identical
with acceleration fields. Because as space and time shrink as objects
move faster, it was apparent that the same kind of shrinkage of space
and time applied to the spaces near massive objects. So, gravity is
also responsible for shrinkage of space and time, but in a complex,
non-linear way.
It should be borne in mind that this equation for the “shrinkage of
time” for moving systems and objects was derived for the case where
the moving system was moving away from the observer at the origin
of the stationary system. The situation where the object is moving
toward the observer produces identical results if the velocity is
considered to be negative, but the distance between the observer and
the object a positive quantity, r, which is simply the radial distance
from the observer to the object, no matter which way it is going.
FIGURE 7
PLOT OF EINSTEIN’S EQUATION FOR A MOVING
COORDINATE SYSTEM
Light in the Local Universe
37
For now, I will simply point out that all of the equations developed
by Einstein for the relationship between distance and time for
moving objects imply that the measurements are referenced to the
galactic system of coordinates.
Figure 7 is a plot of some of these relationships.
Here, the equation for the time experienced by one who is moving
with respect to the stationary coordinate system depicted, is plotted
for the translational velocity uncorrected for the shrinkage of time
2'
vxt t
c , EQUATION 11
which is obtained for velocities which are negligibly small compared
to the apparent speed of light, c. This suggests that as
v c , EQUATION 12
'x
t tc
. EQUATION 13.
This is essentially the equation I will use to describe the relationship
between local time and uncorrected galactic time in a subsequent
chapter comparing relativistic effects in the two reference systems.
At the other extreme, when the velocity of the moving system
becomes negligible as compared with the apparent speed of light.
0v , EQUATION 14.
't t , EQUATION 15
so the rate of passage of time in the galactic system is the same for
the moving and stationary observers, no matter how far apart they
are.
Les Hardison
38
VELOCITY MEASUREMENTS
The measurement of velocity is, of course, simply the measurement
of distance at two different times, divided by the difference in times.
If the time interval is large, this gives the average velocity of the
object being tracked over the time period. As the time interval is
shortened it gets nearer to the instantaneous velocity, and the
analysis of motion when the equations for position as a function of
time are known is handled elegantly by differential calculus, where
x dxv
t dt
, EQUATION 16
where the Δs represent finite differences, and the dx and dt represent
infinitely small differences.
Throughout the evolution of Special Relativity, Einstein took all of
the velocities, including the apparent velocity of light, to be
constants. This is not to imply that there is anything special about
constant velocities, because things are accelerating and decelerating
all the time for various reasons. He simply did not include these
things in this part of the theory for the most part. Accelerations play
a major role in the General Theory of Relativity5.
The application of the Lorentz transformation is based on a
presumption of an observer at the origin of a coordinate system
which is “fixed” in that it has no velocity. The choice of the reference
system is, of course, arbitrary; as every point in the expanding
5 Einstein, Albert (1917) Kosmologische Beltrachtungen zur allgemeinen
Relativistitaheorie. Sitzungberichte der Preubischen Akademie der
Wissenchhaften 142
Light in the Local Universe
39
universe seems to be much like every other point, save for presence
or absence of matter. In developing the equations, Einstein
presumed the existence of a second coordinate system, moving
relative to the “stationary” one.
After deriving the equations for the shrinkage in both measured
distances and time, the calculation of velocity with respect to the
stationary system is straightforward.
For two reference systems with their origins initially at the same
place in space and time, the equation for the velocity relative to the
stationary system is
x v tv
t t
, EQUATION 17
And for the moving system
' ' '' '.
' '
x v tv
t t
EQUATION 18
Because
2
2 22
22 2
2 2
1
' 1
1 1
vvx ttc vct t
cv v
c c
, EQUATION 19
OR
2
2
'1
t v
t c , EQUATION 20
for the case where the object is at the origin of the stationary system,
Les Hardison
40
2
2
' ' 1
1
t t
t t v
c
. EQUATION 21
So, an observer who regarded his position as fixed would regard the
passage of time on a moving system as slower than his own. The
ratio of the two rates of tame passage would depended on his
measurement of the velocity of the other system. Were the roles of
the observer and observed exchanged, precisely same equation
would hold true.
This appears to say that the velocity of an object measured with
respect to one system would be identical to that measured by
another, moving system. This is not correct.
Time, whether referenced to a moving system or a stationary one,
must go forward, and never backward, v must always be less than c.
This pertains to velocities of any sort whatever, whether light rays,
or space ships or neutrinos (more on those later).
Seemingly, the velocity v could be the velocity measured by
determining two distances to the moving object and the two times
at which each measurement was made. If we see a body move a
measured distance in one second by our clock, this suggests that the
velocity measured on the moving object would be measured as zero
Einstein does not take into account the curvature of space over very
great distances, nor will, I in the subsequent comparison of the
Relativity in the galactic and local systems. The effect of the
curvature of space, represented in our analogy by the curvature of
the surface of an expanding balloon, is negligible when the distances
between two objects which are apart from each other by an amount
that is negligible in comparison when compared to the
circumference of the balloon. Thousands of light years does not
constitute a very significant distance on this scale.
Light in the Local Universe
41
RELATIVISTIC MASS
After determining the basic equations for distance, time and velocity,
Einstein had a problem to dispose of that might have upset the
whole apple cart of relativity.
Very simply put, the problem is this. If one imagines a mass, m, and
applies a constant force F to it, Newtonian mechanics says that the
mass will accelerate according to
dvF ma m
dt . EQUATION 22
The velocity will increase as long as the force is applied. Suppose we
choose to apply a force F to accelerate the mass m, the acceleration
rate will then be
dvF ma m
dt , EQUATION 23
or
.Ft
vm
. EQUATION 24
So, every second the velocity would increase by a constant amount,
F/m, no matter how gentle the force was applied. Eventually v
would reach c. It would, according to Equation 24, do so in mc/F
seconds. Obviously, the velocity would exceed c, and would keep on
increasing toward infinite velocity as the force continued to be
applied for a very long time. One of the premises of Special Relativity
was that this could not happen, as nothing can go faster than c in the
coordinates used in the galactic universe.
Now, up until this point, Special Relativity had dealt strictly with the
relationship between space and time. There had been no mention of
forces, accelerations and the like. But the problem was too pressing
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42
to let go, so Einstein proposed a unique solution to the problem,
which has been good enough to convince almost everyone since.
He said that what happens is that the mass of an object increases
with velocity, according to
2
2
' 1
1
m
m v
c
. EQUATION 25
This ingenious solution allows us to keep some reasonable and
useful Newtonian concepts, while embracing the contractions in
space and time that Special Relativity implies.
While this is an ingenious solution to the problem described, it once
again defies certain elements of logic. For example, my clock, which
I insist keeps good time no matter what the motion of your reference
system, weighs one kilogram (it has a built in radio and iPod music
port). My perception of its mass is precisely the same if you choose
to make me the center of your stationary coordinate system, or if
you choose to use the center of the star, Arcturus as the origin of
your coordinate system.
Never the less, this is what is commonly accepted as the true state of
affairs. That is, as you accelerate something to high velocity, its time
system is slowed down, its length in the direction of motion is
decreased, and its mass increases as the velocity becomes appreciable
as compared with the speed of light.
ENERGY CONSIDERATIONS
Once the concepts of mass and acceleration were imported into
Special Relativity, it was necessary to account for where the energy
went that did not go into increasing the velocity of the mass, but
rather increased the mass.
Light in the Local Universe
43
Einstein’s answer to this was another startling concept, and that is
that energy could be converted into mass, and conversely, that mass
could be converted into energy. This, while completely outside the
space, time, velocity relationships developed in Special Relativity,
was the most important practical result of Special Relativity, and one
that led indirectly to the evolution of atomic energy and countless
other technological marvels.
It was, of course, the most famous equation since F=ma.
2E mc . EQUATION 26
This is, of course, the equation for the rest energy mass. Einstein
explained that this is a simplification of the more general equation,
2
2
21
mcE
v
c
, EQUATION 27
for the case where the velocity is zero.
He goes on to explain that the approximation by expanding the
denominator using the well-known series
2 4 6
2
1 1 1 3 1 3 51 ..
2 2 4 2 4 61a a a
a
,EQUATION 28
Reduces to
2 42
2
3..
2 8
mv vE mc m
c , EQUATION 29
And for
2
21,
v
c EQUATION 30
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22
2
mvE mc , EQUATION 31
Which has the Newtonian expression for kinetic energy as the
second term.
Here again, these equations have been accepted as gospel since their
introduction in 1905, and continue to form the foundation of
modern physics.
I cannot leave this chapter without saying that this entire collection
of equations are not physical laws, but rather derive from the single
main premise of Relativity, which is that light travels through empty
space at the apparent velocity c, which is invariant. All of these
equations, which comprise Special Relativity, absolutely require that
this be true, and beyond question.
I am questioning this basic “fact”, and with it all of the resulting
derivations.
Light in the Local Universe
45
CHAPTER 4 RELATIVITY IN THE
LOCAL UNIVERSE
The derivation of the relativity equations in the local universe is
simpler than that used by Einstein, because it is not necessary to try
to make the speed of light come out the same when measured by
two observers moving relative to one another.
In the local universe, with the velocity of light taken as infinite, or
the time interval between the emission of light and reception at a
distant point in space taken as zero, it is apparent that all observers
would agree that the speed is the same so long as they were moving
at finite speeds, relative to each other, or to anything else. So, there
is no great mystery to be reconciled, and perhaps Special Relativity
would never have been necessary to explain the velocity of light
experiments.
Quite possibly, Einstein would not have proposed that matter and
energy are different forms of the same thing, and that nuclear fusion
or fission theories would not have evolved. Fusion and fission
would, of course, continue to exist, but just not a theory to explain
them
But he did create an explanation that fit the facts as he knew them,
and it has been a good and useful theory, all be it with some parts
which are difficult to grasp. The physicists have been expert at
providing chinks in the structure of physics wherever they did not
seem to fit well together on their own.
Einstein pointed out that, if the speed of light is taken as infinite, the
relativistic correction factor which appears in every one of the
equations of Special Relativity,
2
21
vF
c , EQUATION 32
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46
Becomes 1, and the equations for distance, time, and velocity and
energy reduce to the Newtonian values. This is certainly true if you
are presuming that c is the speed of light. So, one way to arrive at
values to apply to the local space-time universe is to simply take the
velocity of light as infinite in the equations of Special Relativity.
I will, in subsequent chapters, make the argument that the proper
value of c in Equation 32 is, in fact, infinity, so the relativistic
shrinking factor F is always equal to 1 regardless of the velocity of
the coordinate system, or the object being observed. Elsewhere in
the equations of Special Relativity, v is the velocity and c is the rate
of expansion of the universe, which is numerically about 300,000
Km/sec.
That means that, following the path of a light beam from a source in
the past to the future, which appears to be traveling at velocity c in
the galactic universe, rate of passage of local time is decreased to
zero. The light passes from the source to the receptor in zero time,
regardless of how far apart in space, and in galactic time, they may
be.
However, this is not the whole answer, because there are still
corrections to be made in the position, and the apparent time
experienced for moving objects, due to the fact that the universe is
expanding and we experience the change in position in the T
direction with the passage of time. Newton was entirely right in his
understanding that the key to going beyond Newtonian mechanics
lay in allowing observers moving at different velocities to experience
time differently. Or, to at least accept that their time-keeping would
appear to us to be different, as ours is to them.
We can never see anyone else’s clock in our present moment by
galactic standards. We are always looking at images of their clocks in
our galactic past, when they read differently than ours do now. We
must use of the local universe as the background for formulation of
the laws of physics for bodies moving rapidly, or bodies at a long
distance from us, because everything we see is in our present
moment in our local time. Each observer has his own universe,
Light in the Local Universe
47
where the local for any distant object is different for different
observers. However, the local time at his location is the same as that
of all other observers at that same instant in galactic time.
This understanding leads us to a different role in physics for the
value c, which is not the velocity of light in the local world we live in
at all. It is, instead, the velocity of our universe in the fourth spatial
dimensional direction, or in the direction of the progress of time, if
you prefer.
Because we are not stationary with respect to the four dimensional
universe, ever since the beginning of time with the Big Bang at the
center of the universe, some 13 or 14 billion light years away from
us, in this same, extra dimensional direction we still have to take the
velocity of movement of our “stationary” observers in this direction
into account.
The value of c doesn’t change in the local space-time universe, and
is the same approximately 300,000 Km/sec. measured so precisely
by the physicists over the past 100+ years. They were just attributing
their measurements to the wrong thing. So, the local relativistic
system still uses c, and it is measured to be exactly the same for
objects moving relative to our own position in space and time, but
not because space and time contract around moving objects, or
masses become heavier, or energy equivalent to matter.
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DISTANCE MEASUREMENT IN THE LOCAL
UNIVERSE
The measurement of distance is a simple concept, experienced by all
of us, and it can be done in a number of familiar ways. However,
when we talk of making measurements of distant objects, which we
cannot reach with a yard stick or tape measure, we get into a little
deeper water.
The ultimate measurement of distance, particularly long distance,
involves radiation. Distance can be measured in many ways, such as
the use of a RADAR-like detector, or visual sighting using brightness
of an object, or the apparent size of something of known size. More
simply, the measurement of distance can be assumed to be by having
laid out a system of mile markers stretching out away from the
observer’s location, so that it is apparent where in space an object is
placed by looking at the mile markers which are in front of and
behind the object.
In any case, the measurement is made, not of the position of the
object at the present moment in galactic time, but rather of the
position at some time in the past by galactic standards. The fact that
we can see it at the instant defines it as part of our local present time.
So, it is apparent that the distances assigned to objects that are
stationary with respect to our local observation point will be the
same as those assigned by the galactic measuring system. However,
if the object is moving with respect to our present position (which is
the same in terms of both local and galactic reference systems) it will
change position in the interval between when we see it in the galactic
past, and when it arrives at its position in the galactic present.
The rules appropriate to the local universe are that the distance to a
point in space or an object from our present position is only the
distance in our three dimensional universe. We cannot measure, nor
do we count, the distance in the T direction, which has to do with
where, on the galactic time scale, the point is at the time of the
measurement.
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49
Here, and in the remainder of this book, the subscript “L” is used to
denote a value which is measured in, or calculated with reference to,
the local coordinate system, as depicted in Figure 8.
FIGURE 8
DISTANCE AND TIME IN THE LOCAL UNIVERSE
In the local universe, the rule is that what you see is what you get.
That is, the universe as you see it at a particular moment, is your local
universe, and you cannot see or make measurements outside of it.
All of the points along the xL Axis in our analog diagram constitute
the local universe, and, correspondingly, everything you can see in
any direction constitutes your real three dimensional world.
That is, the only spatial dimension shown in the Figure 8 is xL, which
would be the distance from the observer at the origin, rL in the three
dimensional universe, with y and z coordinates equal to zero.
This is the difference along the local xL Axis, which represents the
three dimensional distance
2 2 2 2
:L L L L Lr x y z T . EQUATION 33
However, in the diagram showing only the xL and TL dimensions,
with T unchanging with distance along the xL Axis, this reduces to
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L Lr x , EQUATION 34
where the distance, xL, is measured horizontally.
Distance is always taken as the horizontal distance, parallel to the x
Axis, and the vertical distance T is not considered. Were distances in
the local universe measured parallel to the xL Axis rather than the x
Axis, they would always come out longer by a factor of 2 , and this
is a matter that will be left for consideration later.
FIGURE 9
DISTANCE TO A STATIONARY OBJECT
If the object is moving with respect to the observer, it will follow a
path in the T direction that is not parallel to that of the observer, so
that at the instant in time depicted, the local observer sees the object
AL (now renamed to distinguish it from the later occurrence of the
object as A) at a distance xL, (now renamed to distinguish it from the
distance x in the galactic coordinate reference system).
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51
Figure 10 shows the path of an object through space time, when
there is a component of the velocity of the object in the x direction
relative to the stationary observer.
It is apparent that the distances measured to the object at points AL
and BL are not the same as they would be in the galactic system. The
important thing here is not that there are differences from the
galactic system of measurement, but rather that the distances are
simply what they appear to be, and each measurement is not
corrected for the fact that the object is moving.
FIGURE 10
LOCAL DISTANCE FOR A MOVING OBJECT
If one considers the measurement of distance from the standpoint
of a moving observer, one has only to note that the moving observer
would see himself as static (which he is, relative to his own local
universe coordinate system). Now in his position of static observer,
he would see his local universe comprised of the things he can see at
the present moment, exactly the same as the original stationary
observer would have done at various times in his past.
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TIME IN THE LOCAL UNIVERSE
Time, in my way of thinking, is in a sense absolute, and everywhere
the same. That is to say, the time is defined at every point in the
universe by the distance the universe has moved in the T direction,
and the constant rate, T=ct. Thus, if all observers, wherever located,
possessed a precisely accurate clock, all of them would read the same
at any instant in galactic time, because we would all have moved out
from the point in space and time of the Big Bang by the same
amount.
The rate of expansion of the universe is constant, simply because
there is nothing to exert a force in the T direction to cause the matter
moving in this direction to speed up or slow down. So, time has been
progressing at pretty much the same rate for millions of years, and
we can probably count on it continuing to progress at the same rate
in the foreseeable future.
Unfortunately, we can never see anyone else’s clock at the present
instant of galactic time, but instead, can only see their clocks as they
were at some time in the galactic past.
In the local coordinate system, the time is taken as being the same
along the xL Axis, just as in the galactic system, but the position of
the x Axis is not perpendicular to the T Axis. In the local system, it
is bent downward on the galactic x – T diagram at a 45 degree angle.
The angle is set by the rate of movement of the universe in the T
direction at the velocity c. Now, because everything we can see at a
given instant is located along this x Axis, and comprises our real,
local universe, it is necessary that light traveling along the x Axis
from a distant source, or from a nearby source, depart from the
source and arrive at the receptor (our eyeball) at the same instant in
local time. In other words, the speed of light has to be infinite in
reference to this coordinate system.
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FIGURE 11
AN OBJECT MOVING TOWARD THE OBSERVER
While Figure 11 is drawn for a generalized object presumed to have
a defined velocity relative to the stationary observer at the origin, it
should be apparent that the T Axis and the hypothetical observer at
the origin could be chosen such that at the time of the original
observation, the observer and the object are at the same point in
space. This variation is shown in Figure 12.
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FIGURE 12
A MOVING OBJECT PASSING THROUGH THE ORIGIN
This simplifies the picture somewhat, with regard to the relationship
between the local and galactic time systems, but does not limit the
generality of the results.
Local time at the origin is always the same as the galactic time. Thus
our clock would read the same as that of an observer working in the
galactic system, should it be possible for a hypothetical observer to
work in that system.
The local observer, who sees time as constant along the 45 degree
cone with its apex at the origin, would place the objects he sees
L LT T x , EQUATION 35
or
LL
xt t
c .. EQUATION 36
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55
When the galactic time is taken to be zero, the local time is the same
at the origin, but at other points along the x Axis it becomes
LL
xt t
c , EQUATION 37
which defines the right hand half of the local x Axis. The half to the
left of the T Axis is also defined by this same equation, for negative
values.
FIGURE 13
RELATIVE VELOCITY OF TWO OBJECTS
The time the local observer reads on his local clock when making
the observation is simply what he reads, without correction for the
motion or lack of motion of the object. Again, what you see is what
you get, without the necessity for correction. When the object is at
point A, the time on the observer’s local clock can be set to zero,
and when he observes it one second later, it is at point BL, and one
second has passed by his clock. As with distance measurements,
what you see is what you get.
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Two further situations should be of interest relative to the time the
local observer experiences. First, how does he perceive the time of
observation of two or more moving objects, and secondly, how
different is the time perceived by a second observer, moving relative
to the first.
The simple answer in the case of two moving objects is that he sees
each of them in his own local time, and he records their distance
from him as the observed distance without correction. He perceives,
or would if he had sufficient good vision, that each galactic clock, if
carried by each of the objects, would read an earlier time than his
own, and would be aware that the difference in the times would be
earlier than his own local time by exactly the x/c value for each of
them. There are no correction factors other than that associated with
their distance from him.
In the second case, that of a second observer who is moving with
respect to the “stationary” observer, and whose path, at some point
crosses that of the stationary observer, we would be interested in
how the stationary observer’s clock looked to him. Both the
stationary observer and the moving observer will, of necessity, see
their relative velocities as the same value, vR, because either might
have been presumed stationary, and the other the moving coordinate
system.
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57
FIGURE 14
LOCAL TIME FOR A MOVING OBSERVER
In the case where the moving object is actually a second observer,
time is measured exactly the same way for the moving observer as it
is for ourselves. That is, he would perceive his own coordinate
system as moving in his own local T direction, and his galactic x Axis
perpendicular to it through his origin. He would define his local
universe, as he sees it, lying along his x Axis, according to
MM
xt
c , EQUATION 38
where I have used the subscript M to denote the measurements
made with respect to the moving system, where things existing at
clearly defined points in galactic space time, are viewed differently
than by the fixed observer.
Where the stationary observer sees himself as moving in the T
direction at the velocity c, with no motion in the x direction, the
moving observer sees him as moving in his T direction at velocity c,
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but with the added component of velocity in the x direction. That is,
he sees the distance ctL for the local observer as being
2 2 2 2
M L Lct c t v t , EQUATION 39
or,
2
21L
m
t v
t c . EQUATION 40
Thus the stationary observer would observe that time is passing
more slowly at the moving observer’s position, and the converse
would also be true. The moving observer would see things as though
he were stationary, and the stationary observer’s clock would be
running more slowly than his.
Both of these observations are, of course, mistaken, as all galactic
clocks, everywhere, are running at exactly the same time, and the
galactic time at any location in space time reads exactly the same as
the galactic time at that place.
The local observer knows this, and does not try to infer things about
the galactic time observed by the intergalactic space ship crew which
is influenced by the speed at which he is traveling.
Only when the moving observer and the stationary observer finally
cross paths and are at the same point in space and galactic time will
it appear that local time is exactly the same for both of them. Both
would continue to collect data which would seem to indicate that the
other’s time was passing more slowly than his.
We have no need to use this kind of calculation, in that we can
determine the time clock reading for any object in space simply
based on its linear distance from ourselves, and the illusion of the
time discrepancy is of no consequence.
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59
VELOCITY IN THE LOCAL UNIVERSE
The measurement of velocity in the local universe is a much simpler
matter than is the case when the velocities are presumed to be
representative of the galactic universe. In the local universe, we can
actually see objects and events, and identify the local time of the
observation. In the galactic coordinate system, we cannot see them,
and must calculate, from our observations of past positions, where
they would be “now” if we could actually see them. Of course, for
objects which are nearby, in terms of light seconds, or moving
relatively slowly, for example less than 100,000 miles per hour, there
isn’t much difference between the two systems of representing the
physical universe.
In the local universe, one simply measures the distance of an object
(using the brightness of a star, or the sight of an automobile passing
over a mile marker on the highway), notes the time reading on his
clock, and then repeats the measurement at some later time, again
noting the reading on his clock. As pointed out in the preceding
section, both the distance observed at any time, and the time itself,
are simply the values observed, and no corrections of any sort are
applied.
STATIONARY OBJECTS
His measurement of the distance to a stationary object will be exactly
the same as that attributed to the object in the galactic frame of
reference, because the distance does not change with time, even
though the two observers are unable to see the object at the same
time. Time doesn’t matter in this case.
In Figure 15, a reference system is sketched in which the local and
galactic coordinate systems have the same origin and there is no
motion of one coordinate system relative to the other.
On this coordinate grid, the path of an object is shown which is not
moving in three dimensional space relative to the local observer.
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That is, the direction to the object – the x direction – is not changing
with time, and the distance along the x Axis to the object is not
changing with time.
FIGURE 15
LOCAL REFERENCE TO A STATIONARY OBJECT
In order to determine that an object is, in fact, stationary with respect
to the position of the stationary observer, it is necessary for him to
make a series of measurements of distance and the times elapsed
between them. If he does this and finds that the distance has not
changed in any of the readings, it is reasonable to say that the velocity
is constant at zero.
Objects which are stationary with respect to a local observer would
also appear to be stationary when they are referenced to the galactic
system. The distances to the object measured horizontally from the
T Axis to the object would appear to be constant at x in the local
system, as the universe moves from AL to BL, and ∆x=0. This
distance and ΔT, and the distance in the T direction, would also be
constant as the galactic universe moved from A to B which is the
same time interval, ΔT .
Light in the Local Universe
61
The local observer would determine the velocity of the object to be
Δx/Δt = 0, and would also calculate the velocity for the galactic
system to be zero. The observers would not agree on the value of
time at the object, but they would agree that the same amount of
time elapsed between their respective readings, and that the distance
was unchanged.
MOVING OBJECTS
The picture becomes more complex if the object under observation
is moving with respect to the local coordinate system, or according
to the galactic coordinate system (for which the origin, linear scale
and direction of motion are all identical to that of the local observer).
However, if the object is moving with respect to the local observer,
he will see the object as being in his present time, but in the galactic
past. The galactic coordinate system presumes the observer to be in
the galactic present. That is, in the future with respect to the local
observer. So, it is necessary to calculate the position of the object (or
event) as it will probably be when we reach that future time.
OBJECTS MOVING TOWARD THE OBSERVER
In Figure 16, the stationary observer, with the same origin location
as the galactic origin, sees a moving object represented by the shaded
arrow. The moving object is approaching the origin as time passes
(T=ct increases), and will reach the origin at some future time.
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FIGURE 16
A MOVING OBJECT OBSERVED BY A STATIONARY OBSERVER
For convenience, the time interval shown in Figure 16 between the
two measurements is one second, so the ∆T dimension is
numerically equal to c, the rate of expansion of the universe, or the
apparent speed of light.
As the object moves from point A to point B referenced to the
galactic coordinate system, the distance traversed is the horizontal
difference between the x values at the points A and B. Because the
time interval chosen for the measurements is one second, the ∆T
dimension is c. Thus, the velocity of the object as measured in
galactic coordinates is
GG
G
xv
t
, EQUATION 41
where, for ∆t=1 second,
G Gv x , EQUATION 42
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63
which is the velocity in the galactic reference system by definition.
Hereafter, the subscript G will be omitted for the values referenced
to the galactic system.
The local observer sees the time differently, as he defines constant
time along the 45 degree lines as being the same as his local time at
the origin, whereas the galactic system defines time as being constant
along the horizontal x Axis. The coordinates for the two systems
were chosen in this figure so that the time interval depicted is the
same. That is there is one second of elapsed time between points A
and B along the path of the moving object, and also between points
AL and BL, which reference the positions of the object as seen by the
local observer.
Because the galactic origin and the local origin coincide, and move
together in the T direction, there is no disagreement about either the
time or the location in space between the two systems at the origin.
However, the local observer sees the object at an earlier time and at
a closer distance than the galactic observer.
It should not make any difference where the reference origin is
located for any given set of measurements. It is easier to establish
the locations in space time of the object as it moves along its path if
the origin is chosen so that the object passes through the origin at
the end of the one second observation period. This slightly modified
situation is shown in Figure 17.
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FIGURE 17
THE MOVING OBJECT SHIFTED TO ARRIVE AT THE ORIGIN
There is one exception, which is that the location of the coordinate
origin is immaterial, so long as the object is either moving at constant
speed toward the origin throughout the measurement period, or
moving away from the origin throughout the period. This distinction
requires a lengthy explanation, and will be dealt with later.
It should be clear that the local observer sees the object at the
beginning of the time period, not at Point A, where it is with
reference to the galactic system, but at an earlier time, and a greater
distance from the origin, at point AL. However, at the end of the
time period, the location of the object coincides with both the
galactic and local origins.
Here it is more apparent that the path lengths seen by the local
observer and the galactic observer differ by the addition of the
amount of the distance moved by the moving object from the time
the object is seen by the local observer at Point A’ and the time the
object reaches point A in the galactic system of measurement. The
distance traversed is A’–A, which is Δx. However, during this same
Light in the Local Universe
65
time period, the local observer sees the distance traveled by the
object as ΔxL, which is a considerably greater distance,
L L
vx x x
c . EQUATION 43
This can be rewritten as
. 1L
x v
x c
,
EQUATION 44
and because the time periods are the same for both systems,
L L
v x
v x
, EQUATION 45
so
1L
v v
v c . EQUATION 46
From this, the expression for the galactic velocity corresponding to
any value of the local velocity can be determined algebraically to be
1,
1 LL
v
vv
c
EQUATION 47
where:
Lt time interval in the local universe
(always a positive value)
t time interval in the galactic universe.
(always a shorter positive value).
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There is some caution which must be exercised here, in that the
velocity is determined by measuring a distance moved, and dividing
it by the time between the measured starting and ending positions.
The distances moved are actually distances away from the origin, and
may be considered as the scalar distance in the three dimensional
universe.
It should be apparent that either the time elapsed may be taken as
the same in the local and galactic systems, and the distances traveled
by the moving object will be different, or the distance traveled may
be taken as the same in the two systems, and the time required for
the travel to take place will be different.
It is a bit simpler if the latter case is used for comparison of the
velocity measurements, and the object is presumed to have traveled
a fixed distance, Δx in the galactic system, and the same identical
distance, ΔxL in the local system.
OBJECTS MOVING AWAY
The foregoing derivation was based on observations of an object
moving toward the observer. One would expect that the same
derivation would yield similar results for an object moving away
from the observer. The choice of the observer’s location is arbitrary,
and might just as easily have been chosen “on the other side” of the
moving object, so it would now be moving toward, rather than away
from the observer. However, this situation is not so straight forward,
and leads to some incorrect conclusions.
This situation is depicted in Figure 18 for an object moving away
from the fixed observer. In this case, the distance traveled in
reference to the two systems is taken as the same, so the time
intervals involved are different. However, this choice is of no
consequence, as the results would be exactly the same if the time
intervals had been taken as equal for the two systems, and the
distance traveled accepted as different.
The galactic observer sees the velocity as represented by the change
in distance in the time period between the two positions of the
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67
horizontal x Axis, which moves in the T direction a distance of cΔt
as the object moves through the distance Δx in time period Δt.
The distance moved by the object may be taken as the same for both
measuring systems,
L L Lc t v t c t , EQUATION 48
FIGURE 18
VELOCITY OF OBJECT MOVING AWAY FROM OBSERVER
in which the time interval measured in the two systems is different,
as shown in Figure 18.
This indicates that the ratio of velocities in the galactic and local
reference systems is inversely proportional to the time required for
a given distance of movement of the object, and
1Lt v
t c , EQUATION 49
or
Les Hardison
68
1
1 Ll
v
vv
c
. EQUATION 50
This is quite anomalous, as the velocity immediately before the
object passed the observer would have been calculated as
1
1 Ll
v
vv
c
. EQUATION 51
These ratios can only be the same if the local velocity is zero.
Obviously, the velocity of an object does not change abruptly as it
passes the observer, and the two calculated ratios cannot be equal to
each other unless both are zero. There is something wrong with this
analysis.
This is an important point, because Equation 51 is always right, and
Equation 52 is not, but this is a subtle point, and a very important
one. It is important enough to devote a whole chapter to the
explanation.
Light in the Local Universe
69
RELATIVE VELOCITIES
There is, finally, the question of how the velocities of two moving
objects appear to relate to each other in the local universe described.
Figure 19 illustrates this situation.
In Figure 19, a second moving object has been introduced.
FIGURE 19
TWO MOVING OBJECTS REFERENCED TO THE LOCAL
UNIVERSE
It should be apparent by inspection that the velocities perceived for
these two objects, vLO1 and vLO2, both follow the previously derived
relationship.
That is,
1
11
1
1 LL
v
vv
c
, EQUATION 52
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70
and
2
22
1
1 LL
v
vv
c
. EQUATION 53
So,
2 1 1 22 1 2 1 ,L L L L
L L
v v v vv v v v
c c EQUATION 54
from which it appears that the differential velocity observed by the
local observer is
2 1 2 1L Lv v v v , EQUATION 55
which is identical to the calculated differential in the galactic system.
The suggestion here is that, in the local system, the velocities are
simply the velocities measured, with no need for correction factors.
When the measured velocities are recalculated with reference to the
galactic coordinate system, they are more complex, but differences
in velocities should be identical to those measured with reference to
the local system.
Light in the Local Universe
71
WHY LIGHT APPEARS TO MOVE AT 300,000 KM/SEC
Now, it is apparent that the velocity of light reported by the local
observer would be infinite, whereas in the galactic geometry, it would
appear to be c, the apparent speed of light.
It is of critical importance to recognize that any velocity observed to
be very large (approaching infinite velocity, or instantaneous
transport through space) would appear to be equal to c, the apparent
speed of light, if it were to be assumed to have been measured in the
galactic universe.
It is true that all velocities based on observations in the local universe
(which is the only place where observations can be made) will always
be lower when recast into the galactic universe, for objects moving
either toward or away from the observer. This is because, as was
demonstrated, the velocity, v, in the galactic universe corresponding
to vL measured in the galactic universe is
1
1 LL
v
vv
c
. EQUATION 56
The question is, what is the velocity of light in the galactic universe
which corresponds to the observed infinite velocity of light in the
local universe? This can most easily be seen by rewriting Equation
56 as
1
1L L
v
cv v
c c
, Equation 57
or
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72
1
L
L
v
v cvc
c
. EQUATION 58
It is easy to see that as vL/c becomes very large, the significance of
the 1 in the denominator decreases, so the limiting value of v/c
approaches 1 as vL/c approaches infinity. In short, an infinite
velocity in the local reference system corresponds to the velocity c
in the galactic reference system.
This accounts for the presumption that light moves through three
dimensional space at the apparent speed of light c, and also explains why
nothing---no solid object in motion, or any phenomenon like the
force of gravity---ever appears to move faster than c, so long as one
is relating all observations to the galactic reference system.
This is one of the reasons why I am so sure the OPRA scientists
working with the CERN Large Hadron Collider, who presumably
measured the velocity of neutrinos passing through the earth as
slightly greater than c, were in error. I will deal with this in a separate
chapter, and suggest a reason for the error.
But, you may say, the scientists have measured the velocity of light
many times, and are in good agreement that the velocity is very close
to 300,000 Km/second. What were they measuring if it was not the
speed of light in a vacuum?
I have proposed that they were measuring the speed of the universe
in the fourth dimensional direction, and that their experiment looked
like this.
Light in the Local Universe
73
FIGURE 20
THE MEASUREMENT OF THE SPEED OF LIGHT
Here, the scientists presumed that they were working entirely in the
galactic reference system, and had no concept of the motion of the
universe in a fourth dimension. So, instead of imagining themselves
moving from Point A0 to Point A1 to Point A2 as the universe
expanded in the T direction, they presumed that they were
“stationary” and that time was simply passing.
To measure the speed of light, they sent a series of short beams of
light out toward point B1, where there was a mirror at a known
distance, and recorded the time it took the light to return to the
starting point after being reflected from the mirror. These events ---
the emission of the light, reception at the mirror and reflection back
toward the source, and receipt of the light pulse at very nearly the
same place it originated --- were all presumed to take place in the
galactic plane, and that, as time passed, the light moved through the
intervening space like a fish swims through water, only much faster.
However, had they taken into account that the universe was
expanding, they would have recognized that their view of the
situation was limited, because they could not actually see the light
moving through the empty space toward the mirror, and their only
actual measurements were of the distance to and from the mirror
Les Hardison
74
and the amount of time which passed between the emission of the
light and its reception at the point of origin.
Instead, they presumed that the light was making its way relatively
slowly to the mirror during the first half of the elapsed time period,
and making its way back during the second half. Its velocity was, of
course, calculated as
2
2
c tv c
t
. EQUATION 59
I believe that the correct way of viewing the experiment involves
recognizing that the location of the experimenter and the mirror are
both “stationary” in reference to the three dimensional everyday
universe, but are moving at the velocity c in a fourth dimensional T
direction. The experimenter is able to see things which are in his line
of sight, which extends outward in the three spatial dimensions, but
also extends backward in galactic time, and that the things he can see
at any instant comprise his local universe at that instant.
Thus, things he sees simultaneously exist at the same local time, so
far as the local observer is concerned.
So, the local observer is able to see the mirror at any time, but he is
always looking at a position of the mirror that is in his past. He
cannot look forward into the future, and see the mirror as it will be
at some future time. He has to wait for the time to elapse for it to
come into his view.
So, he sees the experiment as shown in Figure 21.
Here, the observer at A1 cannot see the mirror at Point B1, because
it still lies in his future. He could, were he at the location of the
mirror, at Point B1, see the light source at A0, and he would presume
he was seeing it at the exact same local time as he experienced. He
should not be able to see the mirror at Point B1 until he had, in fact,
reached point A2, where he would presume the time at B1 and A2 to
be at the same identical local time.
Light in the Local Universe
75
FIGURE 21
THE SPEED OF LIGHT EXPERIMENT FROM THE STANDPOINT
OF THE LOCAL OBSERVER.
Thus he would perceive that the light had crossed the gap between
A1 and B1 in no time at all, and that he would see no additional time
difference between point A2 and B1. So, it appears to the local
observer that it moved through the distance from A0 to B1 in no time
at all. In other words, the speed was infinite. It is relatively obvious
that this is how local time is defined.
So, the question is, what did the local observer actually measure?
Clearly there was an elapsed time difference for according to his
clock, the light left the source at t = t0, and was next observed at t =
t2. The distance moved by the source and the receptor during this
time was 2VΔt, where V is the rate of expansion of the universe. So,
it is apparent that the local observer measured the velocity V of the
expansion of the universe in the T direction. His measurement is
simply that
2 2V t c t EQUATION 60
or
V = C. EQUATION 61
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76
That is, the velocity of the universe moving in the fourth
dimensional direction is c, the apparent speed of light.
A minor question arises from this presentation of the experiment in
terms of measurements by a local observer. Does the mirror need to
be stationary?
Were the mirror in motion with respect to the source of the light and
the receptor (which are in fixed positions relative to each other), as
shown in Figure 22, the result would be exactly the same, provided
the position of the mirror at the point half way between the time the
light was emitted and when it was received was known accurately.
FIGURE 22
LIGHT SPEED ECPERIMENT WITH A MOVING MIRROR
The motion of the mirror only has to do with determining its
position in space at the time the light signal is received.
The same must be true for the situation where the receptor is moving
with respect to the location of the light source and the mirror. If the
T Axis were rotated a few degrees clockwise, such that the path of
the mirror through time were vertical, the same geometry would
exist with respect to the relative positions of the source, the mirror
at the time of reflection and the receptor. So, one can conclude that
Light in the Local Universe
77
it is not important that the elements involved in the experiment
should all be stationary with respect to one another.
Les Hardison
78
MASS IN THE LOCAL UNIVERSE
In the local universe reference system, there is no need to account
for the invariance of the speed of light. It is infinite, and would
simply be measured as infinite by any observer who confined his
measurement to the system in which he made them; that is, the local
universe reference system.
Because this is true, there is no concern that the velocity of an object
subjected to a uniform force for a very long period of time would
exceed the speed of light. Nothing can exceed the speed of light
because it is infinite.
The fact of the matter is that there is nothing in the universe with
any substantial mass that is presently moving faster than c, because
c is the velocity imparted to all matter at the time of the Big Bang,
and it is that velocity which defines the rate of expansion of the
universe.
When the universe got its start with the big bang, all mass got an
equal share of energy, all of it being accelerated to the same velocity
c, the apparent speed of light which I think is what it has had more or
less ever since. Nothing can go faster simply because there isn’t
anything already going faster to give it a push.
So, there is no basis for supposing that mass actually changes with
changes in velocity. Our ordinary concept of kinetic energy as
2
2
vE m , EQUATION 62
is completely compatible with an invariant mass.
This whole line of reasoning makes me rest easier at night, knowing
that my mass (weight while I am near the earth) is not subject to
someone’s arbitrary choice of a reference system. I am, already,
Light in the Local Universe
79
moving at the apparent speed of light in a direction that I have no way
of detecting, and while the precise direction may be altered by, say,
a collision with a moving automobile, the total velocity will not be
changed.
The exact direction of my path through space time determines how
much of my velocity, c, the speed of expansion of the universe, can
be detected by other earthbound observers. This has nothing
whatever to do with the amount of material composing my body.
All my belongings are, likewise, immune to arbitrary weight
adjustment by observers choosing arbitrary reference coordinates.
There is no reason, when measurements are made in the local
reference system of the observer, and interpreted correctly as
applying to the local system, to determine that mass and energy are
different forms of the same thing, or that one is convertible into the
other.
I can’t prove that they are not, but there doesn’t seem to be any
reason why they should be. Fortunately, the mistaken impression
(from my point of view) that mass is convertible to energy has
produced a great deal of technological advancement. Which proves
to me that you don’t necessarily have to be right to succeed, you just
have to have a consistent set of rules that work well.
Les Hardison
80
ENERGY IN THE LOCAL UNIVERSE
Just as mass is, in terms of all the measurements one can make in the
local universe (and there is no place else to make measurements),
constant, regardless of the velocity of the mass or of the observer
making the measurements, energy is likewise very simple and nearly
as unconvertible.
The energy of a body moving in the direction of the expanding
universe is simply
2E mc . EQUATION 63
I have conjectured that the kinetic energy due to the velocity in the
T direction of expansion of the Universe in the fourth dimensional
direction is only half that,
2
,2
cE m EQUATION 64
with the other half attributable to the spin of the electrons and
protons making up the majority of all matter. I have no sound basis
for this.
It could be that the distances in the local universe ought to be
measured from the T Axis along lines parallel with the local x Axis,
in which case, all measurements of distance in the local universe
would be larger by 2 than those in the galactic universe. Were
this the case, the velocity of light in the galactic universe would be
2 c, and, in the galactic universe, E=mc2 .
However, for the time being, I will stick by my guns, and maintain
that all matter has the velocity c rather than 2 c in the T direction,
and the velocity we are able to recognize for objects moving relative
to our own stationary position is simply the component of the
Light in the Local Universe
81
velocity vector c which is out of parallel alignment with our own
vector in the T direction.
An observer at the apex of his own cone, representing his local
universe, perceives himself to have no motion. Indeed, he has no
motion relative to his own private coordinate system in the three
dimensions he can perceive.
When he sees a body in motion, he can determine the velocity
component in the three dimensions he can perceive by direct
measurement. He is led to believe that the moving object is moving
in the T direction at the velocity of expansion of the universe, and
he natural assumes that that velocity is the same for everyone.
It is, of course, slightly different for everyone, but so far as he can
tell, the energy of the moving system is that due to his own velocity
in the T direction, c, plus the velocity component he can measure,
vL. Hence the appearance that the energy of the mass is
2 2
2 2
Lmc vE m . EQUATION 65
The second term, the one he measures, is really part of the first term,
which he does not measure, for massive bodies.
Einstein took this same energy to be
2
2
2
,
1
mcE
v
c
EQUATION 66
Which he expanded by the series
2 42
2
3...,
2 8
mv vE mc m
c
EQUATION 67
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82
and goes on to say this is approximately
22 ,
2
mvE mc EQUATION 68
when v/c is relatively small.
However, it is, of course, only the case where v/c is appreciable that
calls for the application of relativistic mass. So, Einstein concludes
that the Newtonian concept, plus his idea of relativistic mass, holds
for ordinary, everyday velocities, but is not a good approximation to
the energy of bodies moving at speeds which are appreciable to c.
In the local system of measurements, where
2 2
2 2
Lmc mvE , EQUATION 69
exactly, Newtonian mechanics seems to hold just fine, if you
recognize that only a part of E is visible in the ordinary three
dimensional world we live in, and where we make our observations.
Were one to translate the Energy equation, which I believe to be
exactly as shown in Equation 69, to the galactic system and do so
correctly, it would be by substituting the value of velocity v in the
galactic system for the corresponding measured value, vL in the local
system.
Thus the correct expression for the total energy of matter in the
galactic system is
2 22 2
22
2 1
Lmv mvE mc mc
v
c
. EQUATION 70
Light in the Local Universe
83
The expression for Energy referenced to the galactic system given in
Equation 70 is not the same as that derived by Einstein, as illustrated
in the following figures.
.
FIGURE 23
COMPARISON OF EINSTIENIAN ENERGY BASED ON LOCAL
VELOCITY
It is apparent that the energy levels calculated by either approach is
very close to mc2 at values of galactic velocity less than about 70%
of the value of c. and that both result in the energy becoming
infinitely great as the value of v/c approaches 1.0. However, the
energies calculated on the basis of the observed local velocity are
much greater than those based on Special Relativity the range of
velocities between 0.6c and 1.0 c.
Furthermore, E is the kinetic energy associated with all matter, and
there seems to me to be no other form of energy at all. This may
sound like too broad a statement, but I believe it to be true.
Radiant energy I believe to be associated with the velocity of
electrons orbiting atomic nuclei, and not waves moving through
space. Thermal energy is associated with the mostly random
velocities of atoms and molecules making up a matter.
0
100
200
300
400
500
0.0
00
.10
0.2
00
.30
0.4
00
.50
0.6
00
.70
0.8
00
.90
1.0
0Re
lati
ve E
ne
rby,
E
Velocity v/c
Energy as a function of Galactic Velocity
EinsteinEnergy
Les Hardison
84
Potential energy, relating to the distance masses are from one
another, seems to be a device used to account for the increasing
velocity or objects as they “fall” toward one another, instead of
recognition that the direction the object is moving in the four
dimensional space must, at all points along the path of the object be
perpendicular to the three normal spatial dimensions. The curvature
of space is simply the variation of the slope of the T Axis to our
concept of the right angle direction at our location. It seems likely
that the curvature of space is, in reality, a reflection of the changes
in the direction of time in the presence of gravitational masses, or
electrical charges.
Finally, I do not believe energy can be converted into matter, or
matter into energy. I think the processes which appear to be doing
this have alternative mechanisms involved. I will also get into this
later.
Light in the Local Universe
85
SUMMARY
In this chapter, I have developed a series of equations corresponding
to the equations of Special Relativity, as presented by Einstein in
1905. His equations have stood up pretty well, although I think they
have also raised a great many questions which physicists have had
only partial success in answering.
All of the derivations have been based, like those of Albert Einstein,
on the presumption that motion involves something moving toward
or away from the observer at the origin of the arbitrary coordinate
system. He took, for his derivation, the motion of a beam of light
leaving the origin of his coordinate system and being observed as it
moved away from the observer.
It should be apparent that one cannot, under any circumstances,
observe a beam of light moving away from himself. One only sees
things by directly emitted or reflected light when the light moves
from the emitting or reflecting object toward the observer, and is
finally registered when it actually coincides with his location in four
dimensional space.
However, if one defines his present local universe as all he can see
at the moment, the light reaches him as though it were moving at
infinite speed. In this universe he would determine that the universe
is moving through the fourth dimensional direction at the apparent
speed of light, c. If he prefers to use the model of the universe which I
have called the galactic system, he must calculate the values to use in
that universe from those he observed in his local universe.
I am suggesting that the equations of Special Relativity were derived
by Einstein to do just that, but that he did not take into account the
possibility of radiant energy transfer taking place instantly, as it
appears to do in the local universe, and therefore derived his
equations based on an incorrect set of premises.
In the local universe, there is no need to explain the invariance of
the apparent speed of light. It appears to move at infinite velocity in the
local universe, and is, of course, the same for any two observers,
Les Hardison
86
regardless of the relative velocity of the two sets of measuring
apparatus with respect to each other or to anything else.
Velocity (at least constant velocity) is likewise simply measured in
the local system. It is the decrease in distance to our observation
point divided by the change in clock time at our location. For objects
moving away from the observer, it must be calculated, rather than
observed directly, because the observer cannot see the path of the
object into his future. He can see the past positions, and thereby
calculate where it should be at his galactic time, but he cannot see it
at this time.
In order to get a correct assessment of the velocity of an object, he
must use the calculated distance to the object in his immediate
future, rather than rely on the historical measurements made in his
past.
Again, it is not necessary to correct the velocity in order to prevent
things from moving faster than c, nor to presume that space and
time are shrinking as the result of objects moving through space and
time relative to our own position.
We have to recognize that others moving relative to our own
position will measure velocities differently than we do, but not
because the velocities are actually different. It is only because they
will see the time at which the objects reach specific points in space
as different from those of any observer moving relative to their own
position.
Velocities measured for two moving objects can be added and
subtracted in the local system, based on observations in the local
system, without any necessity for limiting velocity to c, or any other
value, and without applying the relativistic shrinking factors derived
by Einstein.
The relative velocities of two systems will appear to be exactly the
same in magnitude from each of the two systems, although the
Light in the Local Universe
87
direction may appear to be to the left for one observer and to the
right for the other.
The laws of Newtonian physics hold for physical interactions
described with reference to the local coordinate system without
correction. The mass of objects is unaltered by velocity relative to
the observer, and the momentum of an object and its energy, both
quantities which can be described only in terms of their velocity
relative to the observer, are calculated simply from the observed
velocities, and there are no relativistic correction factors.
The proper use of the galactic system of coordinates, which may
appear to represent the “real” physical world better, requires
modification of the observed local data, but the modifications are
not those derived by Einstein. The picture of the galactic universe
using these correction factors does not require the relativistic
shrinking factors for measurements of distance, time, mass and
momentum.
Using local measurements properly to calculate galactic velocities
and positions, no matter how fast a body is moving in the local
system of measurement, it cannot appear to be moving faster than
c, the apparent speed of light, when translated to the galactic reference
system.
This is why it is impossible, in terms of the geometry of the space
time system used by modern physicists, for anything to “exceed the
speed of light”. Light or anything else moving at infinite speed in
the local reference system would appear to be moving at the apparent
speed of light in the galactic system.
Les Hardison
88
Light in the Local Universe
89
CHAPTER 5 VELOCITIES OF OBJCETS
MOVING AWAY
In the previous chapter, an anomalous result seemed to indicate that
the observed velocity of an object viewed by a local observer would
be translated to the galactic frame of reference by
1
1 LL
v
vv
c
, EQUATION 71
when the object under observation was moving toward the observer,
and
1
1 LL
v
vv
c
, EQUATION 72
when the object was moving away from the observer. In other
words, the velocity of an object which was by definition constant in
galactic terms, would have to decrease significantly in the eyes of a
local observer as it passes him by, and he would have to revise his
estimate by changing the sign of the velocity in equation 71.
This anomalous condition was due entirely to a misconception about
the way local observers translate visual information about the world
to the theoretical construct I have called the galactic universe. If one
agrees that an observer can only see an object if light moves from
the object to his eye, and that light always moves from the past to
the present or the future, and never the other way around, then it is
apparent that the local observer can only see objects in the galactic
past.
Les Hardison
90
But, the observe is moving through a static universe in the T
direction, and seeing things at any moment of his local time as the
way things are right now. He is unaware of his motion in the T
direction. Rather, from his point of view the universe is moving
downward in the negative T direction. In effect, he sees the future
coming toward him, and the world passing him by. If we picture the
universe this way, our coordinate system is static, and all of the
objects in the universe have paths within this moving, four
dimensional space time, which we can see whenever and wherever
the path of the object crosses one of our lines of sight. The path is
coming toward us from the future, whether the object is moving
toward us or away from us
Picture a marble thrown into the air, not as a sphere which moves
through space under the influence of gravity, but rather as a four
dimensional tube-like object, the three dimensional cross section of
which is a sphere. The curving path actually consists of the
continuous four-dimensional marble, looping through three
dimensional space, but having continuity and persistence, if you will,
for as long as it remains a marble. So, think of the trajectory of an
object moving through space not as the history of where it has been,
but rather as the continuous existence of the object fixed in four
dimensional space, the cross section of which we see when our
three-dimensional universe intersects the four dimensional object in
the local present.
If the object gives of light, or other electromagnetic radiation, we
can see or sense its presence in our local present at any particular
moment. Thus it will appear that over any relatively short period of
time, the path of a moving object shifts downward relative to our
apparently fixed position.
Figure 24 illustrates this slight shift in viewpoint, where the observer
sees an object to his right moving toward his position. Initially, at
point 1, he sees it to his right along the xL Axis at some time in the
galactic past. After a short time has passed, the path has moved
downward, but to him it appears that it has moved to his left and
now coincides with his position. He calculates the velocity of the
Light in the Local Universe
91
object as the ratio of the distance moved in the x direction divided
by the time elapsed as measured by his clock.
FIGURE 24
THE STATIONARY OBSERVER IN A MOVING UNIVERSE
In essence, he uses the shaded triangle in Figure 24 to determine the
position of the starting point of the object at the initial time in the
galactic coordinate system. The end point, in both systems, is at the
origin, where the observer is located.
This would work exactly the same if the object were approaching his
position from the left, where the diagram would be essentially a
mirror image of Figure 24.
However, when the object reaches the observer and passes by him,
it becomes an object moving away, and Equation 71 doesn’t seem to
work quite right any more. We would calculate the galactic velocity
higher than the local velocity using Equation 71. If, instead, we say
that he must calculate the local velocity, and then reverse the sign we
Les Hardison
92
can get a galactic velocity consistent with the approaching galactic
velocity. Although this point of view is a little reasonable, it still
leaves the problem of the object moving away appearing to move
more slowly than it did when approaching, and we know this is
contrary to our actual experience.
FIGURE 25
OBJECT MOVING AWAY FROM THE FIXED LOCAL OBSERVER
These anomalies lead me to believe that we should look at the picture
I have been presenting of the relationship between the two
coordinate systems and the construction of the four-dimensional
universe a little differently. In particular, we, the local observers, do
not see ourselves sitting on the point of a cone, where peculiar things
appear to happen to the velocity of objects which approach and then
pass us by. Rather, our world looks like we are in the center of a
sphere, and can see things pretty much as they are in any direction.
This leads me to believe that the representation of our local universe
ought to be the one with a straight, horizontal x Axis in the one-
dimensional diagram we have been using, as shown in Figure 26.
Light in the Local Universe
93
FIGURE 26
ANALOG UNIVERSE WITH THE LOCAL AXIS HORIZONTAL
The straight line xL Axis is the one dimensional representation of out
three dimensional universe. In two dimensions it would be a segment
of an enormous circle, or on the surface of a sphere representing the
three-dimensional universe. With all three dimensions present, it
would be a sphere, with ourselves at the center, and space stretching
out in all directions, and the fourth, spatial dimension capable of
depiction only as a series of spheres which change as time passes.
In this picture, the coordinate system is oriented properly to the
spatial dimension, the xL Axis, and the time-like T dimension, so
objects we perceive as moving at a uniform speed and direction of
motion change position in a uniform way.
In this diagram, the present local time, represented by the horizontal
xL Axis, divides all of space-time into the past, below the line, and
the future, above the line. The present is, of course, moving in the T
direction at the velocity c, but we are unaware of this motion.
Everything we see is moving in this direction at the same speed.
Les Hardison
94
Figure 27 illustrates how the reorientation of the x and xL Axes
removes the problems connected with the observation of objects
going away from the observer.
FIGURE 27
OBJECT MOVING AWAY ALONG A HORIZONTAL XL AXIS
In this picture, a uniform velocity from left to right in our local
universe results in a similar path from left to right in the galactic
universe. The mythical galactic observer will see the velocity of the
moving object as lower than does the local observer by the factor
given in Equation 71, and this velocity will not change as the object
passes him. Nor will there be any confusion as to whether the object
is moving into the past or the future relative to the local observer.
He will see the object continually in his local present, as it
approaches, passes, and then recedes from him, just as we might see
the baseball fly past us and recede into the distance.
Were the object moving from right to left, the picture in Figure 27
would be exactly the mirror image. The velocity relationships would
be precisely the same.
Light in the Local Universe
95
In this picture, light is transmitted in the horizontal xL Axis, where it
appears to move instantaneously, or at infinite speed in either
direction, but only coming toward the observer. In the
corresponding galactic universe, it appears to move more slowly,
along the 45 degree lines and appears to have the velocity c. This
follows from Equation 71, where the limit of v is c as vL approaches
infinity.
We have previously envisioned the horizontal x Axis as the dividing
line between the past, below the line, and the future, above the line,
as shown in Figure 28.
FIGURE 28
PREVIOUS REPRESENTATION OF COORDINATE SYSTEMS
This is in keeping with the viewpoint that the galactic universe
represents reality, and that the surface of the sphere properly divided
the four-dimensional universe into that volume inside it (the past),
and the remainder of four-dimensional space-time outside it (the
future). The proposed revision essentially reverses the roles of the
two coordinate systems, as shown in Figure 29.
The coordinate systems are, of course, completely arbitrary,
manmade constructs, which have no influence on the way the
universe is constructed, and are simply to help us make sense of it.
Les Hardison
96
FIGURE 29
THE COORDINATE SYSTEMS REVERSED
In figure 29, we have a local coordinate system which satisfies all of
the observations of objects which have linear motion with respect to
the observer, and which correspond with the way we actually see
things. The inconsistency in the velocity attributed to a mythical
galactic observer is an artifact of the construction of the galactic
system, which is, itself, artificial. The local observer can, with
complete consistency, map the path of an object through space-time
based on his observations and accurately establish the corresponding
path as it would be observed in the galactic system, were it possible
to make observations in the galactic system.
The lines forming the cone represent the paths of light to or from
the galactic observer. The paths of light are not changed by altering
our reference coordinate system, and the 45 degree angle lines
continue to represent infinite velocities with respect to the local
system, and the apparent speed of light, c, in the galactic system. So,
the properties of light, unaltered by the change in the coordinate
Light in the Local Universe
97
system, continue to limit real object velocities to c in the galactic
system, but place no limit on them in the local system.
A stationary object at a distance from the observer which appears to
be at a distance d from the local observer will also be at a distance d
from the galactic origin at some time in the past (the lower right hand
dot) and will be at the same distance d at some time in the future.
If the object is moving at velocity vL in the local system, it will appear
to be moving at a lower velocity given by Equation 71 in the galactic
system.
The present position of the object measured by the local observer
appears to be exactly the average of the past and future positions of
the object as they would be projected to be in the galactic past and
the galactic future at that particular time.
So, the system seems to behave consistently.
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SPECULATIONS ON THE POSSIBILITY OF HAVING
TWO TS
There exists another possibility, and that is that there are two extra
spatial dimensions, and two separate directions of motion of the
universe through space, as shown in Figure 30.
FIGURE 30
TWO T DIRECTIONS
Here there are three dimensions shown. T1, T2 and x. T, as we have
been using it, is simply the sum of T1 and T2, and the rate of motion
of the universe in the T direction would be the vector sum or the
rates in the T1 and T2 directions. If the velocities in each of these
two directions were c, then the velocity of the universe in the T
direction would be 2c .
This speculation has a couple of interesting possibilities associated
with it.
Light in the Local Universe
99
First, it would help account for why the energy of matter is given by
2E mc , rather than by
2
2
cE m .
Also, it would give some rational basis for the fact that light is
transmitted only along the 45 degree lines in our conventional view
of the four-dimensional universe. I had speculated that the
mechanism of light transmission involves the direct contact of two
atoms separated by both space and time, by virtue of the lines of
sight being wrapped up like strands of yarn around a very tiny ball.
Two special directions at right angles to each other and at 45 degrees
to the direction of motion of the universe would make this more
plausible.
This is, of course, mere speculation, but it seemed to me to be an
interesting possibility.
CONCLUSION
This rather tedious explanation of why the appearance that objects
moving away from a local observer appear to be moving more slowly
than they really are with reference to the local coordinate system
does not alter any of the conclusions reached elsewhere in this book,
and it is more convenient to continue to represent the three-
dimensional universe as the very small, approximately planar,
segment of the vast sphere which represents the entire three-
dimensional universe at some arbitrary point in four-dimensional
space.
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100
CHAPTER 6 TIME IN THE TWO
UNIVERSES
In this chapter, I would like to convince you that the difference
between the two systems of measurement is that the local observer
sees time differently than the theoretical observer who keeps track
of things using galactic coordinates. This is the only real difference
between the two systems. People make measurements in their own
local universe, and the common practice is to plot the results on
graphs which have scales calibrated using the galactic reference
system coordinates.
I hope to make the case that the observations made in the local
universe, and used for calculations within the local universe
reference system are consistent and meaningful, and that all sorts of
complexities arise when the time associated with events is measured
in this local system but used as though it had been measured in the
galactic system.
WHERE THE TWO TIMES AGREE
In the galactic system, time is uniform everywhere in the entire
universe, and is presumed to be progressing at a constant rate. The
universal expansion is defined by T = ct, where c is the apparent speed
of light and t represents the time starting at zero at the time of the Big
Bang. There is no reason I can see why the rate of expansion of the
universe should be changing with time, as all of the forces we are
familiar with --- gravity, electrostatic attraction and repulsion and
magnetic attraction and repulsion --- appear to act in the normal
three spatial dimensions. The Strong and Weak Forces, which have
to do with the binding of the components in the nucleus of the atom
are beyond my limited means to make measurements, but I believe
that they, too, could be presumed to act only within three
dimensional space.
Light in the Local Universe
101
The T dimension is the direction in which the universe is moving as
it expands, and it is at right angles to all of three of the spatial
dimensions, so there is nothing to cause an increase or decrease in
the velocity of expansion in the T direction. Only forces acting in
the T direction can cause accelerations or decelerations in the T
direction. The only such force apparent in my model of the
expanding universe is the attraction of gravity due to the matter on
the opposite side of the universe, which is billions of light years away.
This should have essentially no effect on the matter expanding in the
T direction on “our side” of the universe.
In the local system, the things an observer can see in any direction
are what the galactic observer would say were in his past.
For two observers located at the same point in space and time, but
with their own separate coordinate systems --- that of the local
observer, and the second of the hypothetical galactic observer ---
both of them agree on the time at their common location at the
origin, where the galactic observer is in the center of a nearly flat
plane with the same value of T everywhere. The local observer is at
the same point, and experiences the same time. However, he deems
all that he can see at the present instant as having the same time as
his own. It is only at this point in space that the observers can agree
on the time.
FIGURE 31
STATIONARY OBJECT AT THE ORIGIN
This is illustrated in Figure 31, which simply shows the galactic x
Axis, labeled x Axis, and the local x Axis, labeled xL Axis.
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102
At the instant of time pictured in Figure 31, the two observers would
both presumably have their own clocks, and the two clocks would
read exactly the same time.
However the galactic observer would look out his window in the
positive x direction, and (were he actually to see any part of his
present world out there) he would presume that anyone or anything
out there would have his clock set to exactly the same time as his
own. This is, essentially, my definition of the galactic universe. It
consists of all of the points in three dimensional space where the
time, represented by a clock at that point, would agree with our own
clock. The best I can tell, this is the picture of the universe used in
the development of the Special Theory of Relativity, and used as a
reference coordinate system by physicists and astronomers.
Now, even those points in space or objects closest to him would not
be visible to him at his galactic time, because, in his own perception,
light or other forms of electromagnetic radiation would take a finite
amount of time to reach him, so whatever he actually saw would not
be objects which coexisted at his own present time. True, that nearby
objects might only be microseconds or picoseconds in his past, but
they would still not qualify as being exactly in his present time.
So, I believe the galactic observer who sees the entire universe as
existing at the same time he is experiencing is a purely imaginary
creation, and the world, as it really exists at this moment in galactic
time is completely unknowable. Were he a god-like creature, who
could determine the time and position of events and objects as they
exist in his galactic universe, he would have to do so without the use of
electromagnetic radiation.
That is, he would have to be able to see things as though light
traveled at infinite speed in his galactic universe. But it doesn’t seem
to. It seems to move more slowly, at the velocity c. So, he must agree
that either he cannot see beyond the end of his nose in the galactic
universe, and will have to rely on what a co-located local observer
tells him he calculates for the location and velocity of objects, or he
might try to convince us that the light he is seeing actually moves
Light in the Local Universe
103
through space infinitely fast. I don’t think it appears to move
through his galactic space infinitely fast, but it does move through
the local observer’s space infinitely fast. That is basically how we
defined his local universe.
What the real observer sees, when he looks out his window to the
right, is all of the objects arrayed along the xL Axis as they were in
the galactic past --- the very recent past (like a microsecond ago for
nearby things) to a million light years ago (for a distant galaxy). But
what he sees is, in short, what I have defined as the local universe,
and that the local universe is just as “real” as is the galactic universe.
Both systems of measure are mathematical constructs, created by
humans attempting to generalize the laws of nature. They represent
the way things seem to be to us, as observers of the universe. The
two systems are so close together than ordinary life can be conducted
as though they were identical. It is only when in very special cases
where things move very, very fast or are very, very far away from us,
that it seems to make any difference at all which one we use. But, in
those cases, it seems very important to keep them clearly sorted out,
and not confuse one model with another.
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WHERE THE TIMES DISAGREE
But, for the moment, let us presume that a god-like galactic observer
exists and can deduce from the observations of his local companion,
determine the galactic positions and velocities of all the local
observer sees. Thus he can “see” the galactic universe at the present
moment, at least in his mind’s eye. We can compare what he “sees”
with what the real, local observer sees, and examine the differences.
The local observer, looking out the same window, recognizes that
his world, including all that he can perceive, is the closest he will ever
get to seeing the universe as it is at present. He recognizes that any
measurements he makes of distance, length, velocity, mass, energy,
or any other physical property of anything will be based on his view
of the universe. He can construct mathematical models of the
galactic universe, or of any number of other space time constructs,
but he will have to base them on his observations in his local
universe.
In his local universe, he realizes that if he sees an object at a distance,
the clock associated with that object will read an earlier time than his
own. He can calculate exactly what it will read if he knows the
distance to it, according to
( ) (0) ,L L
xt x t
c EQUATION 73
where the left hand term gives the reading on the clock located at x
units of distance from his observation point, and c is the velocity of
expansion of the universe. The value of the local time at his location,
x = 0, is always greater than at any point where x has a larger absolute
value, because x actually represents the distance from the observe to
the object, and is always a positive real number...
Light in the Local Universe
105
It is obvious that x is not an algebraic quantity, where the sign
matters, as the local universe appears symmetrical, and distances to
the left of the observer appear to be earlier locations than at the
origin, just as distances to the right do. So, x must be, and rather
obviously is, simply the distance to the point in question in the one
dimensional model of the three dimensional universe. That is
2 2 2x x y z , EQUATION 74
and would be more reasonably described as rL, the radial distance
from the observer to the object. However, for simplicity, it is useful
to continue to think of this as a distance along the x Axis, but always
a positive distance, when considering the local universe, consisting
only of objects which are in the galactic past.
Now the square root can be taken as either positive of negative, and
the geometry of the situation requires that the positive value applies
to those things in the galactic past, which the observer can actually
see at the moment. The negative root would apply equally well to the
future, or to the distance from the object to the observer. That is,
things located distant from the origin but at a future time would be
represented by Equation 74, but with the negative root rather than
the positive one.
The galactic observer, “seeing” the same object, says that the time is
( ) (0)t x t . EQUATION 75
They obviously disagree by the difference
( ) ( )L
xt x t x
c . EQUATION 76
That is to say, they see the time at the distance x to be x/c earlier in
the local system than in the galactic system. Or, in other words, the
galactic observer would see the point xL to be in the past by a time
period xL/c, while the local observer would say it was in his present
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time. Points xL and x represent the same point in space at two
different times.
This difference between the time assigned to object locations and
events will exist everywhere in the entire universe and at any time in
the past, present or future, except for the exact present location and
the exact present moment in time.
If x represents a point in space which is at a fixed distance from the
common origin of the two measuring systems, the distance to x will
be equal to xL, only at t =tL.
OBJECTS AND EVENTS
This equation applies equally well to objects and to events, and it is
reasonable to pause for a moment to define the difference between
these two. It appears, from my point of view, that the universe
consists of objects, which include everything from electrons to
galaxies, which have persistence and continuity in time. That is, they
seem to be four dimensional entities, which have dimensions in our
three dimensional space, but which are present in the three
dimensional universe as though they were three dimensional cross
sections of a four dimensional entity. If every electron, proton,
neutron, etc. were, in fact, a very, very long (in the T dimensional
direction) thin (in the x, y, z direction) string, where the embodiment
we are aware of is simply a three dimensional cross-section, this
would account for their continuity.
It would also account for their apparently unchanging properties
with time, while allowing for them to assume varying locations in
three dimensional space as time passes. Strings which are straight
represent objects, or points in space which are either stationary or
are moving at constant velocity relative to the observer.
This continuity would not allow for the favorite exercise of the
quantum mechanics devotees, which is the presumption that the
positions are probabilistic in nature, and that electrons can change
location in a discontinuous way. Bending of the strings represents
acceleration or deceleration relative to the observer, but for now we
Light in the Local Universe
107
are only concerned, as Einstein was in the development of Special
Relativity, with bodies which are moving at constant velocity.
Objects have a significant persistence, and exist for a finite, and
usually substantial period of time. Objects have continuity, which
means that if something is present at one instant in time, you can
count on it being present at some later time.
Events, on the other hand, occur at a particular time, and have no
existence outside that period. For example, the emission of
electromagnetic radiation from an excited atom is an event. The
atom is an object, but the change of its state is an event. So, objects
can have velocity, which involves changing their position, but events
cannot.
VELOCITIES
Things are a little more complicated if x represents the distance to
an object which is moving with respect to the position of the
observers. Here they disagree about the time at which any point
exists at a given location in space, and the disagreement is linear with
the distance of the point from the observers. The greater the distance
to the point, the greater the disagreement about the time at that
point.
It is necessary to think of the point in three dimensional space as
being represented by a line in four dimensional space, and the
disagreement between the two observers as to where the point is in
space at a given time, or in time at a given location, is the difference
between the positions along this line of the observations.
The difference between the two times is simply
x v t vt
c c c
. EQUATION 77
Here they disagree about the time at which any point exists at a given
location in space, and the disagreement is linear with the distance of
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the point from the observers. The greater the distance to the point,
the greater the disagreement about the time at that point.
It is necessary to think of the point in three dimensional space as
being represented by a line in four dimensional space, and the
disagreement between the two observers as to where the point is in
space in time is the difference between the positions along this line
which the observer assigns to it as he makes his observations.
So, it is apparent that, although the local observer and his imaginary
counterpart, the galactic observer, agree completely on the time at
their present location, they are unable to agree about the time of any
point at a distance. The local observer will say that the distant point
exists at his present time, and the galactic observer will say that it
exists at his present time, and they are talking about two different
times. The error can be viewed as a difference in opinion about the
location of a point at any given time, but it is more realistic to regard
it as a disagreement about the time, in the history of the point, that
is being considered by each of the observers.
However, we will have to talk about measurement of distance before
we can get into the influence of velocity on the measurements of
time.
For the most part, the differences in time between ourselves and all
of the things we observe around us are very, very small, whether
measured according to the galactic system or the local system. For
example, the time difference between ourselves and someone we see
on TV, broadcasting from Europe, perhaps 5000 miles away, is only
5000/186,000≈1/37 seconds,
Which is essentially the difference between the times assigned to the
event in the two systems.
The galactic observer describes the delay as the time it took the
electromagnetic radiation to move through the space between the
European broadcaster and our eyes, and the local observer would
say that the signal moved instantaneously from the broadcaster to
Light in the Local Universe
109
his eyes, but that his eyes had to have moved through the T
dimension 5000 miles at 186,000 miles per second in order to get to
where he could the signal had arrived.
So, there is no complexity in the relationship between time as seen
by the real observer using the local coordinate system for his
observations and the “galactic” observer, who, blessed with god-like
vision, can see how things are throughout the universe “right now”.
The two observers agree absolutely on what time it is right now, and
if they could perceive, other than by virtue of the time indicated by
their respective clocks, where they stand in terms of the expansion
of their point in the universe in the T direction, they would agree
about that also.
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AGREEMENT ABOUT THE SPEED OF CLOCKS
Both the galactic observer and the local observer experience the
passage of time as their position moves through space in the fourth
dimensional direction at a velocity which appears to be constant, or
very nearly so, with the passage of time. That is, both would find
their clocks running at exactly the same rate, and if they had more
than one clock (or means of producing regular, recurring motion,
like a pendulum by which they could measure the passage of time)
the clocks could all be depended upon to run in synchronism.
The complexity arises when the real observer carries out his carefully
done experiments with moving objects, and tries to translate his
findings to the galactic universe, which he cannot really experience.
When working with local objects, the galactic observer and the local
observer could scarcely tell the difference between their two bases.
That is why, for several centuries, Newtonian mechanics seemed to
hold a complete description of how physical objects interacted with
each other. The observations were made in the local universe, and
the laws of motion, gravity, etc., were treated as though they had
been determined by observations in the galactic universe. Even the
motions of the planets are slow enough and near enough to us that
the deviations from Newtonian laws are almost unnoticeable, except
with the closest of observations.
Time, in the two universes, is so nearly identical that it is very
difficult to tell the difference.
The same similarity in the observations of time and distance between
the galactic and the local reference systems applies to velocity as well.
As long as we are concerned with objects and events relatively close
at hand, where disagreements about time and distance measurements
are insignificant, velocities measured by local observers will appear
reasonable if they are presumed to be the same when used as though
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they were measured in the galactic system. However, even for nearby
objects moving in reasonably short time periods, anomalies will crop
up if the velocities are very, very high.
For very long distances over significant periods of time, some
problems began to emerge.
FIGURE 32
DIFFERENCES IN VELOCITY BETWEEN THE TWO SYSTEMS
When physicists began to be concerned with things that moved very
fast, such that they had to look carefully at changes in location over
very short periods of time or otherwise look at things moving over
very great distances over longer periods of time, inconsistencies
began to appear.
Figure 32 illustrates how, as the observers move through time,
traveling in the fourth dimensional direction, they would fall into
disagreement about how fast a moving object is traveling, because
of their disagreements about the length of time which passed
between their two observations on the distance to the moving
object. Not about the time on their own respective clocks, because
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these would always be in perfect synchronism, but rather how each
regarded the time at various distances from their present position.
As the object illustrated in Figure 32 moves to the right, initially
approaching the observer at the origin, and then passing him, it
would occupy positions numbered 1, 2, 3, 4, and 5 along the x Axis,
so far as the galactic observer was concerned. In each case, he would
assign his galactic time to the position. However, the local observer
would recognize that he could not perceive the position of the object
moving into his future, and could only calculate its position is space
and time from observations when the object was in his past. Thus,
when the galactic observer placed the object at point 3C, the local
observer would have only reached point 3B, and would assign an
earlier time to its location.
The galactic observer would see point 3 out his window at time t,
counting from the time it left point 1. He would have moved in the
T dimensional direction a distance ct, and the object would have
moved through this same distance in the T direction, and would also,
according to his system of relating time and distance, have moved
through the distance vt in the x direction away from his location. So,
he would calculate the velocity of the object as
v t x , EQUATION 78
or
x xv
t t
. EQUATION 79
The local observer, on the other hand, would not be able to see the
object yet, but would calculate that, if it continued at the same
velocity, it would be at point 3C already. Thus the local observer
would presume the distance the objet traveled took less time than
the galactic observer thought it did.
ΔT. =ΔX/C. EQUATION 80
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113
At each point along the way from point 1 toward point 5, the galactic
observer and the local observer, sharing a laboratory, as it were,
would agree absolutely on the time according to their respective
clocks. However, as the galactic observer drew even (in the T
direction) with point 3, he would proclaim that point 3 had moved
the distance Δx in time Δt, and would therefore have velocity v.
At this point in time, the local observer, who had been tracking the
object on his radar screen, would say that it reached that point some
time back and was really moving faster than the galactic observer
thought it was. His determination of velocity as the object passed
him by would be exactly the same as it had been while it was
approaching him. That is
l
L
L
xv
t
, EQUATION 81
and goes on to compare his findings with that of his galactic
colleague, making the following calculations:
l LL
L
x xv
xtt
c
. EQUATION 82
Because xL and x are the same in this example, we could simply write
LLL
x xv
xtt
c
. EQUATION 83
One can replace x in this equation with vt, yielding
1L
vt vv
vt vt
c c
. EQUATION 84
It is convenient to look at the ration of vL to v, which is
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1
1
Lv
vv
c
, EQUATION 85
or
1
1 LL
v
vv
c
. EQUATION 86
This indicates that the velocity registered by the local observer will
always be greater than that which would be “seen” by the galactic
observer, could he in fact measure distances in the galactic universe.
This correction factor, which must be applied to the local observer’s
data to get the data to be used in the galactic system is very small if
the velocity of the object or event is relatively small compared to the
apparent speed of light, c.
This rather involved explanation can be summarized simply by
saying that the local observer and the galactic observer’s clocks
always agree on the time at their common location, but disagree on
the time of things everywhere else. The disagreement is proportional
to the distance of an object from the observer, so if it isn’t moving,
they will agree exactly on the time difference between two
observations of the object. On the other hand, if it is moving, and
they will always agree on whether it is moving or not, but not
necessarily on whether it is moving toward or away from their
position. The local observer will always assign a greater velocity to
it, because he will see a shorter time interval between successive
sightings than does the galactic observer, whichever way it is going.
In the case of objects moving toward the observer, he can see them
clearly and calculate their velocities directly. In the case of objects
moving away from him, they are moving into his future, where an
observer located on the object could see him at his present position,
but he won’t be able to see the object at that position until sometime
Light in the Local Universe
115
in his future. So, he has to calculate, rather than observe, the preset
position of the object moving away from him. Or, for a given
position of the object, calculate the time at which he can expect to
see it.
The galactic observer, on the other hand, can never actually observe
anything in his present time, because light from the object won’t
reach him until sometime in his future. This applies to objects both
stationary and moving. So, he is always going to have to ask his local
observer partner for the information about the local time and
location, and calculate the position of objects at his present time.
The local observer will be similarly limited and unable to help when
the object is moving away from his position. He might, however, be
able direct a beam of light toward the place where the object might
be at some time in the future, and then see the reflection at some
later time and use the distance and the time interval to calculate the
velocity of the object.
He could share this information with the galactic observer, and both
of them might calculate the position of the object at some time in
the galactic past. The local observer would know for certain where
the object was “right now” in terms of his local clock, but the galactic
observer would still think of this as a past position, which he might
use to calculate the present galactic position, provided nothing has
changed the velocity of the object in the meantime.
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MEASURING THE APPARENT SPEED OF LIGHT
At the time of the publication of Einstein’s Special Relativity, in
1905, no distinction was made between the two systems I have been
describing, and it did not seem that there was any real problem with
the use of the commonly accepted (galactic) system of coordinates
for making measurements in the real world. In my opinion, this
distinction is still not made most of the time, and it still does not
matter most of the time. However, when dealing with large velocities
and great distances, it does, and should always be taken into account.
At the beginning of the 20th century there was a very troubling
problem which had arisen because it was found that the velocity of
light did not seem to follow Newtonian mechanics. If one really
could see the world at the present moment, then the velocities he
saw would be simply, the change in distance over a given period of
time divided by the length of the time period.
If a second observer were moving relative to the first, his
observations would simply differ by their relative velocities. That is,
if you saw a train moving 60 miles an hour along a track in front of
you, an observer in an automobile moving in the same direction as
the train at 20 miles an hour would see it as moving relative to his
position at 60 – 20 or 40 miles per hour. It wouldn’t make any
difference if you were using the galactic system or the local system
of measurements, you would get the same answer as close as you
could measure.
However, if the train were moving at the apparent speed of light, and
you clocked it at 186,000 miles per second, you would expect that
the observer in the automobile would see it as moving 20 miles per
hour more slowly. It would take some petty fancy measuring
apparatus to determine this, but it is what you would expect.
Very carefully done experiments, using ingenious physical
arrangements to time the travel of light from one point to another
had established the apparent speed of light fairly accurately before the
Light in the Local Universe
117
end of the nineteenth century. The experimenters made their
measurements essentially by causing a light beam to leave a location
in their laboratory, reflect from a mirror a significant distance away,
and return to the laboratory. By using one of several ingenious ways
of determining the time between when the light beam left and when
it returned, they determined the apparent speed.
FIGURE 33
LIGHT MOVING THROUGH SPACE IN THE GALACTIC TIME
SYSTEM
In the experiment, the observer, initially at point A0 caused a beam
of light to reflect off a rotating mirror momentarily in the direction
of the stationary mirror at point B1, and back to the same rotating
mirror at point A2. The distance from A1 to B1 was not important,
but it had to be known quite precisely, and it had to be far enough
away that the time interval between A0 and A1 was great enough to
measure accurately.
Their universe was the galactic universe, by default. It was what they
inherited from Newton, and had no reason to change.
That is, they presumed that light moved through empty space much
like a fish swims through water, or a sound wave passes through air.
That is, traversing the space in between, little by little, and occupying
each point in space in a straight line between the origin and the end
point of the travel.
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Thus they set up their experiments in a way crudely represented by
Figure 33, with the light source in their laboratory, a mirror (or
complex series of mirrors) some distance away, and a system for
measuring the time between the light leaving the source, and arriving
at the receptor, having traversed twice the distance to the mirror in
the measured interval. It is important to note that the light source,
the reflecting mirror and the light receptor were all stationary with
respect to each other. So, they were moving with the expanding
universe in the T direction at the same velocity, but were not moving
relative to each other in the three ordinary spatial dimensions.
This system provided quite accurate measurements of the velocity,
around 186,000 miles per second, or 300,000 Kilometers per second.
They had no reason to ascribe the measurements they made to the
local universe, as opposed to the galactic universe as I have defined
it, and no reason to suspect that the measurement could represent
anything else other than the speed of light, making its way through
space like a material object travels through space.
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119
THE APPARENT SPEED OF LIGHT TO A LOCAL
OBSERVER
I submit that these experiments were made by scientists in the
position of the local observer using both his measuring tools and his
clock in the local coordinate system, as I have described it, rather
than with reference to the galactic system, as they assumed.
This all seems very straight forward, except for two items. First of
all, the observer at point A0 cannot see light leaving his position. One
does not see beams of light, but only recognizes light falling on his
eyes from some source in his past, so he must presume that light
departed from his location and headed through space toward point
B1. At point A1, he cannot see point B1, as it is in his future, and he
has no ability to tell what is happening at a distant point at his exact
time. So, he takes it on faith that the light leaving his source does go
away from him into his future, behaving much like light coming from
a distance source, which he can see, behaves.
However, if he places a mirror at point B1 (prior to starting the
experiment, point B is on the same horizontal line with Point 1,
representing his galactic present time and a local future time), he can
avoid this difficulty by presuming that the mirror (having moved
through space in the T direction just as he, the observer did)
reflection occurs instantaneously, and that the light beam moved
through twice the distance to B1 in the time 2Δt.
So, from the point of view of the classical physicist, he has observed
that light moved away from his position, and moved through the
vacuum of space much as a fish swims through water, changed
direction instantaneously at the mirror, and arrives back at his
location at a later time, t0+2Δt, having covered the distance 2Δx, and
arrives at the velocity
2.
2
xc
t
.EQUATION 87
Being familiar with fish swimming through water, it makes sense that
this is what happens.
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However, this is not how the local observers would have interpreted
the experiment at all, yet they would have to admit that they got
exactly the same measured result. They were good physicists and
experimenters, and got substantially the same answer when they
repeated the experiments. However, knowing that they were in an
expanding universe, and that their position in space time was
changing continuously as the experiment progressed would give
them a different perspective.
FIGURE 34
THE LOCAL TIME SYSTEM OBSERVATION OF LIGHT SPEED
Figure 34 shows the experiment from their respective viewpoints.
As the diagram shows, the galactic observer would assume that the
light moving away from him toward the mirror would get there at
some time in the future, but he would not be able to see it until it
had time to make its way back from the mirror to his position at A2.
The light beam seemed to be traversing the distance to the mirror,
which is vΔt. Of course he could not see the light beam moving away
from him, nor could he see the present position of the mirror when
he is at Point A1, because a galactic observer can only see things in
the galactic past. However, after the time interval 2Δt has passed, he
Light in the Local Universe
121
arrives at point A2, just in time to see the reflected light return from
the mirror. He definitely sees the reflected light return to his location,
again traversing the distance c, and now two seconds have passed.
So, he concludes that the velocity of light is
2.
2
c tv c
t
EQUATION 88
The local observer would, if he assumed himself to be a local
observer in a universe expanding in the direction of increasing time
at a fixed velocity v, describe the local velocity of light as infinite,
and his task that of determining the rate of expansion of the universe
in the T direction.
So, he would see his experiment as that of sending the burst of light
into the future, presuming it to move through space at infinite speed,
reaching the mirror when the universe had expanded through the
distance VΔt. He would presume that it reflected from the mirror
back to the starting point, now at A2 in the same amount of time,
again traversing the distance VΔt, but again, with no lapse in local
time. As the light made the return trip, he would, by definition, say
that
0L
cv . EQUATION 89
Clearly, neither observer can see the light leaving his location and
moving toward the mirror. The local observer can, however, see the
light which is reflected back toward point A2, and deduce that it took
no time for it to make the trip back. It is reasonable for him to
assume that the speed of light was the same in both directions, as
this is what all of the experiments to date had seemed to indicate.
So, there are two interpretations which can be put upon the results
of the “speed of light” experiments.
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1) The conventional interpretation, which is that light
moves through empty space like a fish through water or
a sound wave through air, as the universe coincidentally
expands as time passes, so the velocity of light is c, and
the velocity of the universe moving in the fourth
dimensional direction is unknown, let’s call it vT, and of
no particular importance, or
2) The “New Theory of Light” interpretation, which is
that, at least in the local universe, transfers of radiant
energy between atoms take place instantaneously,
without anything passing through the intervening
space, provided the emitting and receptor atoms are
properly lined up. Thus, the light is transferred
instantaneously from the source to the mirror, and
again instantaneously from the mirror back to the
receptor in the laboratory, but at a later point in time,
without ever having traversed the intervening empty
space. Thus, what the experimenters measured was the
velocity of the expansion of the universe, c.
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123
THE INFLUENCE OF TIME MEASUREMENT ON C
Let us look at the classical picture of the path of light moving
through the space from the source in our laboratory to a mirror at
some distance, and back to a photocell in the laboratory, and
presume that we had measured the velocity as c. We have agreed
that both the galactic observer and the local observer, sharing the
same laboratory would have no disagreement about the time, as their
clocks would run in synchronism. Nor would they disagree about
the spacing of the light source and the mirror.
The two observers would differ as to when the light beam arrived at
the mirror. The galactic observer would insist he had measured the
speed at which the light traversed the distance to the mirror as the
distance c divided by Δt, and the local observer would complain that
he got the times wrong, because he (the local observer) didn’t see
the light reach the mirror during that time at all, but rather saw it at
the mirror at the end of the time interval 2Δt, but believed that the
light had arrived the same instant in local time that it left the source.
What took the two seconds for the receptor and the light source to
get together was that it took the observer two seconds to reach the
location in the future where he could see it! It was already there
when the observer arrived at that point in space-time.
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THE SIGNIFICANCE OF C
But, both the local observer and his galactic counterpart measured,
or calculated from measurements, a finite value for c, not an infinite
value, so c must have some other significance. Because something
physically moved the distance 2c during the time interval 2 seconds,
I assert that it was the physical three dimensional universe which
traversed the distance in the fourth dimensional direction, T, much
as a fish swims through water, occupying each increment of space
along the way in sequence, while the radiant energy skipped passing
through both the space and the time between the two points.
By the “physical universe” I mean all the matter within the universe,
so that all of it has the velocity c, and the inherent energy content
E=mc2. /2. There is some question in my mind as to the condition
of the empty space between the massive objects, as I do not see it
fulfilling any particular function. At any point in space, there is either
matter there, which is moving in the T direction at the velocity c, or
there is not. It does not seem to be important whether one thinks of
the space between as having any motion. It certainly has no mass,
and I find the concept of dark energy completely without merit. But
that is a different story.
What is important is that we are all rushing through four dimensional
space at a terrific pace, and don’t have any sensation of doing so. We
are not all rushing through four dimensional space in lockstep,
though, as we each seem to define the direction of expansion of the
universe as slightly different for many other objects, which we see as
moving, relative to ourselves, in three dimensional space.
What we are seeing is a tiny component of the velocity, c, of the
object which is out of alignment with our own velocity c. This
velocity and c itself may be thought of as vectors which have both
magnitude and direction, or simply as the magnitude which has a
direction simply by being associated with a time vector, which always
Light in the Local Universe
125
points perpendicular to the x – y surface of our the two dimensional
analog of our three dimensional universe.
The difference between us and an object moving 60 miles an hour is
a very, very slight disagreement about which way the arrow of time
is pointing
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THE UNIFORMITY OF TIME THROUGHOUT
GALACTIC SPACE
The relationship of time to two observers who are moving parallel
to each other in the T direction (which means they have no velocity
relative to each other in three dimensional space) is fairly straight
forward. Everyone’s clock synchronizes with everyone else’s
whether or not they are moving with respect to our location in space.
However, when a body is moving relative to us, the time clock it
carries reads differently than ours, or at least would appear to if we
could read the time it indicates. This is because we see it in our local
present time, which consists of all of the points in space which are
visible to us. All of these points lie in our galactic past. If we could
see a distant clock, it would always read an earlier time than our own,
because we would be seeing it in our galactic past, and it would be
synchronized with the past galactic time. The difference in the two
times for any moving object increases as it gets farther away from
us, and decreases as it approaches us.
The question is, how can we tell with certainty what the reading on
someone else’s clock will be if they are at a substantial distance?
Provided we know how far away they are, the time will simply be the
galactic time, calculated as
L
L
xt t
c . EQUATION 90
Because everyone’s clock is synchronized to the same galactic time
regardless of location, it does not make any difference whether the
object is moving or stationary with respect to our own position, so
the time we see on his clock differs from ours only in proportion to
the distance from us. It is, however, important that we note that we
can only see objects in the galactic past. When an object is moving
away from us, it is moving out of our galactic past, where we can see
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127
it and make measurements of its position, into our local future where
we will not be able to see it until a later time.
The reason the absolute value of xL is used is because it is the value
of the distance from our observation point, independent of the
direction. This is one of the few points which might be more simply
made with reference to the real, three dimensional world than the
simple one or two dimensional world in our model. The distance to
the remote object with three physical dimensions is
2 2 2
Lx r x y z , .EQUATION 91
when y=z=0.
If the object is moving toward us, its clock will synchronize with
ours when our paths cross at some time in the future. In the
meantime, it will appear to us that his mile markers are farther apart
in his TL’ direction, and we would say that time on his moving clock
must be passing more slowly than ours, but it would not be doing so
by the moving clock. If the object were a moving space ship, the
captain would think it was our clock that was running more slowly
than his.
So, as long as we limit ourselves to talking about things getting closer
to us or farther away, there is no real problem with presuming that
the galactic universe runs on our galactic time, and that in the local
universe, we are surrounded by a continuously varying time zone
system so everyone and everything remote from us has his own local
time that is different from ours. However, it is our local world, so
we can consider that everything in it is at our local time.
We are not troubled, in the local universe by the notion that nothing
can go faster than the apparent speed of light, or that light itself moves
at a finite but invariant speed regardless of the speed of the observer.
Light, in the local universe, moves infinitely fast. There is no
problem explaining why all of the measurements of the speed of light
come out with the same value. They are all measuring the velocity of
expansion of the universe, which is exactly the same for all
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128
observers. The conclusion anyone doing the speed of light
measurement with mirrors ought to reach is that he is really
measuring the speed of advancement of the universe into the fourth
dimension.
This explains why things which seemingly have no relationship to
light or other forms of radiant energy, like the force of gravity, or
the speed of a space ship or a far-away galaxy, all seem to obey the
limitation imposed by the apparent speed of light. The simple answer
to my question, “What gives light the authority to set a speed limit
for space ships?” is that it does not. However, our mistaken
impression that we can see what is happening in our galactic present
makes it look like all velocities are lower than they are to a local
observer.
The fastest any of them could conceivably move involves moving
from one place to another in essentially no time at all, or at infinite
velocity. This is possible in the physical universe in which we make
all of our measurements, but infinite velocities appear, when
translated to the galactic universe, to be equal to the apparent speed of
light. Everything shrinks when measurements in the local universe
are translated into the galactic coordinate system.
There is the case which Einstein didn’t talk about in Special
Relativity, and which I have not addressed up to this point, of objects
that are not moving toward us or away from us, but are rather
moving at right angles to a line from us to them. This has a very
important place in the physics of just about everything, and deserves
its own chapter.
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129
ACCOMODTING THE INVARIANT SPEED OF LIGHT
Because experimenters determined that the apparent speed of light
seems to be invariant according to carefully done experiments, and
they, and the theoretical physicists such as Einstein, were unable to
account for any mechanism whereby it could move instantaneously,
they were hard pressed to explain their results.
So, they reasoned that the relationship between time and space must
be such that the things which were moving experienced time and
space differently than things standing still. If one is limited to
working in the galactic coordinate system, and attributes the
invariance of the speed of light to this system rather than to the local
system in which it was measured, it requires some rather extreme
assumptions about space and time.
These are, of course, the relativistic corrections, which appear to
make the local observations fit into the galactic frame of reference.
This can done primarily by modifying the expression for time
according to
2
2
' 1
1
t
t v
c
, EQUATION 92
or
2
2
' 1,
1
t
t v
c
EQUATION 93
where the primes refer to a second moving observer’s observations
of time, distance and velocity.
This seems to say that clocks run more slowly when they are viewed
from a frame of reference moving rapidly relative to our particular
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130
“stationary” frame of reference. This is not because we actually see
them running more slowly, but because we see them at different
points along their path through space and time.
They appear to slow down, but they don’t.
But, once having accepted that the clocks slow down (even though
it is only an apparent slowing down), all of the other conclusions of
Special Relativity become necessary. The measurement of distance is
different, and moving objects experience a shrinking of their linear
dimensions according to
2
2
' 1.
1
x
x v
c
EQUATION 94
Velocities of objects moving relative to our galactic coordinate
system are never able to reach c, the apparent speed of light, because the
whole scheme was derived to provide a system in which velocities
could never exceed the apparent speed of light.
And finally, because no velocity can exceed c, the apparent velocity
of light in the galactic system of measurement, it is necessary to
postulate that the mass of objects must increase as their velocity
increases according to
2
0
2
1,
1
m
m v
c
EQUATION 95
so as to avoid the problem of where the energy goes as bodies are
accelerated and v approaches c.
This leads to the a revised expression for the energy a moving mass,
Light in the Local Universe
131
20
2
1
1
E
E v
c
, EQUATION 96
where E0 is the “rest mass”, or what we think of as the ordinary mass
of an object, which leads to
2 22
0 0 0 02 2.
v vE E m m c m
c c EQUATION 97
And, finally, mass becomes interchangeable with energy according
to
2E mc , EQUATION 98
for objects at rest relative to our coordinate system.
These corrections are all required because of the misinterpretation
of the passage of time, which is, in turn, due to making observations
in the local universe, and treating them as though they were made in
the galactic universe. This point is important enough to have its own
section in the book.
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132
CHAPTER 7 COMPARISON OF THE
TWO SYSTEMS
My objective in this chapter is to examine how the galactic system
of coordinates used by Einstein and other physicists relates to the
local system. In doing so, I will point out how observations, which
must of necessity, be made in our local universe, can be properly
translated to the equivalent values which will probably exist in the
galactic universe at subsequent times. This would allow the galactic
system to be used precisely when dealing with uniform velocities,
and some forms of non-linear motion such as orbital velocities.
However, this translation does not account for the apparent
shrinkage of time and space with motion which is built into Special
Relativity, and is the most difficult concepts to understand based on
everyday experience.
I will offer a rationale for the inclusion of these shrinkage factors,
which results, I believe, from the failure of physicists to distinguish
between the local system of coordinates, in which the measurements
are made, and galactic systems of reference, to which they are being
attributed.
I will take this one step at a time, first defining the translation of
measurements of time, distance and velocity from the local system
in which the measurements are made to the galactic system, using
the presumption that the velocities being dealt with are constant.
Then I will move on to the more complex situation where two
observers make measurements, each in reference their own local
coordinate system, and compare the translations to the galactic
system for differences which would be unexpected.
This is, basically, the route followed by Einstein in the development
of the basic equations of Special Relativity, which still serve as the
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133
cornerstones of modern physics. I will point out that Einstein
applied this comparison of the apparent velocity of light c, which was
determined to be the same when measured by pieces of apparatus
moving relative to each other, and was presumed to apply to other
velocity observations as well. The misinterpretation of the meaning
of c led to many of the complexities associated with Einsteinian
space time.
I will also point out how the equations derived from the
presumption of two systems moving relative to each other have
mistakenly been translated to the case of a single observer making
measurements of a single object moving relative to his position. This
has resulted in the general application of the space and time
shrinkage factors to all objects in motion.
Finally, I will consider the case where the a single observer, making
measurements of distance and velocity in his local coordinate system
mistakenly uses these measurements without correction as though
they were made in the galactic system. This is the error which results
in the calculation of the shrinkage factors to space, and time, and the
increase in mass with velocity of objects moving with respect to the
observer.
This is not an easy comparison to make, because both use coordinate
systems involving time, which is not only difficult to describe, but
which is also a bit difficult to define.
Furthermore, in the local system, I have replaced time with a fourth
physical dimension, which is even harder to visualize. We have
experienced the passage of time in various ways, but we do not
perceive the motion of our universe through a fourth dimension, just
as we do not sense the very rapid motion of our earth with respect
to the sun. I believe the velocity of the universe in the fourth
dimensional direction is steady and unchanging, except for minute
differences in direction, which we recognize as accelerations or
decelerations of objects in our three dimensional world.
Yet, if the universe is expanding as time progresses, then the fourth
dimension must be there for it to expand into, and our location in
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the three dimensional universe must be moving in this fourth
dimensional direction. These seem to me to be inescapable
conclusions once the expansion of the universe is accepted as real.
Both the galactic and the local systems are simply attempts to
describe the universe we experience, and fit the measurements
relating to how it works into the description. I maintain that we can
only observe how it works in the context of the local universe I have
described, and that the galactic universe, which may be the more
appropriate measure of things, is beyond our reach. It can only be
constructed graphically or mathematically, but cannot be
experienced. Not only can we not see into the future, but in a very
real sense, we cannot even see into the galactic present.
Once again, I will emphasize that ordinarily we are dealing with
objects which move at relatively low velocities. These are slow
compared to the speed of expansion of the universe, which I have
consistently referred to as the apparent speed of light. And, we are
usually dealing with short distances, which are small compared to the
distance light travels in a few seconds. So, in our everyday experience
it makes no practical difference which of the two reference systems
are used. The measures used by physicists – length, time, velocity,
mass and energy – all come out pretty nearly the same in both of
them.
Only when the velocities of objects relative to one another become
significant compared to the apparent speed of light, or when the
distances become large relative to the distance light travels in a
second or two, does there seem to be any problem with the use of
the Newtonian laws of motion. But, it is those cases which have to
be considered to make a comprehensive picture of the way the world
works, including a consistent theory for the properties of light, a
consistent model of atoms, and the behavior of the galaxies.
I am going to start by presuming that we make all of our
measurements in the local universe where we live, and that these are,
or should be, translated by rational means to the galactic universe
coordinate system used by Einstein and other physicists. The
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135
translation ought to fit the actual measurements into the framework
of Special Relativity, and, with some exceptions, they do.
For the most part, despite all of the modifications of General
Relativity, the development of Quantum Mechanics, Quantum
Chromodynamics, and the Standard Model used by physicists to
describe the internal workings of atoms and molecules, the basic
concepts of Special Relativity are still pretty well taken as being
correct. I do not presume to understand all of the complexities of
modern physics, and for the moment, ask the reader who is well
versed in these things to give me license to simply deal with the
elementary concepts of Special Relativity as it was originally
presented.
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136
MEASUREMENT OF TIME
I am going to try to go through the comparison between the
measurement system I have described as the local coordinate system,
within which all of our physical measurements are made, and the
idealized picture of the universe, in which time is everywhere the
same, regardless of the distance of an object or event from the
observer.
My aim is to present a relatively concise picture of the relationship
between the two systems of measurement, and the means by which
an observer, working in his local universe can produce an adequate
picture of the galactic universe, at least so long as the objects he
observes do not change their velocities between the time he sees
them and measures their properties and what he considers to be the
“galactic present time” in reference to the galactic coordinate system.
The difference between the two systems boils down to a difference
in the measurements of time. When the translation from the local
system of measurements to the galactic frame of reference is made,
the result does not correspond with the equations of Special
Relativity. Something is clearly being left out, and my main objective
in this chapter is to establish the difference between my derivation
and Einstein’s, and to offer an explanation of how it comes about.
All the difference between the two derivations and much of the
complexity in Special Relativity seems to result from making
measurements using one system (the local system), and then
applying them improperly to the other (the galactic system), without
using the corrections defined in this section.
In particular I will point out how the failure to recognize the
difference between the two systems has led to much of the
complexity in the equations of Special Relativity, and the application
of the ubiquitous correction factor, F, to the measured times,
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137
distances and velocities of objects moving with respect to the
observer.
2
21
vF
c , EQUATION 99
In the local system of coordinates, each observer regards the time at
his location as the time his clock reads. I will postulate that he has a
clock which reads the precise time in terms of fractions of a second
since the time of the Big Bang origin of the universe, and that it reads
the same as the galactic time at his location. This is true for all
observers, regardless of location in our ordinary three dimensional
space, so everyone, everywhere, sees the same time on his clock if
they are all in the same galactic present. The local observer will,
however, ascribe his own local time to everything he can see, or
detect by means of electromagnetic radiation. That is, his present
time will apply to all the universe he can see.
So, he would see, if he had a sufficiently powerful telescope, which
points in his local universe remote from his location would have
clocks which read an earlier time than his own. He would have no
trouble understanding that his present represented a collection of
points in the galactic past. So he would think of each distant point
as having two distinct times. According to which system of keeping
time he chose to use.
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THE LOCAL TIME ZONE ANALOGY
A more familiar case of the use of two different time systems
involves the earthbound traveler’s use of Universal Time (UT),
which used to be called Greenwich Mean Time (GMT). This is the
time at the Prime Meridian which runs north and south through
Greenwich, England, and has been used as a reference time
throughout the world. We all have our local time zones, in which our
clocks are set more or less in keeping with when the sun passes
overhead each day. I live in the Eastern US time zone, where the
clocks are normally set to a time five hours earlier than Universal
Time, or,
5:00EST UT .EQUATION 100
This is complicated a bit by the use of Daylight Savings Time, which
advances the local (EST) clock one hour during the summer months,
for reasons that are debatable. There are, arbitrarily, 24 irregularly
drawn time zones forming irregular segments of the spherical
surface of the earth, such that nearly all of the clocks can keep the
minute hands synchronized while only changing the hour hand.
So, at the equator, one could, by counting the time zone immediately
west of Greenwich as 1, for the first time zone, and numbering them
consecutively around the globe, write the equation for the local time
as
L Gt t N , EQUATION 101
where:
tL = Local time in hours
tG = Greenwich Mean Time in hours.
N is, of course an integer running from 1 to 24. Between the 12th
and 13th zones lies the International Dateline, where, when it is 12:00
Light in the Local Universe
139
Noon in Greenwich, it is midnight locally, and the date increases by
one calendar day.
One could easily imagine a time zone system consisting of many
more time zones than 24, in which the minute hand on the clocks
would not all be in synchronism, just as the hour hands are not in
the present system. As an extreme, one could consider that, instead
of 24 time zones, there were, instead, an infinite number, so that
each individual would have to have a clock which read the time
applicable to his unique position, and whose clock would have to be
reset each time he moved any finite distance to the east or west. The
setting of each individual clock would require knowing exactly how
far east or west of Greenwich the clock happened to be at the
moment. It could then be set to read
360L G o
Longitudet t , EQUATION 102
where 360o represents an angular velocity of 360o/day.
It is not hard to imagine that, faced with this complex situation,
individuals would prefer to simply set their clocks to UT, which is
the same at every point on the surface of the planet, and abandon
the local time concept altogether. This is, essentially what aircraft
pilots do.
So, we each have our own local time, which is changing at a
presumably uniform rate due to the rotation of the earth. We have
no sensation of the velocity of rotation, but we can, in easily perceive
the changes in the location of the hands on our clock, or of the sun’s
passage overhead, and conclude that these motions are related. The
common factor is, of course, what we call time. And it is, on earth,
related to the rotary motion of the earth, which cannot sense directly.
If, instead of using the observatory at Greenwich, England as the
location of the reference time zone, we instead used our own present
location, wherever that might be on the surface of the earth, we
would have a situation comparable to my concept of local time in
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140
the four dimensional model of the universe. We would, of course
think of our local time being the same through the world, although
we would understand that everyone else had a local clock that read
their local time, not ours.
The relationship between our CDT and Universal Time is quite
analogous to the relationship between local time and galactic time,
L G
xt t
c , EQUATION 103
indicating the relationship between the local time on the surface of
the two dimensional sphere of the analog universe, which changes
with distance from the observer, and galactic time, which is exactly
the same at every point on the surface of the sphere.
In this analogy, the speed of the earth’s rotation is the analog of the
expansion of the universe in the T direction. Were we to depart in
an aircraft to fly westward from the our initial location, say at
London, at about 800 miles per hour, we would find that the local
time along our path did not change at all, and we would appear to
be moving instantaneously from point to point. If we left London at
noon, we keep resetting our local clock continuously as we flew
westward, we would arrive at our destination, wherever it was,
at…..noon, by our local time clock.
In terms of Universal Time, we would be moving 800 miles per
hour, or at about the rotation speed of the earth at his latitude.
Or, one could say that we were, in fact, standing still, and the earth
was rotating beneath us at 800 miles per hour. In terms of local time,
our departure time and arrival time would be exactly the same, and
our velocity would be, not 800 miles per hour, but infinite.
Were we to use a cell phone to call ahead and advise friends at our
destination of our departure, the message would arrive at the
destination as we were leaving London, in substantially no time at
all. However, we would not be at the destination to check that the
Light in the Local Universe
141
message was received, and could only attest that the message was
there when we got there, so it might appear to us to have traveled
only 800 MPH instead of at essentially infinite speed.
If we then postulated that the telephone call progressed across the
ocean at 800 MPH, and that nothing could possibly go faster than
that, we would have arrived at a lot of misconceptions about the way
the world worked.
When there are two alternative ways of defining time, keeping the
differences between the two in mind is very important.
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TIME IN THE LOCAL AND GALACTIC SYSTEMS
The relationship between galactic time at any given location and the
local time assigned to that location is simply
L
xt t
c , EQUATION 104
and the differences in time between measurement of distance is
L
xt t
c
, EQUATION 105
or
L
v tt t
c
, EQUATION 106
for objects moving toward the observer, from which
1Lt v
t c
. EQUATION 107
Finally,
1
1 LL
t
vt
c
. EQUATION 108
This corresponds to the difference in time between two events
presumed to take place at the different measured distances. That is,
for example, at the beginning and end of the timing of a race, or the
motion of a space ship between the earth and the moon.
The relationship between the elapsed time for any two events in the
galactic and the local systems depends solely on the local velocity
observed, and is independent of the placement of the origin of the
Light in the Local Universe
143
coordinate system. Wherever it is, the origin is presumed to be
stationary.
The local time is what one can measure by looking at his own, local
clock. The galactic time at his location is presumed to be the same,
because the local observer is at the origin of his own local coordinate
system. And the time at all other points is presumed to be the same
as his local time. However the galactic time is the same everywhere.
Any other observer at a different location at the same galactic time
would be presumed to have the same local time.
It is noteworthy that there is no F factor which shows up repeatedly
in the equations of Special Relativity.
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MEASUREMENT OF DISTANCE
The measurement of distance in the local system is a purely
mechanical problem, but there are many mechanical solutions. For
example, the distance to an object can be measured against a pre-
established grid, with mile markers spaced evenly apart like the
yardage lines on a football field. Or, the object can be detected by
RADAR, or SONAR. More complex methods may come into play,
such as the brightness of a star of known type, or the apparent size
of an object of known size. The method of measurement is not
important, but it is important that all of the possible measurements
depend in some way or another on the transfer of electromagnetic
energy from the object to the observer. This is done in the local
universe, and it is presumed that the objects seen exist in the local
present.
The location of the object in four dimensional space is simply
determined from the distance measurement in three dimensional
space, and has been represented by the single x dimension in one or
two dimensional analogs used in the derivations so far.
There is no ambiguity about where the object is in space at any given
moment in either local time or galactic time. If one chooses to use
the local time system for measurements, the distance to the object is
simply the x coordinate of the object at that time. If the object is
stationary, the x coordinate will be exactly the same as in the galactic
system, because the distance in the galactic coordinate system will
not have changed during the passage of time between tL and t. The
measurement in the galactic system will be exactly the same,
Lx x , EQUATION 109
for stationary objects. However, if the object is moving, the position
will be measured differently for different velocities, according to
Light in the Local Universe
145
Lx x v t , EQUATION 110
where Δt is the galactic time difference between two events, like the
beginning and the end of a race. We would ordinarily presume that
Δt is a positive time difference, and time is progressing in the normal
fashion. The velocity, however, may be either positive or negative.
If it is positive, xL will be greater than x, and the object under
observation will be moving farther away from the observer, with the
distance increasing with time if the object is on the right hand or
positive side of the x Axis. If the velocity is negative, the distance
will be getting shorter, and the object is moving toward the observer,
if on the right hand side of the x Axis. When the time interval is zero,
Equation 110 reduces to Equation 109, as it does when the local
velocity is zero.
When observations of change in distance with time are made, the
changes are related by
2 1 2 1 2 1( ) ( )L Lx x x v t x v t x x . EQUATION 111
It is apparent that the measurement of length in both systems should
give the same results, regardless of velocity of the object whose
length is being measured. There is no shrinkage of the dimensions
with motion relative to the observer. Only if the object were actually
growing longer or shorter, would there be a difference when the
measurements made in the local system were applied to obtain values
to be used in the galactic system.
There is one possible ambiguity which arises if one presumes that
the measurement of distance in the local system should not be made
by taking the difference in the x values along a horizontal line,
representing a constant galactic time, but rather along the 45 degree
line representing a constant local time. The ratio of measurements of
the distances by these methods is obviously 2 , and would suggest
that distances measured at constant local time should be reported
higher by this ratio than the corresponding galactic distance. This
might well account for the energy of a mass “at rest” with respect to
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146
the observer being mc2 rather than mc2/2, as conventional dynamics
would have it. However, this would lead to some confusion, because
the local observer is only able to recognize the location of objects in
three dimensional space. So, for the remainder of the discussion, the
local distance xL will continue to refer to the distance between the
observer and the object measured as though both were at the same
galactic time.
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147
VELOCITY IN THE TWO SYSTEMS
The measurement of velocity in the local system of coordinates is
quite straightforward, at least in the case of objects moving directly
toward the observer. It is simply the observed change in distance in
a measured time period. The time period is exactly that indicated by
the local observer’s clock. Remember that this clock always reads
exactly the same as the galactic observer’s clock at the observer’s
position at the origin of both coordinate systems.
It is a bit more complex in the case of objects moving away from the
observer, because he cannot observe future positions of the object
(neither “future” according to his own definition of the present time,
or in terms of the galactic present) because light simply does not move
from the future to the past. However, he can observe past positions
of the object at various times, and therefore calculate the speed of
the object prior to it reaching his present position. As all of this
discussion has been based on the assumption that we are dealing
only with objects which move at constant velocity, this doesn’t cause
any problem.
There is no way an observer can determine the velocity of an object
in the galactic present by direct observation, because he cannot see
anything removed from his location at the origin of the coordinate
system at the present moment in galactic time. What he really sees
are the items in his galactic past which are a part of the local present. But,
making the conversion from local velocity to galactic velocity is
perfectly straightforward, and has been dealt with in several previous
chapters.
The conversion is done according to
,
1
L
L
vv
v
c
EQUATION 112
regardless of whether the object is moving toward or away from the
local observer.
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148
The galactic velocity is always lower in value than the local value
determined by observation, and always appears to be less than the
value of c, the apparent speed of light, whereas the value of vL, the local
velocity, has no such mathematical limitation.
Thus, if the velocity is determined for an object in the local
coordinate system, the corresponding velocity can be calculated in
the galactic coordinate system.
FIGURE 35
PLOT OF GALACTIC VELOCITY VS OBSERVED LOCAL
VELOCITY
For velocities toward the observer, the velocity in the galactic
coordinate system are taken as positive in Equation 112. When the
velocity is away from the observer it is taken as negative, but is
subtracted rather than added, so the same equation applies to motion
in either direction.
Thus the galactic velocity will always be less than the observed local
velocities. This is illustrated in Figures 35 and 36, which show that
the velocity for the local system is always greater than for the galactic
system.
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
v/c
vL/c
v/c vs vL/c
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149
If for example, the local velocity is c, the elapsed time will be twice
as long as the galactic system, while the galactic velocity will be half
as high (i. e., the galactic velocity will be only c/2. Conversly, if the
galactic velocity is c (as is usually assigned to the velocity of light) the
velocity in the local system is infinite.
FIGURE 36
GALACTIC VELOCITY FOR LARGER VALUES OF LOCAL
VELOCITY
Another way of comparing the velocities in the two systems is by
noting that the slope of the path relative to the T Axis is a direct
measure of the velocity. The value of the velocity is different for the
local systems, as indicated in Figure 34.
It is apparent that the vertical line, corresponding to motion which
coincides with the motion of the universe in the fourth dimensional
direction, involves no motion in our three dimensional universe, so
the local velocity is zero. Motion at 45 degrees to the x Axis
represents velocities which are infinite. Light moves from one point
in space time to another located along these 45 degree lines. The
velocity c measured in the local universe corresponds to c/2 in the
galactic universe.
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120
v/c
vL/c
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150
FIGURE 37
ARRAY OF LOCAL VELOCITIES
The same motions in referenced to the galactic universe, as depicted in
Figure 37, show the 45 degree slope, where
Δx = cΔt, interpreted as the velocity c. It apparent that to reach this
velocity, and object would have to be moving infinitely fast when
referenced to the local coordinate system.
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151
FIGURE 38
ARRAY OF GALACTIC VELOCITIES
These charts illustrate the very great difference in the interpretation
of velocity in the two coordinate systems. It should be emphasized
that the velocity of matter at the time of the Big Bang and
subsequently has been c, most of which is directed in the fourth
dimensional direction. The velocities we observer in the three
normal dimensional directions are usually only a small fraction of
this. So, it is unlikely that any objects in the universe near our
location will have a velocity approaching c with respect to the local
coordinate system, which would appear to be only about c/2 in the
galactic system.
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TABLE 1
RELATIUNSHIP BETWEEN LOCAL AND GALACTIC
VELOCITIES
vL/c v/c=1/(1+vL/c)
0.0 0.0000000
0.1 0.0909090
0.2 0.1666670
0.3 0.2000000
0.3 0.2307690
0.4 0.2857140
0.5 0.3333330
0.8 0.4285710
1.0 0.5000000
2.0 0.6666670
3.0 0.7500000
4.0 0.8000000
5.0 0.8333330
7.5 0.8823530
10.0 0.9090910
20.0 0.9523810
30.0 0.9677420
40.0 0.9756100
50.0 0.9803920
75.0 0.9868420
100.0 0.9900990
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153
By way of summary, the distance, time and velocity measurements
are all, of necessity, made within the local system of measurements,
and the conversion to the galactic reference system universally used
by engineers and physicists can be made using Table 1.
The concept of mass in the local system is completely different than
it is in the galactic system. In the latter, Einstein was led to the
conclusion that mass had to be a variable quantity for any physical
body. Were it not, he reasoned, a force tending to accelerate the body
long enough could cause it to reach velocities exceeding the apparent
velocity of light, c, and this was not, in his estimation, possible. So,
he derived the famous equation,
220 2
0 02
2
21
m c vE m c m
v
c
, EQUATION 113
in which m0 represents the “rest mass” of an object which is not
moving with respect to the observer, and
0
2
21
mm
v
c
, EQUATION 114
where m is the relativistic mass of the object. In other words, objects
become more massive as they are accelerated to high velocities
relative to the observer. This prevents the velocity of an object from
ever reaching the apparent speed of light, c.
In the local reference system, there is no limitation on how fast
things can move, although nothing can achieve the true speed of
light which is infinite. So, there is no need for the relativistic
conversion factor as it applies to mass.
There is no reason implicit in the geometry of the local system why
a mass could not exceed the velocity c, the velocity of expansion of
the universe in the fourth dimensional direction. However, there is
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a strong suggestion that the energy imparted to all matter by the big
bang, and accelerating it to the velocity c, would make it difficult for
any body with a substantial mass to be accelerated to a higher
velocity, simply because there is nothing of significant mass which is
already moving at a higher velocity than c.
In the local system, mass is simply mass, and it is not influenced in
any way by acceleration with relationship to any coordinate system.
There is, in the local coordinate system, no concern for what
happens to the mass of my lunch pail if someone chooses to use a
coordinate system moving a significant fraction of the apparent speed
of light.
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155
ENERGY CONSIDERATION
The need for the relativistic increase in the mass of an object
accelerated to a high velocity with respect to any arbitrarily
established coordinate system was explained away in the previous
section. Along with the need for the increase in mass with velocity,
the need to modify the energy of a moving body so that the galactic
velocity could not exceed that of light also disappeared.
So, in the galactic system based on proper conversions of physical
measurements, there is no shrinkage factor applied to the energy of
an object at high velocity. The total energy is simply
2E mc , EQUATION 115
where the mass is invariant with velocity, and c is the apparent speed of
light, but actually the speed of the expansion of the universe.
The part of the energy that is observable in the local universe is the
part which represents a velocity in the three spatial dimensions we
can observe. Essentially all physical masses have the same intrinsic
velocity, c, with nothing to indicate that it is changing with time. The
velocities of all objects in four dimensional space are not perfectly
aligned with each other in the T direction (where time seems to be
pointed slightly different for one body than for another) and the
misalignment is what we recognize as observable velocity.
So, in the properly treated galactic system, there is no need to modify
the energy calculated on the basis of the local velocity to prevent the
violation of any physical laws.
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COMPARISON OF RELATIVISTIC AND LOCAL
VALUES
A relatively straightforward comparison of the local system of
measurement is given in the table below. In this table, the relativistic
contraction factors are shown where appropriate, and are used for
measurements of the position and velocity of a moving object even
when there is only a single reference coordinate system involved,
because this is how the contractions are used.
TABLE 2
COMPARISON OF LOCAL MEASUREMENTS WITH
CONVENTIONAL RELATIVISTIC VALUES
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157
The values of local velocity, energy and mass may be calculated
either by using the time difference for a given distance traversed or
the distance traversed in a given period of time.
As has been demonstrated, the use of the relativistic contraction
factors for time, distance, velocity and energy, and for the increase
of mass with velocity, are artifacts of the misinterpretation of data
obtained by observation in the local universe. Were it properly
corrected to give the corresponding values in the galactic system,
rather than used without correction, a much simpler system could be
applied for the galactic calculations.
The proper correction factors are shown in Table 3 below. In this
table, the values actually measured in the local coordinate system,
but incorrectly assigned to the galactic system without correction,
are included with the subscript “A”, indicating that they are
“Apparent” values.
This table makes the point that there is no shrinkage in time for
moving objects. Instead, the time associated with the objects can be
alternatively the time read by our clock, as observers, or the time
read by a clock associated with the moving object, but read at an
earlier galactic time. Both readings are valid, and there is no conflict
between them, just as my clock may simultaneously indicate US
Eastern Standard time, and Universal Mean Time (Greenwich Mean
Time), without either reading being in error.
The length of moving objects does not shrink because they are
moving, but the local time associated with the two ends is not the
same when the object is moving with respect to the observer’s
position.
The velocity is not limited to the apparent speed of light in the local
universe, but the simple geometry of the expanding universe makes
it look like anything moving at infinite velocity in the observer’s view
is moving at the velocity c in the galactic universe.
Again, the velocity measurements may be taken as the distance
traveled in a given period of time common to both systems, or as
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the time required to traverse a given distance which is the same in
both systems. The energy and mass calculations are the same for
either method.
TABLE 3
GALACTIC VARIABLES CALCULATED FROM LOCAL
MEASUREMENTS
In Table 3, the velocity vA is understood to be unlimited, as it is
measured in with reference to the local coordinate system, whereas
v, the correct value in the galactic system, cannot exceed the apparent
speed of light, c.
The light is not slowed by its progress through empty space, because
it doesn’t really come through the empty space at all. It bypasses both
space and time in getting from the source to a receptor.
Light in the Local Universe
159
Because velocity is not limited to c in the local universe, the energy
an object can obtain is not limited, and could, theoretically, become
infinite in time. However, in order for it to do so, there would have
to be a massive object already moving at greater than the velocity c,
from which to transfer the energy. There is no evidence that massive
bodies with velocities above c exist in the universe although one
might suppose that, if one could travel a quarter of the way around
the universe, he would find that the bulk of matter there would be
moving at the velocity c referenced to our local coordinate system.
All things considered, I believe that the use of the galactic reference
system as the setting for physical events and objects is valid, but that
the translation from the local system of observation to the galactic
coordinates should be made so as to avoid the complexities of the
relativistic corrections and the misconceptions of how velocities,
masses and energy are interrelated in the galactic system.
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WHY THE SQUARE ROOT FACTORS?
These are the ubiquitous shrinkage factors which are applied in
Special Relativity to the measurement of time, distance, length,
velocity and mass. So far in this discussion, they have not appeared
to be needed. The question arises as to where they fit into the picture,
where do they come from, and what they actually mean.
It is easy enough to account for the appearance of these factors in
the development of Special Relativity. If one represents the motion
of an object or a point in space relative to the arbitrarily chosen
stationary reference system to describe the galactic universe, there are
two ways of looking at a velocity vector. One viewpoint is that of
the stationary observer, who applies his own time standards, and
reports distances as though he had determined them at the exact
instants in time read by his clock. This is, of course, impossible, as I
have pointed out several times, but it is necessary, if one is using
galactic space and time coordinates.
The other way of looking at the same velocity vector is from the
viewpoint of someone traveling along with the moving object,
whose own clock is used as the time reference, and who sees things
as located differently relative to his coordinate system.
Because the galactic system is, in a way, a fabricated system, really
outside our normal experience, it is a bit difficult to ascribe a
meaning to the observations which would be made by a moving
observer at any location along his path except at the exact same point
where we are at the moment. This is because any time we can actually
see him or obtain any information about him whatever is at a time
he would regard as in his past. His present is in our future.
But, supposing we both observed his path through space, each using
his own clock and distance measuring tools but each of us had the
god-like ability to see how the world actually is at the present
moment in galactic time.
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161
FIGURE 39
COMPARISON OF REFERENCE SYSTEMS
We could compare our measurements and see how they differ. This
is most easily pictured with the help of Figure 39.
Here, the velocity of the moving observer is depicted according to
his reference system which is moving along with him. His clock is
synchronized with that of the stationary observer, as they will read
the same when their paths cross, and the origins of their two systems
are located in exactly the same place. Each clock will read the time
at the horizontal galactic x Axis it is crossing, which physically
coincides with the surface of the two dimensional balloon
representing our three dimensional universe.
Each will presume his own velocity in his T direction is c, the apparent
speed of light. So, the moving observer will take the hypotenuse of the
triangle as equal to ctL, using his local time, and assuming he has no
velocity other than this. However, he will agree that his velocity
could consist of any two components at right angles to each other
which add up to his velocity.
The vertical side of the triangle, paralleling the motion of the
stationary observer and the horizontal side, representing the velocity
assigned to his motion by the stationary observer, are two such
components. The moving observer agrees that his stationary
position in space may be represented by the two vectors the
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stationary observer assigns to him. These are, of course the same
vectors, but the viewpoints are different.
In particular, the stationary observer sees the vertical component as
c, the apparent velocity of light. The moving observer views this
same velocity as
2 2 2 2'ct c t v t , EQUATION 116
so
2 2 2 2 2 2'c t c t v t , EQUATION 117
or
2
2
'1 .
t v
t c
EQUATION 118
This can also be expressed in terms of the time differences between
two events, presumably observed by both the stationary and the
moving observer.
2
2
'1 .
t v
t c
EQUATION 119
This suggests that the moving observer’s clock must run slower than
that of the stationary observer. This is, however, a total misreading
of the situation based on the presumption that we live in and observe
events which take place in the galactic frame of reference. Nothing
could be further from the truth. In actuality, everyone’s clock runs
at exactly the same speed, but when we see a distant clock, we do
not see it in the galactic present time, but rather in the galactic past,
and the distance in the past is proportional to how far it is away from
us in space. So, the correction we make for the speed of their clock
is a reflection of our misunderstanding the circumstances under
which we are reading the clock. It is not a measure of change in the
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163
performance of the clock, but rather a measure of our error in
perception.
Thus, if we observe a distant clock far away from us, but stationary
(not changing in distance from us with time) the clock would appear
to be running in synchronism with ours, as it truly is. But set at a
different time.
However, if the far away clock is moving relative to our position,
then it is either going farther back into the galactic past or moving
closer to our galactic present time as we make subsequent
observations of the time it reads. The rate of change of the readings
will differ from those of our local clock, although the two clocks are
running at identical speeds. The time contraction factor is an illusion,
brought on by the failure to differentiate between the local system in
which the measurements are made, and the galactic system, to which
we mistakenly attribute the measurements.
We need not expect to see our astronauts who eventually depart in
spacecraft which move through space at a significant fraction of the
apparent speed of light to return to earth much younger than their
counterparts who remained behind. They will age exactly like we do,
who only wait out their return.
Once the shrinkage factor is applied to time, in the galactic system,
the other measureable quantities, velocity, energy and mass all have
to be corrected also. So, the ubiquitous shrinking factor gets into
every aspect of physics. However, while it is easy enough to
understand that the shrinkage of time, it is difficult to grasp the
concept of physical lengths of objects also shrinking, and mass
increasing as the velocity of the object increases.
A CREDIBLE MISTAKE
The relativistic correction factor as it is ordinarily used is not limited
to the calculation of how the universe would look with respect to
someone else moving relative to our own “fixed” position. It is, in
fact, attributed to anything moving relative to our own point of
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reference. That is, if we want to make calculations of the force
required to deflect an electron from its path when it is moving at
appreciable speeds relative to the apparent speed of light, we customarily
apply the relativistic factor, F, to the mass of the particle. We are not
looking at the properties with respect to a second reference system
moving relative to us, but simply of an object moving relative to
ourselves, in our own system, with no second reference system
entering into the picture.
As followers of Einstein, we understand that the mass of the particle
must increase as its velocity approaches the apparent velocity of
light, and we need the correction factor to make the laws of physics
produce calculated results in tune with what we observe.
This seems to be true even if there is no second coordinate system
involved, and the derivation of the F factor derives directly from the
assumption of a second reference moving with respect to our own,
and observing the speed of light to be constant when measured by
observers using the two separate reference systems. The question is,
why do these corrections seem to apply in a situation entirely
different from that for which they were derived?
I think I have an explanation for how this comes about, but it
requires a bit of speculation. I believe that the ubiquitous F Factor is
there because of a chronic and nearly universal use of the measured
local distances as though they were really galactic distances. While
they are distinctly different quantities, the differences between them
are not important for objects which are essentially stationary or
moving at relatively low velocities (compared to c) relative to the
observer. All of our day to day observations fall into the category
where there is little difference between the systems. When we hit a
baseball with a bat, we do not need to take into account that, by
relativistic standards, it becomes slightly more massive as the velocity
increases.
The failure to change points of view when dealing with fast moving
objects or objects very far away from us is quite understandable.
There is no clear-cut dividing line between the situations where
Light in the Local Universe
165
relativistic corrections are important, and when they are not. Failure
to shift points of view, when it is appropriate to do so is a very
understandable mistake.
I will try, in the following paragraphs, to explain how the mistaken
use of the measured local distances and velocities, rather than the
correctly calculated galactic quantities, leads to an error in the
galactic frame of reference which requires the use of a correction
factor which is exactly equal to F. This accounts for the need to apply
the correction factor to objects moving with respect to a single
reference system.
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THE F CORRECTION EXPLAINED
We may begin by looking at a body moving with an appreciable
velocity toward an observer in the local universe, as depicted in
Figure 40. I would like to look at the time required for the object to
move a specific distance, both from the standpoint of the local
observer and the fictional galactic observer. When the object
depicted is at point A, the galactic observer sees it as being on the
lower horizontal line, representing the x Axis at galactic time t = 0,
the starting point of the observation. The local observer does not
see the object to be at point A at this time, but at a later galactic time,
A’, with the time interval defined by the distance the object will move
to reach point B, which is the same for both systems.
FIGURE 40
AN OBJECT IN MOTION WITH RESPECT TO THE OBSERVER
AT THE ORIGIN
For the distance moved, Δx, to be the same for both systems,
L Lx v t v t . Equation 120
Light in the Local Universe
167
Because both observers see the object move the same distance, their
velocities are, necessarily related by
L
L
tv
v t
. EQUATION 121
The relationships worked out previously for use in calculating the
galactic velocity from the observed local distance of movement of
the object and the measured local time period still apply, even
though the conditions of the example have been altered somewhat.
These relationships are
1
1 LL
v
vv
c
, EQUATION 122
and
1
1
Lv
vv
c
. EQUATION 123
However, in this example, we will substitute the ratio of times
required for the object to move a specified distance for the ratio of
velocities, so
L
L
t v
t v
, EQUATION 124
and
L
L
vt
t v
, EQUATION 125
so
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168
1
1L
t
vt
c
, EQUATION 126
and
1
1
L
L
t
vt
c
.
.EQUATION 127
In the latter equation, we assume that the observer has measured the
local velocity but mistaken it for the galactic velocity. So, we may
simply drop the subscripts and call the velocity “measured” by the
local observer the velocity, v.
Now, to evaluate the relationship between t, the correctly calculated
galactic time period and tL, the local time period measured, one can
simply take the product of the expressions in Equations 126 and 127,
to obtain
2 1
1L
v
t cvt
c
. Equation 128
The evaluation can be simplified by multiplying the numerator and
denominator of the fraction on the right side by the quantity
1v
c , EQUATION 129
to obtain
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169
2 2
2
2
2
1 1
1 1 1L
v v
t c c
v vt v
c c c
, EQUATION 130
from which one obtains
2
2
1
1
A
L L
v
tt c
t tv
c
. EQUATION 131
One can interpret this ∆tA value as the apparent value of the galactic
time, and compare it with the true value as obtained from
1
1
Lt
vt
c
, EQUATION 132
to obtain
2
2
11
11
A A L
L
vt t t c
vt t t vcc
, EQUATION 133
or,
2
2
1
1
At
t v
c
. EQUATION 134
Or, one could simply compare Equation 134 with the value used for
the Einsteinian time correction given in Table 3, which is
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170
2
2
1
1L
v
t c
t v
c
, EQUATION 135
and note that this is exactly the expression derived when the
measured values of time and distance obtained with reference to the
local system are used without adjustment to represent the galactic
values, but where the velocity in the table was for an object, or
system, moving away from, rather than toward, the observer.
In short, the Einsteinian shrinkage factor applied to time differences
appears to be entirely due to making measurements in the local
system, which is the only one actually available, and using them,
without modification, as though they were obtained in the galactic
system.
As has been pointed out several times, the correction factor, F,
which must be applied to time measurements, requires similar
correction factors for the measurements of position, and velocity,
and leads to the presumption that, size and velocity of objects
decrease with increasing velocity and that time and mass grow larger
for objects moving with respect to the observer.
The galactic time period used for velocity measurements is always
longer than the corresponding local time period for a given distance
traversed, so the galactic velocity is always lower than the local
velocity. Misusing the local distance measurements, and using them
as galactic measurements, causes the velocities to come out lower
yet.
The one application which is not explained is that pertaining to the
increase in mass of moving objects, generally cited as
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171
0
2
21
mm
v
c
. EQUATION 136
This does not relate directly to the measurement error described for
the distance, time and velocity measurements. It comes, instead,
from the postulate that “nothing can move faster than c, the apparent
speed of light.” The application of a force of any magnitude for a long
enough time would necessarily accelerate the mass to a higher speed,
unless, of course, the mass were to increase so as to prevent it from
reaching the velocity c.
I have maintained that nothing can appear to move faster than c when
measurements are properly translated to the galactic reference
system, but that, when measured in the local reference coordinate
system, light actually moves at infinite velocity. The velocity of
massive objects obviously cannot exceed the true speed of light. The
kinetic energy of masses is not limited and the mass measured in the
local universe need not increase as the galactic velocity increases.
While this is all a matter of perception, I believe it is factual that most
measurements of physical properties are made, of necessity, in the
local system, where what we can see at the moment comprises the
universe, and that the local measurements are often used directly,
without modification, instead of being converted to the
corresponding galactic values in a systematic way.
Les Hardison
172
CHAPTER 8 CRITIQUE OF SPECIAL
RELATIVITY
While I think Einstein did a remarkable job, taking on the problem
of the day for physicists and astronomers and producing the Special
Theory of Relativity, I believe he would have done things a bit
differently were he working on the same problem today. The critical
difference is that it is now relatively clear that the universe is
expanding, which suggests that it is moving into a fourth spatial
dimension related to time. In turn, the inclusion of a universe
moving through a fourth dimension in space allows us to speculate
that it is this velocity which was measured by the experimenters who
were trying to determine the speed of light.
In this section, I am going to make an unfettered criticism of the
Special Theory of Relativity, as though it were done by a present day
student trying to make a good impression on his teacher, rather than
the modern era’s most brilliant theoretician. I will assume that the
velocity the universe in the fourth dimensional direction is c, and
that the velocity of light is infinite.
CONSTRUCTION OF THE BASIC DIAGRAM
Let me take Einstein’s approach step by step, and examine each in
terms of the knowledge that the universe is expanding, the
assumption that it is expanding at the velocity c in a direction at right
angles to the three ordinary spatial dimensions.
Let’s start with his diagram, as previously shown in Figure 40. For
purposes of simplicity, the x direction is chosen to be the direction
of a beam of light, and since light can move in any direction from
our position to wherever it is going, there is nothing wrong with
defining our x Axis to be that direction.
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173
FIGURE 41
REPEAT OF EINSTEIN ’S TIME-SPACE DIAGRAM6
I have no problem with using a diagram like this to represent the
relationships between any sort of measurements one could make,
and both distance and time are measureable quantities. We have to
make sure we define what we mean by the variables, and abide by
the conclusions we draw that are consistent with the definitions.
The value of t presumably has to do with the measurement of time
using a clock of some sort, which is near at hand, and represents the
time at our point of observation, x = 0. The value of x represents
the distance from our observation point to any object not at the
origin on the graph. Because time is used as the ordinate, there is an
implicit understanding that the other two of our three spatial
dimensions, y and z, are zero, so far as the diagram is concerned.
6 Albert Einstein, Relativity, the Special and General Theory, Translated by
Robert W. Lawson, Crown Publishers, New York, NY, 1918
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174
Einstein chose time for the ordinate – the vertical scale – in his
diagram, and used x as the abscissa. He didn’t assign units to either
explicitly, and presumed, as physicists often do, that the reader
would, if necessary, supply his own. Here the implicit assumption is
that any consistent set of units will work.
Finally, by placing the intersection of the x and t axes suggests that
the observations of time and distance are made from this
intersection --- the origin on the graph --- and that both the time and
distances have the value zero at this location. Thus it looks like the
measurements may be made with things like a tape measure and a
stop watch.
IMPLICATIONS OF THE DIAGRAM
However, he did choose a pair of scale factors for the time and
distance axes that appears to be more than a random selection, and
we need to look at this selection in detail.
There is a wealth of information in the construct of this simple chart.
First of all, we should consider that when one makes a picture like
this, it can be intended as simply a way of illustrating a correlation
between two variables. For example, the annual average price of corn
can be plotted against the annual average rainfall in the Midwest for
a number of years. In this case it is perfectly clear that there is no
intention to depict any physical relationship between prices and rain,
only the numerical relationship, if there is one.
On the other hand, one could draw sketch of a man walking, and
plot the distance he travels vs. time. Now there is a physical
relationship between the variables, not just a statistical one. If he
walks at a constant speed, his path, on a plot of distance vs. time,
will be a straight line. If he changes his speed occasionally, the slope
of the line will change.
In either case, there is a great deal of latitude in the choice of scales,
and one can select whatever scale factor is convenient to show the
intended relationship to best advantage. For example, if the time
scale for the man walking is chosen as 0 to 3 hours, and he walks
Light in the Local Universe
175
three miles per hour and then stops, it is convenient to choose the
time scale to cover a little more than the three hour period, say 0 to
4.5 hours, and the distance scale to cover 0 to 5 miles. This will show
his whole journey, and that he stopped at a point well within the
range covered by the graph.
Einstein, in drawing his graph, chose to use the distance from the
light source to the receiver as the abscissa, and the time as the
ordinate, suggesting that the data represent measured times at which
a beam of light originating at the origin would reach a series of
measured distances from the origin. This is what one might use to
plot the progress of a race horse or several race horses, moving
around a track, with the time measured at various fixed points along
the track and again at the finish line, which is at the same location as
the starting gate. This follows the test methods used to measure the
speed of light, which timed the interval between the emission of the
light and its return to a receptor a known distance away. It underlines
the belief by both the experimenters, and Einstein, the theoretician,
that light moved gradually through empty space, like a fish swims
through water.
Further, if time is presumed to be at right angles to the x Axis, and
the x Axis serves as an analog for the entire three dimensional
universe, it suggests that, in addition to being a completely abstract
relationship between time and distance measurements, Einstein had
some inkling that time is, as I have been proposing, a kind of fourth
physical dimension, and it is at right angles to the three we ordinarily
perceive.
SUBSTITUTING T FOR TIME
Further evidence in this direction is the fact that the line describing
the path of a beam of light in the x direction is at 45 degrees to each
of the two axes. This has to be more than coincidental. The only
circumstance under which the line will come out at 45 degrees is
when light moves an equal “distance” through time as through
space. That is, the unit in which time is measured has to be the same
as the units used to measure distance. This can only be if there is a
velocity associated with time, i.e.
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176
T Vt . EQUATION 137
Where:
T= distance in the fourth dimensional direction
V=the velocity of light
t=time.
Now the abscissa has linear distance as its units. Still, in order to
make the 45 degree angle possible, for a measured speed of light
numerically equal to c,
V c , EQUATION 138
Or
T ct . EQUATION 139
So, I think Einstein must also have had in his mind some inkling of
the relationship between his simple time function and the notion that
the universe is expanding in the same direction time is flowing, and
further that it might be going that direction at the velocity c, which
was measured as the speed of light in a vacuum.
We can redraw his diagram so that it incorporates these implied
characteristics as shown in Figure 42.
In my picture of the local universe, Einstein’s t for time is replaced
with my T for distance in the direction the universe is expanding.
Also, it is apparent that, in choosing the scales for time and distance,
he selected scale factors which include the apparent speed of light, c as
the ratio of one time unit on the graph to one distance unit. Thus his
line representing the motion of a light beam away from the origin,
x ct is a 45 degree line upward to the right on the positive side
of the graph, and
x ct , upward to the left on the other.
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177
FIGURE 42
T DIMENSION SUBSTITUTED FOR TIME
This is exactly the same graph one would get if the t Axis were
replaced by an Axis on which T=ct, a distance, and the units for
distance on both the T and x axes were identical.
Somehow, it seems that these considerations were implicit in the
simple graph which was used to illustrate the basic Lorentz
transformation used by Einstein.
While Einstein apparently had no intention of implying that he was
depicting the physical universe, rather than just the relationship
between distance and time for a beam of light, he chose his basis
quite consistently with my picture of the local universe, which is
aimed at depicting the physical relationship. In other words,
Einstein, too, drew something of a physical picture of the universe
as he saw it and which resulted in his ground breaking theory.
THE MEANING OF T
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Now, we get into the meat of the matter, which is about what the
variables depict. Because the origin is chosen at t = 0,
x = 0, there is no suggestion that the origin is moving in the t
direction. This implies that the values of time, t, represent values of
time subsequent to the present time, or times in the future of the
observer at the origin. The origin is not moving into the future, so it
must be the difference between the time at the origin and a later
time. In short, it is the reading on a stopwatch of sorts held by the
observer at the origin.
Thus there is the implicit assumption that the x Axis is where the
present time is defined as zero, and anything on the x Axis is at the
same time as the observer at the origin. In short, t, and therefore T
= ct, are constant, and equal to zero anywhere along the x Axis. All
positive values of t or T represent objects or events at a later time
than at the origin, and the entire x Axis at this zero time.
The universe at the present moment (where the x Axis is located) is
not moving into the future. The universe is static and unchanging
with time, at least in this picture. I think this is consistent with
Einstein’s thinking at the time, and that of most other physicists. So,
Einstein did not think it necessary to make his ordinate a physical
space dimension, or to consider the problem of where the origin was
moving in time, because he considered it fixed.
Still, he must have had some inkling that the fourth dimensional
direction, which was related to time, also had to be related to
distance. From which it is a very short step to saying that the ordinate
should be ct = T, rather than just t.
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179
WHICH WAY DOES LIGHT TRAVEL?
A second major difference between what Einstein did, and what I
think he would do were he dealing with the same problem today, is
that he elected to show the light beam in his diagram moving away
from the origin, rather than toward it. I think it is apparent, on
reflection, that you cannot see a light beam moving away from you.
When you shine a flashlight into the midnight sky, you do not see
the beam of the flashlight cutting through the darkness. What you
may see is the reflected light from particles of moisture or dust, or
what have you, but the light itself is invisible to you. You simply rely
on your past experience with light to believe that it is moving away
from the flashlight. You cannot verify this by direct observation.
Only when it shines on something in your field of vision can you be
sure, by direct observation, that the light went where you supposed
it would. And then you are not seeing your light, but rather the light
emitted by the reflecting surface, in response to the energy imparted
to it by the light you directed to it.
So, I would have drawn the figure upside down. That is, with the
light moving toward the origin from some point in the past. It does
not really matter when in the past, or how far away from you the
light originated was, when you saw it. You would believe it
happened, and could verify that you had seen a light from a particular
direction, at a particular time. Specifically at the right now, zero time
at the origin.
So, my picture looks like I think Einstein should have drawn his, and
probably would have, if he were doing so today rather than a
hundred plus years ago.
Les Hardison
180
FIGURE 43
UPSIDE DOWN LORENTZ DIAGRAM
In Figure 43, the light appears to originate at some distance from the
origin, at some time in the past. With only one directional dimension,
x, it could be either directly to the left or to the right. The distance
from the observer at the origin would determine how far in the past,
according to
x v
T c
. EQUATION 140
In Figure 43, there is still no implication that the x Axis represents
the three dimensional universe, or that the time is anything other
than zero for all points along the x Axis.
Also, in Figure 43, the observed light had come to you, as the
observer at the origin, in an essentially straight line from somewhere
along the line x ct .
Here x is a positive distance to your right, and t is a negative time.
So the farther in the past the object of event was – the time interval
Δt - the farther away to the right the source must have been. Of
course, the light could have been on the other side of you, so it would
Light in the Local Universe
181
have come to you along the line x ct , where the negative time
values produce negative distances, or distances on the left side of
you.
The diagram looks much the same as Einstein’s, but now the source
of the light is presumed to be some place other than the origin, and
the receptor is at the origin. This way, the observer at the origin can
see the light arrive at his location, and by one means or another,
measure the distance of the source from his position. The problem
is, how does he know the time at the point of origin of the light, so
that he can determine the velocity of the light? This was addressed
in the experiments by Michelson and others.
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SEEDS OF DOUBT
In the experiments performed to measure the apparent speed of light,
the experimenters set up an apparatus consisting of rotating mirrors
which would direct a beam of light momentarily toward a second
mirror at a known distance, and measure the time at which it
returned to the rotating mirror source. In order to show the essence
of this experiment on the original graph used by Einstein, one would
use his original diagram with the light initially moving away from the
source at the origin.
Let me propose the thought experiment, where the observer at the
origin of the diagram in Figure 44 is intent on measuring the speed
of light, using a mirror placed at a distance, x to reflect the light back
to his position, so he can measure the elapsed time between the
emission of the light and the receipt of the reflected light. In Figure
44, the mirror is shown at a single location, but, like all other objects
in the universe, it also exists at all of the points along its path through
space-time in the T direction.
FIGURE 44
EINSTEIN’S PLOT WITH MIRROR EXPERIMENT
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183
The only location of importance in the picture is that at which it
intersects the beam of light presumably emitted from point A for
only an instant.
The experimenter sends the light beam off along the x ct path,
and at known distance Δx, it is reflected back toward his location.
The progress of the light beam from point A, at the source of the
light, in the experimenter’s laboratory at the origin, is just as Einstein
pictured it; upward to the right at a 45 degree angle. However, when
it strikes the mirror, it is not reflected backward through time to the
observer’s location at the origin, but rather continues upward to the
left, because light never goes backward into the past. It always moves
from the past toward the future.
When the light reaches point c, the time elapsed will be given by
2 xt
c
, EQUATION 141
and the velocity will be calculated as
2.
2
x xv c
xt
c
EQUATION 142
While this is the right answer, the researcher would never know it, if
he were fixed to the x Axis at 0t as shown in the graph. The only
way he could receive the light reflected from the mirror is if he and
his apparatus and the x Axis had also moved the distance 2Δx in the
T direction during the time it took the light to get there.
Thus, the graph used in the application of the Lorentz
transformation to the problem of the invariance of the speed of light
has a basic inconsistency in it.
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THE SPEED OF LIGHT
The thing that has to give here is the assumption that “light moves
through pace at a fixed, finite velocity c”. This has a flaw in it
somewhere. This doesn’t invalidate the results Einstein got using the
Lorentz transform to interpret his input data, but it does tend to
invalidate the input data.
If one makes the assumption that the universe is expanding at the
apparent speed of light, c, and the time represented by Einstein’s diagram
is the absolute time, or galactic time, as I have called it, then the
origin, and the observer, and the x Axis, are all moving upward in
the T direction. The x Axis, where the time is t = 0, must be moving
upward at the same velocity as the origin.
The line representing the motion of light away from the origin must
be replaced by x vt , where v must necessarily be greater than or
equal to c, otherwise the source of the light would be “catching up
with” the light beam as it moved away, and the light would be
moving from the future into the past.
Einstein suggested this himself, saying that if c, the apparent speed of
light, were infinite, the equations of Special Relativity would reduce
to the Newtonian equations for distance, velocity and energy. This
was, of course, because the ubiquitous F factor in all of the equations
of special relativity would become exactly 1, regardless of the
velocity of the object.
This could not be the case, he reasoned, because light would then
not be observed to move at the same velocity when observed by two
experimenters moving at a finite speed relative to each other. But,
this is exactly what happens, if one presumes that it is the universe
itself, moving in the fourth dimensional direction, which is traveling
at the velocity c.
So, there was a built-in problem with Special Relativity, which would
require the observer to be moving along with time, but at the same
time would not allow the x Axis, on which he was located to be
Light in the Local Universe
185
moving with time if the constancy of the speed of light was a true
representation of the situation.
In short, the error seems to have been in presuming that the only
way of accounting for the apparent invariability of the speed of light
was to presume the measurements of the speed was accurate, and
that the universe were constructed rather peculiarly so as to limit the
speed of everything to the value c. Light just happens to be the only
thing that seems to move this fast. This is the reason it appears that
the speed limit which applies to light also manages to limit the speed
of everything, including electrons, space ships and the effects of
gravitational attraction, to c, the apparent speed of light.
To make a more consistent picture of the situation, Einstein would
have had to modify his viewpoint, but not very radically. In
particular, he would need to adopt the notion that one makes all
scientific observations in terms of the local universe he perceives. It
is not in terms of a universe in which time is everywhere exactly the
same, and “right now” does not include anything in the universe that
one can actually see “right now”.
So, it is much more reasonable to view the points on the x Axis as
being those which can be seen from the origin at the particular
instant of time. Thus at 0t , one can see to the left and right all of
the points that are located in the galactic past, along the lines
x ct to the right, and x ct to the left, as shown in Figure 44.
Les Hardison
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FIGURE 45
LINES OF SIGHT FROM ORIGIN
Here, it is apparent that the observer at point A can see objects or
events happening at his local present time, t1, at any distance to his left
or right, and that the time along this line is earlier in galactic time for
greater distances in either the positive or negative direction. That is
to say, if the observer at point A sees a point at a distance to his left
or right, and could read the time on a clock at the point, it would
read an earlier time than his own clock reads.
This is exactly what I have called the local time viewed by the observer,
at A, and the objects and events visible to him comprise his local
universe. The observer can see and attest to those things which are
visible to him at his position and time t1.
It is also apparent that, to the observer at A, his present time is the
same time as would be reported anywhere along the xL Axis, were
he interpreting his sightings according to the galactic system of
Einstein and others. However, he cannot see an object at A ' which
is still in his future. A light switched on at position A ' in space
would not be seen by the observer while he is at A. He would report
seeing it at some later time which is still in in his local future while
he is at A.
The light would appear to be switched on when the observer has
progressed to point B. He would attest to the fact that the light
arrived at his location at his local time t2. From the diagram, he would
infer that it left point A and arrived at point B at the same local time.
In short, it traveled the distance between A and B in zero elapsed
local time.
The observer who references his observations to the galactic universe
described by Einstein would report the speed of light as the distance
from B to A, divided by the time difference between x1 and x2 which
would produce the value for the apparent speed of light, c, but which is
actually the speed of expansion of the universe.
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TRANSVERSE MOTION NOT CONSIDERED
It is important to note that any motion in this limited one
dimensional picture must either be toward the observer, away from
the observer or stationary with respect to the observer. This is not
the case in the real three dimensional universe, where objects can
move freely in other directions. In particular, transverse motion,
which is neither toward nor away from the observer at the origin,
has not, as yet, been dealt with. This is a serious omission from
Special Relativity.
If a body is moving away from the observer’s present position, it is,
in effect, moving into his future. He will not be able to see any of its
future positions until he, the observer, has moved into the future far
enough that the now-present position of the moving object is in his
past. Objects moving toward him lie entirely in his past as they
approach, and are fully observable.
Objects moving transverse to the origin at any given moment are
neither moving toward nor away from the observer, and therefore
are in his present at the moment, just as are stationary objects. This
has some special consequences.
My last and final comment on the development of Special Relativity
has to do with the omission of any discussion of motion transverse
to the origin of the observer’s coordinate system. Motion of an
object relative to the observer at the origin generally consists of both
a radial component (which is the component of velocity either
directly toward or directly away from the observer) and a transverse
component, which is at right angles to the radial direction.
By selecting the observer at the intersection of the x Axis and the t
Axis in the two dimensional diagram, and presuming that light
emanated from the origin and moved into space, only motion which
was directly away from the origin was considered. Motion toward
the origin is seemingly included in the analysis, because the positive
value of v, the velocity away from the origin is simply replaced by –
v for a system or object moving toward the origin.
Les Hardison
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The motion of light through space is considerably more complex
than this, because light moving in either direction in the three
dimensional space has an essentially infinite velocity in the T
direction, so there is a difference in the way the apparent velocity of
light must be viewed if it is moving away from the observer, as
depicted by Einstein, rather than toward to observer.
Transverse motion is another completely different case which arises
when motion is not directly toward or directly away from the origin.
This kind of motion cannot be depicted in the two dimensional plot,
where one of the dimensions is time, or the time-like fourth spatial
dimension. If the only dimension pictured is the x dimension,
motion can only occur along the x Axis, and it must either be toward
or away from the origin, and the presumed observer at the origin.
However, this does not represent the real world in which objects can
move at right angles to a line between the observer at the origin and
the object.
This is the case where an object may be moving toward the origin,
but not on a collision course with it; like an asteroid approaching
earth, but, fortunately, missing it by a million miles. This would not
fit into Einstein’s simple picture used in the development of the
equations of Special Relativity, and there are important
consequences of the omission.
In order to take the possibility of transverse motion into account,
Einstein’s simple two dimensional diagrams would have to be
augmented to include at least a third dimension. All three dimensions
cannot easily be drawn without crowding out the T dimension,
which we really need for relativistic calculations. But, two spatial
dimensions, x and y, are simple enough, and one presumes that the
z dimension, which completes our world, is taken as equal to zero
throughout the discussion.
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FIGURE 46
ILLUSTRATION OF TRANSLATION
The three dimensional plot with x and y representing the expanding
universe, like part of the surface of a balloon being blown up so the
surface is expanding in the direction at right angles to the surface,
labeled T in Figure 46.
In this figure, the two horizontal planes correspond to the horizontal
x Axis in the diagram representing the galactic reference system. A
couple of inverted Vs are included to remind us of the local universe
system coordinate axes.
Here one can see not just the two dimensional x–t or x–T diagram
in which it is presumed that 0y z , and that these dimensions
are unimportant. When both x and y are assigned real value, the x
Axis becomes the x–y plane. Within this plane, motion can be
toward the origin or away from it, as in the simpler x - t diagram.
This is ordinarily called radial motion, as it would take place along a
radius extending out from the origin.
However, when the x – y plane replaces the x Axis, it is now possible
to depict transverse motion which is at right angles to any such radial
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line. Motion of an object that is perpendicular to the particular radius
on which it lies relative to the origin does not, at the moment, bring
the object closer to or move it farther from the origin.
It is a fundamental principle of the science of dynamics that any
motion can be defined as a combination of one component of
velocity in the radial direction plus another component in the
transverse or tangential direction relative to any arbitrary point in
space. Everything that has been said about the relativistic time
contraction/expansion applies only to radial motion.
This is such a significant feature of Special Relativity as it should be
written that I have devoted a separate chapter to the transverse
motion, and in particular to a special case of transverse motion
which is described as orbital motion.
Light in the Local Universe
191
PURE TRANSLATION
Pure translational motion of an object relative to a reference point
or observer who is considered stationary only occurs in special
circumstances.
For an object moving in a straight line at a constant speed, the
motion almost always consists of a radial component which is either
directly toward or away from the observer, plus a translational
component which is at right angles to the radial component. Pure
translation only exists for the brief moment when the moving object
is at the closest it will ever be to the observer, at which time the radial
component is exactly zero. At all other times, the distance to the
observer will be as illustrated in Figure 47.
FIGURE 47
PURE TRANSLATION
Here an object depicted at point 1 at time t=t1 is shown moving to
point 2 at t=t2. The path of the point relative to the origin is such
that it passes the origin at t2, where it is the closest it will ever get to
the observer at moving along the T Axis.
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At any time, the distance from the observer to the object is given by
22
0 0( x yr x v t y v t . EQUATION 143
It takes a bit of thought to recognize that the equations of Special
Relativity were all derived using the radial distance from the observer
to the object or moving system as the only dimension. Thus, we
could substitute r, the radial distance, in any of the equations without
distorting the meaning of them, provided, however, that there were
no transverse component to the velocity.
The equations do not hold if there is a translation component to the
velocity, and the task here is to determine what the different is when
translation is taken into account.
The distance to the object is obviously the minimum when the
velocity component in the radial direction, vx, is zero, and the
velocity in the y direction has just offset the initial distance from the
y Axis. In short, when 0r x .
The relationship between the radial and translational velocity
components for an object moving in the positive y direction past a
stationary observer at a distance x0 from the path line of the moving
object is shown in Figure 46.
It is apparent that the vector velocity in the y direction can be
resolved into components in the radial direction, toward the origin,
and the transverse direction, perpendicular to the radial line to the
object.
Light in the Local Universe
193
FIGURE 48
RADIAL AND TANGENTIAL COMPONENTS OF VELOCITY
EXAMPLE
These components are
22 2
2
1sin
1
rv y
xv x y
y
, EQUATION 144
and
22 2
2
1cos
+1
tv x
yv x y
x
. EQUATION 145
For illustrative purposes the radial and transverse components of
velocity are calculated for an object moving along a path at 10y
at a velocity of 5 meters per second. The radial and transverse
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194
components of velocity relative to the origin are plotted in Figure
49.
FIGURE 49
RADIAL AND TANGENTIAL COMPONENTS OF VELOCITY
EXAMPLE
The transverse velocity is not much of a factor except when the
motion is nearly at right angles to the radial line between the object
and the origin. In Figure 49, it is apparent that the radial velocity
becomes close to the velocity of the object when it is far from this
point. On the other hand, the transverse velocity, which is not much
of a factor when far from the point of closest passage, reaches its
maximum, just equal to the total velocity, when the point of closest
passage is reached.
Now, at, or near this point, the object is not moving toward or away
from the origin at a significant velocity, and the time rate of passage
observed on a clock carried along with the passing object would be
just equal to the rate of time on our clock.
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10Ve
loci
ty, m
ete
rs/s
eco
nd
Tme, seconds
Radial velocity, vr
Transversevelocity, vt
Light in the Local Universe
195
That is, the rate at which the local observer sees the clock associated
with the object is running neither fast nor slow, but is keeping time
at exactly the same rate as his own. It does not read the same time,
but sees it as being slow by the amount of time proportional to the
distance of passage.
0'x
t tc
. EQUATION 146
However, at this point in time, where the path of the object through
space is purely translation, there are no relativistic corrections except
that for the error in clock reading due to its distance from the
observer.
This would not be of very much importance were it not for a special
case in which translation is essentially the only kind of motion
involved. This is the case of orbital motion, where one body is
orbiting another. We are continuously involved with orbital motion,
as describes the motion of the earth around the sun, and also the
electrons around atomic nuclei, of which everything is made.
The whole next chapter of this book is devoted to this special case.
SUMMARY
Einstein did a remarkable job of explaining how light could appear
to be moving through space at the same velocity when measured by
two observers moving relative to one another. In doing so he
introduced new concepts that changed the whole complexion of
physics, and continues to be the foundation on which most of
physics, astronomy and quantum mechanics are based. The new
concept was that time is not the same for all observers.
However, in the development of Special Relativity he accepted as a
basic premise that the speed of light in a vacuum was a finite and
invariant number, independent of the motion of the measuring
apparatus. He did not accept the alternative explanation --- that the
speed of light was infinite, and the measurements of the apparent speed
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of light were actually measurements of the rate of expansion of the
universe, or more concisely, that time is simply a measure of the
position of the universe in the fourth directional dimension.
His application of the Lorentz Transformation introduced several
inconsistencies which might have provided clues to the questionable
nature of his input data.
He might well have:
1. Tried to conform the Lorentz Transformation diagram to
the physical model of the universe he was proposing to
represent. This would have led to a suggestion that the
universe was expanding at the velocity c, and the
presumption of a fourth spatial dimension, which I have
called T, instead of his simple time dimension...
2. He did not recognize that the x – t model used in the
application of the Lorentz Transformation was not one that
admitted of direct measurements of anything not at the exact
position of the observer at the origin of the x – t coordinate
system. That is, at any given moment in time, an observer
cannot see the “present state” of anything even slightly
distant from the origin in his galactic coordinate system. It
is a world which may exist, but it cannot be seen or sensed
in any way. One sees only the universe as it was in the past.
He did not make this distinction between the present he
could actually see, and the theoretical galactic present,
presumed to exist at the present instant in galactic time.
3. By assigning the time 0t to all points along the x Axis,
he precluded the possibility of measuring the speed of light
by the method which was, in fact used to measure it. In
order to make measurements of the speed of light, the
observer at the origin would have to be moving through
time, as light was presumed to do. This should have been a
clue to the inconsistency of the input data he used.
Light in the Local Universe
197
4. He took for his development the case of light moving away
from the observer at the origin. This is a situation which has
to be taken on faith, because there is no way of seeing, at
the present time, what happens to light that moves away
from the observer. It goes, in effect, into his future. On the
other hand, light which originated in the past (in Einstein’s
scheme of things) can arrive at the present time and be
observed by the observer. Einstein pointed his light in the
wrong direction.
5. Had he properly assigned different times to objects and
events seen at a distance from the origin, he would have, in
effect, defined his model identically to my definition of the
observer’s local universe, as opposed to his galactic
universe. It is a very small step to define all that one can see
at the moment as “the present” in the local sense. It is, in
fact, the world we live in.
6. The problems inherent in the inconsistency of making all
physical observations in the local universe and applying as
though they were determined by god-like observations in
the galactic universe would be eliminated by relating all of
the measured values to the local universe. The velocity of
light would be infinite and the velocity of the universe
through time would be the apparent speed of light, c. I think it
was possible to have deuced this at the time of the original
development of Special Relativity.
7. The ubiquitous correction factor F, involving the relativistic
shrinkage of distances and increases in time periods and
masses are mainly the result of making all of our physical
measurements in the local universe, limited to things we can
see at the moment, and then using these measurements
without proper correction in the galactic universe, which is
where all of the physical theories are rooted.
8. With the speed of light accepted as infinite, there are no
corrections needed for the measurement of mass. The pesky
square root correction factors are replaced by simpler, linear
corrections, which account for the fact that we read moving
clocks at a different time, by the standards of someone
moving with the clock, than when we think we read it.
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198
9. The clocks carried by moving observers do not run at a
different speed than that of any arbitrarily defined stationary
observer’s clock. Nor do the lengths, masses, or energy
levels of the moving objects or systems change with relative
velocity. Our perception of them is skewed by the necessity
of using radiation to make observations.
10. Clocks can appear to run either fast of slow when they are
moving relative to our point of observation. They will
appear to run slow when they are associated with objects
moving away from our position, and fast when moving
toward our position. They are, in the galactic sense, running
at precisely the same speed, and when we cross paths with
anyone else carrying a clock, it will read the same time as
ours.
11. All of Special Relativity deals with motion either directly
toward or away from the observer. It completely ignores any
velocity transverse to the direction of the object from the
observer. The corrections of observed position and velocity
by the addition of xv/c2 and v/c are correct only for the
radial components of velocity, and there is no correction
required for the pure translation component.
12. The energy of essentially all mass in the universe is constant
at E=mc2. It does not change with velocity. The mass does
not increase with velocity.
13. The reason “nothing can exceed the speed of light” is simply
that the velocities based on measurements in the local
universe are distorted when translated to the galactic
universe in such a way that the galactic version is always less
than the local version. Infinite velocity in the local
coordinate system is seen as c when translated to the galactic
system. This is true for light and for any moving object or
phenomenon. An actual velocity c in the local system is seen
in the galactic system as c/2.
14. Speeds greater than the apparent speed of light are possible but
not for significant masses of matter.
Light in the Local Universe
199
So, I believe Special Relativity needs to be updated, and many of the
concepts currently accepted as gospel based on Einstein’s version
should be recast in terms of the galactic values correctly translated
from local observations. Or, the local observations ought to be used
as they are made, and not converted at all.
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CHAPTER 9 ORBITAL MOTION
Orbital motion is not, strictly, within the scope of Special Relativity,
because it involves acceleration of the orbiting body toward the
object around which it is orbiting, and the acceleration involves a
“Force”.
Forces are not dealt with well in Special Relativity, and I won’t go
into any detail about them here, except to say that neglecting the
difference between a transverse velocity for a moving system, and
the same velocity in a radial direction has serious consequences.
ORBITAL MOTION AROUND THE OBSERVER
All linear motions may be resolved into radial and transverse
components relative to any point. The pure radial motion has a zero
transverse component, but most motions will have both a radial and
a transverse component. The exception is circular orbital motion,
which is always transverse; relative to the central point of the orbit,
or elliptical orbital motion, which has a small, variable radial
component relative to the translational velocity. Obviously, this is
the case that applies to measurements of the velocity of planets
orbiting a star, or stars orbiting the center of mass of a galaxy.
However, the observer is not, ordinarily, at the focal point of the
orbit. More often, he is either at, or adjacent to the orbital path of
the satellite, or far outside of the orbital path. These are situations
which need to be taken into account to correctly apply the
corrections of local observations to obtain galactic values and
particularly, correct galactic values based on the proper
interpretation of the local observations.
We can start by repeating the development of Table 1, derived for
pure radial motion of the moving reference system, and seeing what
differences arise when the motion is considered to be a combination
of radial and transverse motion.
Light in the Local Universe
201
Figure 50 depicts this situation on the x – y plane, presuming that
the T direction is perpendicular to the x and y Axes. In this figure,
the coordinates of point A are (x, y, T), and the velocity is v, in the
direction of the longer shaded arrow.
FIGURE 50
DEPICTION OF A VELOCITY WITH RADIAL AND TANGENTIAL
COMPONENTS
In dealing with velocities in both radial and tangential directions, it
is convenient to use radial coordinates, with the distance from the
origin to point A taken as r, the radius, and the vector denoting the
velocity of the point taken as V, which also has radial and tangential
components. The distance to the point is given by
2 2r x y , EQUATION 147
and the angle from the x Axis to the point is given as θ, so the
coordinates of point A can be given as ( , )r .
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The shaded arrow representing the velocity of the point relative to
the origin is given by V , and the components in the radial and
transverse directions by RVr
and TVr
. The angle of the velocity vector
with respect to the radius vector from the origin to point A is θA.
So, the radial vector can be equated with the two components
RV V V r r r
. EQUATION 148
Now, these references to the velocity of the point A are all presumed
to lie in the galactic plane representing the present moment of
galactic time. As we have emphasized before, it is not possible to
make measurements of events or objects in the present galactic time,
so we must have a way of converting from local measurements to
their equivalent in the galactic system.
The local time for an observer at the center of the circular orbit is
depicted by the cone in Figure 51. The circular orbit lays in a plane
in the galactic past relative to the observer, at a distance in the T
direction equal to the radius of the orbit r divided by the speed of
expansion of the universe, c. Both the observer and the plane of the
orbit are moving at the same velocity in the T direction, so the path
of the orbit relative to the observer appears to be at a fixed distance,
as shown. The position of the object along the path changes with
the passage of time, but the path itself is stationary with respect to
the observer’s coordinate system.
There is no radial component of the velocity of the orbiting object,
0nly transverse motion.
Light in the Local Universe
203
FIGURE 51
DEPICTION OF AN OBJECT ORBITING THE OBSERVER
It has been demonstrated that the radial motion is subject to
correction for the time at which objects are seen, whereas the
transverse velocity does not call for any correction. So, in calculating
the galactic velocity of an object in orbit around the observer, we
may treat the local velocity as though it is only the radial velocity
component, which is zero.
The galactic velocity of the object is corrected according to
1
1 LL
v
vv
c
, EQUATION 149
which indicates that the galactic velocity of an object orbiting the
observer is equal to the local, or observed, velocity. This is a very
significant point, which will be illustrated in connection with the
observations being made currently in particle physics laboratories.
For generalized motions, which have both radial and transverse
components, Equation 149 is very nearly correct for transverse
velocities relatively small compared to the radial velocity. As the ratio
or transverse velocity to radial velocity becomes large, the correction
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becomes less and less significant, until it disappears altogether for
pure translation.
FIGURE 52
ORBITAL MOTION IN THE LOCAL UNIVERSE
However, for circular orbits, or very nearly circular orbits around the
observer, it is of critical importance to note that there is no
relativistic correction for time or velocity whatever when the
observations are made from the point about which the object is
orbiting. There is no correction, according to Equation 149, because
there is no change in the radius of the orbital radius with time. And
of course, there is no relativistic shrinkage factor F.
The path of the orbiting object is the line of intersection of the
horizontal plane of the orbit at any moment and the observer’s cone
representing his local universe. This plane and the observer move
together in the T direction at identical speeds, so the orbit can be
thought of as being stationary with respect to the observer while the
Light in the Local Universe
205
orbiting object moves around the observer in a circular path as they
both move in the T direction at the velocity c.
The orbit can also be thought of as the intersection of a vertical
cylinder, representing the orbit of the object as it moves through
both its circular orbit and in the T direction with the rest of the
universe at the velocity c. Thus, in the three dimensional analog
universe, the object follows a helical path around the straight line
path of the observer, which is the T Axis. Once again, the
intersection of the moving cone with the static cylinder is a circle
which is stationary with respect to the moving observer at the apex
of the cone.
Circular orbits are simply a special case of the more general elliptical
orbit, which would be formed by the intersection of an ellipse
moving through space. Such an ellipse would have a shape given by
2 22
2 2
x yr
a b , EQUATION 150
which represents a circle of radius r when 1a b . There is little
difference in the interpretation of the measurements of the motion
of an orbiting object when the orbit is elliptical rather than circular.
While there are several situations in which the observer sees orbital
motion around his location, such as observations of the moon from
earth, or hypothetically, the observation of electrons orbiting the
nucleus of an atom, it is far more often the case that the observer
will be outside the orbit, or at some location inside the orbital path
that is not at a focus of the elliptical orbital path.
One case which is of particular interest is that which places the
observer somewhere on the path, or immediately adjacent to the
path, of the orbiting object.
Another case of particular interest is in the physics of satellites such
as those used in the Global Positioning System, which are tracked
very precisely, and the time experienced by the satellites is of critical
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importance. This s a special case of the more general situation in
which the observer is located anywhere in the universe.
Light in the Local Universe
207
ORBITAL MOTION ADJACENT TO THE OBSERVER
There are many situations in which orbital motion around a body
must be observed from a different location than the focus of the
orbit. In particular, one such circumstance is where the observer is,
in fact, located adjacent to the orbital path, rather than at the center.
In this situation, the circular orbit appears to be a circle in the galactic
plane, but the current position of the orbiting body cannot be placed
accurately on the circle because of the time differences between the
observer and the object being observed.
The local observer has no such problem, and might, if he were in
contact with an observer interested in establishing the motion within
the galactic plane, make the necessary corrections for him to use his
local observations. The question which must be answered is, “How
are the local observations of an orbiting object corrected in order to
make them useful in the galactic coordinate system?”
This special case is applicable to the detectors used to determine
passage of the circulating neutrons in the Large Hadron Collider at
the CERN installation in Geneva, Switzerland. The following
chapter is devoted entirely to this special case of orbital motion.
Here, the path of the orbit appears to approach and pass over or
near the observer at one point in the orbit, and then move to the
farthest possible point on the orbit before starting the return trip.
The path of the orbit appears to be an ellipse drawn on one side of
the cone representing the local universe at one moment in local time.
However a “top view’ (looking down on the cone from the T
direction) would show the path to be circular, just as was the case
when the observer was located in the center.
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[LCH1]
FIGURE 53
A CIRCULAR ORBIT VIEWED FROM THE ORBITAL PATH
This is simply a matter of the orbit of an actual object in four
dimensional space being independent of the observer’s location.
The local observer should have no difficulty in determining the
position of the object in orbit at any given local time because he can
measure the angle and distance relative to his reference system at any
local time, and make successive measurements to determine the
magnitude and direction of the velocity. He can, of course, only do
this for past positions of the object (from a galactic standpoint), as
he cannot see into the future.
The critical item here is that the velocity of the object, which appears
to be constant to the local observer, will not have constant transverse
and radial motions with respect to the observer. It was shown in the
previous section that the radial velocities of bodies are correctly
translated using the same equation as applied to motion toward the
body in the one dimensional model used in Special Relativity. That
is,
Light in the Local Universe
209
1
1 LL
v
vv
c
, EQUATION 151
but motion in the transverse direction requires no correction factor
at all. From the point of view of the local observer, as the orbiting
body approaches his position, the velocity is totally radial.
FIGURE 54
ORBITAL MOTION OBSERVED FROM THE PERIMETER
However, when it reaches the opposite side of the orbit and starts
back toward him, it is totally transverse. The velocity is constant in
magnitude, but varies in direction, and he must apply correction
factors which change continuously with time, and with the position
of the orbiting body.
The corrections are easily determined with reference to Figure 54. It
was pointed out previously that the velocity can only be determined
unambiguously for bodies moving toward the observer, which lie in
his local present. Bodies moving away from the observer are, by
definition moving into his local future, and he cannot observe their
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positions until they are in his local past. So, we need only be
concerned about the orbital motion as the object under observation
is approaching the observer from the most distant point in its orbit.
It is apparent that the position is at 0 degrees to the location of the
observer and that the velocity is perpendicular to this radial line, and
totally transverse. As the object moves around its orbital path, the
angle gradually increases until it approaches 180 degrees as it nears
the observer. The velocity always remains perpendicular to the
orbital radius, and at the observer’s position, is at 90 degrees, and is
completely in the radial direction with respect to the observer. As
the angle changes from 0 to 180 degrees, the radial component of
the velocity varies with the cosine of the angle of the orbiting object,
and the transverse component varies with the sine of the angle, such
that
sinLT Lv v , EQUATION 152
and
cosLR Lv v . EQUATION 153
So, at the 0 point in the orbital path, the object appears to be moving
at velocity vL in the tangential direction, and reports that this velocity
requires no correction whatever. For the 180 degree point in the
orbital path (where the orbiting object is adjacent to the observer’s
position), the velocity is totally radial, and requires the application of
the shrinkage factor given in equation 151.
For points in between, the correct factor is
1cos
1 LL
v
vv
c
. EQUATION 154
Light in the Local Universe
211
So, we need to determine this value over half a circuit, or an angle of
θ = 0 to θ = π.
0
1 1cos
1 1L LL
vd
v vv
c c
. EQUATION 155
So, it appears that an observer watching an object more around a
circular orbit toward his position along the orbital path will use the
exactly the same correction factor to get the equivalent galactic
velocity as if it were a linear velocity he were observing.
Numerous other situations can be described, some of which
represent recurring situations. An example is one in which the
observer is moving in orbit around a fixed object, rather than being
stationary at a fixed point on the orbit. This would apply to the
situation of an astronomer studying the motion of the sun or the
other planets, were they sufficiently far away or moving sufficiently
fast to require relativistic corrections.
Or, the observer can be at any other position relative to the orbit,
including inside of the orbital path or outside it. They are all equally
amenable to the same kind of analysis applied here.
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A FINAL OBSERVATION
In converting the velocities observed from local measurements to
the equivalent values in the galactic plane, the relativistic corrections
derived for radial motion of an object (motion directly toward or
away from the observer) do not apply because there is no radial
velocity when the observer is in the center of the orbital path.
Instead, the galactic velocity is equal to the local velocity.
Similarly, if the observer is located anywhere along the orbital path,
the galactic velocity is, again, equal to the orbital velocity, with no
correction factor.
I believe this situation to be true no matter where the observer is
located relative to the orbital of the object, whether it is in his local
past, and can be observed, or is in his local future, which can only
be deduced.
The equation
1
1L
L
v vv
c
, EQUATION 156
Still applies but only when the radial component of the velocity of
the orbiting object is used, rather than the total velocity. Likewise,
the time assignable to a point along the orbit around a fixed observer
is inversely proportional to the velocity when equal distances of
traverse are used, and again, when the velocity is radial, or completely
transverse, the proper value for the local velocity is the radial
velocity, which is zero, so
1 LL L
vt t t
c
, EQUATION 157
so
Light in the Local Universe
213
11
1
LL L L L L
L
vx x v t v t vt
v c
c
. EQUATION 158
This means that an object in motion appears to move at a slower
speed in the galactic universe than indicated by observations in the
local universe, when the velocity is measured over the same time
period in both systems. This kind of comparison can only be made
legitimately when the object exists in the proper quadrant of the
space-time graph. An object which is timed from the moment it
crosses the location of the observer and begins moving away from
him, has moved into the future of the local observer, and the future
locations can only be determined at some future local time.
If the object is stationary, with vL = 0, the location of the object is
the same in both the observed local universe and in the constructed
galactic universe. However, if vL is other than zero, in the radial
direction, there will be a difference in the location when the time
values are numerically equal, or in the time if the distances from the
observer are numerically equal. This is not in indication that time is
compressed when an object is moving nor that velocities are
decreased to avoid approaching the apparent speed of light.
Galactic time is still exactly the same throughout the plane of the
galactic universe. Local time is still exactly the same throughout the
cone of the local universe. There is no shrinkage of time, or distance,
or length of an object, and no change in the mass of the object when
the local velocity is increased, without limit on the velocity, and the
galactic velocity is increased toward the apparent limiting velocity, c.
However, for orbital velocity, there seems to be an exception.
Galactic velocity can also be increased without limit, and there is no
apparent shrinkage of time periods, or change in the length or mass
of orbiting objects as seen by the fixed local observer. There is no
shrinkage of objects with motion approaching the speed of light, nor
is there a foreshortening of the distances.
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It is important to remember that the observations are all made in the
local universe, and are not subject to any corrections at all, but that
the galactic clock associated with a moving object does not read the
same time as the observer’s clock. Observations translated to the
galactic universe are not corrected, but rather translated from one
system of defining time to another. Both systems have
straightforward relationships between distance, time, velocity and
energy, which derive from observations made in the local universe,
albeit mostly at velocities so low that there is little difference between
the two.
When the motion of an object being observed has a component of
velocity at right angles to the radial line connecting the observer and
the object, this translator velocity does not count. That is, only the
radial component of velocity requires any translation from the local
observed velocity to a galactic velocity. The translational component
has the same value in both systems.
In the case of orbital motion, there is no radial velocity at all, so there
are no relativistic corrections needed to get the galactic orbital
velocity.
It appears to me that Newton’s laws of motion hold quite precisely
when the measurements of position, time and velocity are made with
reference to the local system I have described. And when the
translation is done to the galactic system, they apply there also, but
are more complex.
It should be possible to show that just as the velocity of an object
seen in the local system must be translated when used in the galactic
system, so the momentum associated with an object, and the energy
content must be translated from one system to the other.
In the local universe, the momentum of an object is seen as the mass
of the object times the observed velocity, with no correction of the
mass due to the velocity. So,
L Lp mv , EQUATION 159
Light in the Local Universe
215
Where, once again, we have assumed that the local velocity was
measured along a radial path. Then there is a transverse component,
there will be a transverse momentum, which will be the same in the
two systems, whereas the apparent mass, in the galactic system,
increases without limit as the radial component of the galactic
velocity approaches c, the apparent speed of light. Again, the mass
of the object is an intrinsic property of it, not different in the two
observational systems. It is the same in both systems when the object
under observation has no velocity, and is called the rest mass in the
galactic system.
In the galactic universe, the mass is presumed to increase with
velocity of the object relative to the observer,
2
22
2
1
1
m vmv v
cv
c
, EQUATION 160
where the mass of the object is presumed to increase by division with
the relativistic shrinking factor, and the velocity decreases by the
same factor. When the velocity is orbital, there is no relativistic
shrinking factor to be applied. And the galactic value for momentum
and mass are both equal to the observed local values.
Les Hardison
216
CHAPTER 10 THE LARGE HADRON
COLLIDER
The questions relating to the orbital velocity of objects was given
considerable space in the previous chapters, although the situations
in which it is of significance are relatively rare. Most observations of
astronomical objects with orbits which may be observed from earth
are relatively slow-moving compared to the apparent speed of light, c,
and the corrections are minor.
The most troublesome situation, in my estimation, relates to the
velocity of the particles accelerated to very high velocities in particle
accelerators. While the velocity of major masses is probably limited
to a fraction of the apparent speed of light, there is no theoretical limit
on the velocity a particle can reach when subjected to acceleration
by very strong electric or electromagnetic fields. In these
accelerators, the energy from very large masses of matter can be
applied to a limited number of sub-atomic particles, and there does
not seem to be any limit as to how fast these can be made to move
relative to the fields which accelerate them.
The largest and most well-known of the particle accelerators in
recent years has been the Large Hadron Collider (LHC) at CERN in
Geneva, Switzerland. At CERN thousands of physicists are running
many experiments with various objectives, but much of the core
research is involved in trying to duplicate the conditions they think
may have existed near the moment of the big bang at the beginning
of the universe we live in.
They are hoping to create the ultimate transport particle, the Higgs
Boson, which is credited with being the thing which makes protons,
neutrons, electrons and everything else have the property we call
mass.
Light in the Local Universe
217
The Higgs Boson is a kinsman of the photon, which is supposed to
transfer light from place to place, the gluon, which is supposed to
transfer the strong force between constituents of the atomic nucleus,
and the graviton, which is supposed to carry the gravitational force
between masses which attract each other.
Without understanding all of this in much greater depth than I have
just displayed, I think they are on the wrong track. I just can’t bring
myself to believe in photons, because I think light is transmitted
instantaneously by direct contact of atoms across distances in both
space and time, without actually traversing the space or time. No
photons are needed.
The photon is the basis of the whole of quantum mechanics, so I am
suspicious of the whole system involving supposed transfer particles,
of which the photon is the prototype. No one has ever gotten ahold
of a photon, nor will they ever. The same is true of gluons and
gravitons. I used the word “supposed” purposely, because I question
whether such particles are real, in the sense of having a physical
embodiment which can be sensed in some way. The alternative is
that they are simply concepts which have been created to explain the
behavior of “real” particles, which can be sensed and measured.
So, good luck with your Higgs Boson, all you CERN guys. I would
be happy to be proved wrong but it will take more than an
unexplained occurrence during one of the proton head-on collisions
in the LHC to convince me.
But, while I am sometimes skeptical of their interpretations, I have
great respect for the experimental physicists’ ability to measure
things and accurately report what they measured. By and large, they
are a much more diligent and carful a breed than I am.
But, the LHC was designed to accelerate protons and other heavy
hadrons up to very near the speed of light (but that, of course they
can’t get to the speed of light because that is impossible. Einstein
said so.) In the process, they are increasing the mass of the protons
enormously, from almost nothing to about the mass of a butterfly,
Les Hardison
218
according to the physicist who took my Scientific American Tour
Group through the CERN establishment late in October, 2010.
So, I want to take a close look at what measurements they are actually
making, and how they use the velocity and mass of the protons in
their calculations.
Light in the Local Universe
219
GENERAL DESCRIPTION OF THE LHC AT CERN
The Internet abounds with descriptions of the Large Hadron
Collider, which is a physics super-project that rivals the US space
program in cost and time span. Its aims are no less spectacular.
Where space exploration strives to go start the journey toward the
myriad stars which we can see in the night sky, by taking the first
baby steps toward our moon and out sun’s other planets, the LHC
project is attempting to explore the nucleus of the atom, and by
doing so, trace our history back in time, perhaps to the time of the
Big Bang, the presumed beginning of our universe.
I will spare you all of the descriptions of the LHC which you can
find elsewhere, and try to outline only the aspects of it which are of
particular interest to me. These have to do, not with the technology
of accelerating the protons or other heavy ions (hadrons) like the
lead ion, or controlling the path using superconducting magnets and
high frequency electrostatic fields, although these border on the
miraculous. Rather, I am interested in how they know where the
protons are at any given time, how fast they are moving, and what
their energy level is.
The main reason I am interested in these things is that, from my
perspective, the velocity of light is not limited to c, the apparent velocity
of light which has been measured time and again, but rather moves
instantaneously, short circuiting both space and time as energy is
transmitted from one atom to another, which may be far removed
in both space and time. At least, this is what one would presume one
sees when making observations in the real world, where radiant
energy transmission can only be detected by an observer when it
exists within his local universe, defined by his local time.
Although the CERN physicists do not locate the protons they are
studying by sight (according to my perspective, there is no way to
see a proton or electron), they are still limited to the use of electrical
sensing devices which are subject to the same sort of velocity
constraints when the measurements of time and distance are referred
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220
to the galactic universe, where time is the same at all points within
the universe. Nothing can move faster than the speed of light in this
galactic plane, simply because it would have to be moving faster than
an infinitely great speed in the local universe.
So, how do the CERN physicists know how fast the protons are
going? They accelerate the protons by means of electrostatic fields
between charged orifice plates. The bunches of protons pass
through the plates, which must be at near zero charge at the time,
but must be negatively charged as the protons are approaching, so
the electric field accelerates them toward the plate, and positively
charged after the bunch passes through, so they are further
accelerated by repulsion from the plate.
The particles are moving fast and are speeded up by a negligible
amount according to the physicists, as they are already going at
almost the apparent speed of light, so the mass must increase to account
for the energy gained. Or. Alternatively, from my viewpoint, they are
going at many times the speed of light and are speeded up by a great
deal, with no change in mass at all. We can’t both be right, and there
are a lot more of them than there are of me.
Now, the Large Hadron Collider is designed with the objective of
reaching a proton velocity of some 0.99999999 times the apparent
speed of light, and there are numerous ways of corroborating their
measurements that this actually occurs. So, I am on pretty thin ice
when I say that they are mistaken about how fast their protons are
moving, by a factor of some 100 or so.
How could anyone be that wrong about anything?
I don’t know enough about particle physics to give a good, coherent
description of the way the physicists at CERN accelerate the protons
and other large hadrons to high velocities, so here is theirs:
The design of the LHC is for each ring to contain
2808 particle bunches in 3564 slots that are
separated by 25 nanoseconds. It is understood
Light in the Local Universe
221
that the wire scanner front end returns two
types of 1-dimensional profile data: transverse
profile information for each bunch and for each
(possibly empty) slot, and integrated profile
data over all bunches. These modes are
mutually exclusive. The wire scanner
application will be able to show these basic
data, both textually and graphically. These data
can be stored in a way that can be retrieved
later by the wire scanner application, by an
individual or by another program.
The aim of the collider is to direct streams
moving in opposite directions at 99.999999% of
the speed of light into each other and so
recreate conditions a fraction of a second after
the big bang. The LHC experiments try and
work out what happened.
Les Hardison
222
THE RADIOFREQUENCY ACCELERATION SYSTEM
Here is a description of the design of the electrostatic acceleration
system from the Journal of Applied Physics.
The RF system is located at point 4. Two independent sets of cavities
operating at 400MHz (twice the frequency of the SPS injector) allow
independent control of the two beams. The superconducting cavities
are made from copper on which a thin film of a few microns of
niobium is sputtered on to the internal surface. In order to allow for
the lateral space, the beam separation must be increased from 194
mm in the arcs to 420 mm. In order to combat intrabeam scattering
(see below), each RF system must provide 16 MV during coast while
at injection 8MV is needed. For each beam there are 8 single cell
cavities, each providing 2MV, with a conservative gradient of 5.5
MVm−1. The cavities are grouped into two modules per beam, each
containing four cells (figure 55 in this presentation).
Each cavity is driven by an independent RF system, with
independent klystron, circulator and load. Although the RF
hardware required is much smaller than LEP due to the very small
synchrotron radiation power loss, the real challenges are in
controlling beam loading and RF noise7.
7 New Journal of Physics 9 (2007) 335 (http://www.njp.org/)
Light in the Local Universe
223
FIGURE 55
ACCELERATION SECTION OF THE LHC
The segment immediately ahead of the bunch of protons passing
through the acceleration tube is charged negatively, exerting an
attractive force on the protons, and the segment behind the bunch
is charged positively, repelling them. Both fields tend to accelerate
the bunch of protons in the direction they are moving through the
tube.
As the bunch passes, the charges must change from positive to
negative and negative to positive, and the frequency of the
alternations would, it seems, be timed so that the frequency increases
as the velocity of the electrons increases. This is not so. A constant
frequency of approximately 400 MHz is applied to the single
acceleration station.
Ideally, the charge on the acceleration plate would be negative as the
cloud of protons (called a bunch by the LHC personnel) approached
the orifice plate, and would drop to zero just before they reached it,
to avoid the protons becoming strongly attracted to the cylindrical
inner surface of the orifice. After the protons passed through, the
charge would become positive, repelling the proton and accelerating
them on their way.
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I had presumed that there were accelerating orifices located all
around the perimeter of the 27 Km circle of the LHC, but
apparently, this is not the case. There is only one, although it has
four stages in it, each furnishing one quarter of the acceleration.
Here is CERN’s description of the acceleration chambers, or
cavities.
Cavities: The main role of the LHC cavities is to
keep the 2808 proton bunches tightly bunched to
ensure high luminosity at the collision points and
hence, maximize the number of collisions. They
also deliver radiofrequency (RF) power to the
beam during acceleration to the top energy.
Superconducting cavities with small energy
losses and large stored energy are the best
solution. The LHC will use eight cavities per
beam, each delivering 2 MV (an accelerating field
of 5 MV/m) at 400 MHz The cavities will operate
at 4.5 K (-268.7ºC) (the LHC magnets will use
superfluid helium at 1.9 K or -271.3ºC). For the
LHC they will be grouped in fours in cryomodules,
with two cryomodules per beam, and installed in
a long straight section of the machine where the
transverse interbeam distance will be increased
from the normal 195 mm to 420 mm.8
8 CERN Website http://public.web.cern.ch/public/en/LHC/Facts-
en.html 12/5/2011.
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225
The interesting point here is that the cavities operate at 400 MHz,
which means that they deliver a push to each passing bunch of
protons once every 2.5 nanoseconds. Yet, the rate of circulation of
the 2808 bunches of protons, moving at essentially the apparent speed
of light, (c~300,000,000 m/second) has a bunch passing through the
acceleration cavity only every 24 nanoseconds.
TABLE 4
CALCULATION OF FREQUENCY OF PASSAGE OF BUNCHES
Les Hardison
226
THE EXPERIMENTS AT CERN
One of the subjects which caused me great concern was the fact that
the massive Large Hadron Collider (LHC) at the CERN facility in
Geneva, Switzerland was built around the concepts developed in
Special and General Relativity, and seems to work well. I have been
critical of the foundation on which Special Relativity was built, and
suggested that physicists, as a general rule, fail to distinguish between
the local universe, in which their observations are made, and the
galactic universe where time is uniform throughout all of our normal
three dimensional space.
This inconsistency is insignificant when dealing with relatively slow
moving objects, like supersonic aircraft, but makes measurable
differences for fast-moving objects, and becomes really important
when the velocity approaches the apparent speed of light. At CERN, the
objectives involve accelerating protons and other heavy hadrons to
velocities which are said to come very close to the apparent speed of
light. Velocities as high as 0.99999999c have been reported.
I do not want to comment in detail on any of the particular
experiments, or the objectives being sought, but rather on the
general question of whether the data being collected is being
interpreted correctly. I don’t think it is.
I realize that the odds are against one mechanical engineer with a
BS degree versus 20,000 PhD physicists, almost all of whom are
smarter than I am, particularly when playing on their own home
field. But, I bought a lottery ticket once, with just about the same
odds of winning.
So, let’s start with the consideration of the speed to which the
protons are accelerated and the measurement of the velocities when
they are moving at nearly the velocity c, according to the observers.
An interesting place to start is by noting that the acceleration cavities
operate at 400,000,000 cycles per second, yet only 41,000,000
bunches of protons are passing through them per second, .according
Light in the Local Universe
227
to the CERN reports. How does the frequency of the polarity
reversals in the acceleration cavities relate to the speed of the protons
being accelerated?
This situation is akin to that of a father standing next to the old
fashioned playground merry-go-round, giving it an occasional push
as his children ride around. If the merry-go-round has six segments,
he can give one push for every revolution, skipping five of the six
segments as they go by, or he can push each and every one , but not
so hard.
FIGURE 56
MAN PUSHING A MERRY GO ROUND
If he chooses to push each segment, the frequency of his effort is six
times the RPM of the merry-go-round. If he chooses to push only
one, it is the frequency is equal to the RPM. Or, he can keep it
spinning by only giving it one push every other rotation, in which
case his frequency is half the RPM.
At CERN, we have an acceleration section which administers (or is
at least capable of administering) ten times as many pushes per
second as there are bunches of protons passing through the cavity,
presuming that they are traveling at very nearly the apparent speed of
light, c. Of course, a push administered when there is no bunch of
protons approaching is simply wasted.
Les Hardison
228
However, the possibility exists that, once the roughly circular 27 Km
tunnel is filled with the 3705 bunches of protons, they might actually
be going around twice as fast as they are supposed to be able to go.
That is, if they were moving at almost twice the apparent speed of light,
they would be accelerated just as frequently as if they were going at
almost the apparent speed of light. In fact, the acceleration cavities could
accommodate speeds of up to 10 times the apparent speed of light,
without putting out much extra effort.
Now, the problem of relating what seems to be going on at CERN
with what would be the case if either A) the observations were
actually being made in the local universe (as I have been suggesting
is always the case) but interpreted as though they were made in the
galactic universe, or B) They were made in the local universe and
correctly placed in the context of the galactic universe.
Light in the Local Universe
229
HOW ARE MASS AND VELOCITY MEASURED AT
CERN?
This question bothered me, as I hadn’t a clue as to how they could
measure velocities like this, when there is no way to sense the
presence of a single proton other than by its electric charge, and that
doesn’t have a very long distance range. So it would take some
phenomenal timing to get a velocity by measuring the change in
distance with time if something were moving at or in excess of the
apparent speed of light, over a range of a few centimeters in the local
universe. Likewise, the measurement of the mass of the protons
moving at very high speeds seems to be a difficult task.
Apparently, what the CERN Physicists know with much better
accuracy is the energy which has been absorbed by each proton as it
passes through the electric fields of the accelerator.
Here is a summary of the explanation given on the Internet.9
The relativistic energy-velocity relationship is:
220
2
21
m cE mc
v
c
, EQUATION 161
where m0 is the rest mass of the proton, and m is the mass under the
high velocity conditions in the LHC. From these equations, and the
energy imparted to the protons (and apparently measurable when the
protons impact ordinary matter), we can calculate the mass and
9 http://physics.stackexchange.com/questions/716/relativistic-speed-
energy-relation-is-this-correct
Les Hardison
230
velocity of the protons, although neither is measurable directly in the
LHC.
Here is the calculation as summarized in the CERN Outreach pages
on the Internet.10
Because the energy of the fast moving proton is taken to be mc2 as
per Special Relativity, the mass is directly calculable from the energy
10 http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/lhc-
machine-outreach-faq.htm
How much do the protons weigh in the LHC at 7Tev?
The energy of a proton is 7 TeV. Via E = mc2 the mass is simply 7
TeV/c2 - and these are the units usually used.
7 TeV/c2 divided by the rest mass .938272029 GeV/c2 gives us
7460.52 times the rest mass
Working in SI units we can do the same thing more explicitly:
At 7 TeV:
Energy = 7 *1012 *1.60206 *10-19 Joules
c= 2.99793 108 m/s
m = Energy/c2 = 1.2477-23 Kg
At rest (rest mass proton = mp):
Energy = mp c2 = 0.938272029 *109*1.60206*10-19 Joules (or just say
mp = 0.938272029 GeV/c2 )
mp = Energy/c2 = 1.672009-27 Kg
m/mp = 7460.52 as before
Light in the Local Universe
231
each proton is observed to have. So, if you accept the premises of
Special Relativity, the mass of the proton increases enormously as it
is accelerated.
TABLE 5
CALCULATION OF APPARENT MASS AND GALACTIC
VELOCITY
Symbol Value Units Formula Result
Ep Energy of a proton TeV 7.00E+00
Ep Energy of a proton Joules 1.12E-06
c Velocity of light m/s 3.00E+08
mP mass kg E/c2 1.25E-23
mp0 Rest mass of a
proton kg 1.67E-27
mP/mP0 Ratio of m/m0 - 7.46E+03
Gamma - 1/Sqrt(1-
v2/c2) 7.46E+03
F2 - 1-v2/c2 1.80E-08
- v2/c2 0.99999998
vp Calculated proton
velocity - v/c 0.99999999
The velocity of the proton may be calculated from the relationship
between mass of the proton at rest and the mass at high velocity.
For any given increase in velocity, there is a corresponding increase
in mass. I have repeated this calculation in slightly different terms
for clarity.
Les Hardison
232
So, there appears to be no question that the mass and velocity
relationships are based on an explicit belief in the equations derived
by Einstein in Special Relativity, which have not been altered nor
reinterpreted in the intervening 100 plus years since their
development. The mass-energy relation is based explicitly on the
presumption that no matter can move through space faster than the
apparent speed of light. On this basis the mass is presumed to increase
to account for most of the energy added to the protons, and their
speed is then calculated from the calculated mass.
I would, of course, put an entirely different interpretation on the
measurements, based on the presumption that the value c is the rate
of expansion of the universe into the fourth spatial dimension, and
that light, in the local universe which we observe, moves infinitely
fast, and does not, therefore, establish a universal speed limit for
material objects, or anything else.
In the local universe, the mass does not increase with velocity at all.
The velocity of protons is not limited to the apparent speed of light, c,
but may go many times as fast. The only things that do not seem to
be different when measured in the local universe are the rest mas of
the protons, and the energy. This is simply because one of the basic
formulae of Special Relativity is not true.
2
0
2
21
m cE
v
c
. EQUATION 162
I have pointed out previously that this equation, involving the
relativistic F factor, is the only one not based on the Lorentz
transformation, relating to the appearance of time, distance and
velocity when seen by a second moving observer. Rather, equation
162 is based on the presumption that v cannot, under any
circumstances exceed c, and the whole point of my approach is the
presumption that it can.
Light in the Local Universe
233
When v<<c, the relationship given in galactic terms by Einstein is
very nearly the same as is the exact relationship given in terms of the
local velocity.
2 22 0 0
02
2
21
Lm v m cE m c
v
c
. EQUATION 163
However, at velocities approaching the apparent speed of light, it is a
poor approximation to what I believe is the correct, and exact,
formulation shown in Equation 164.
22
2
smvE mc , EQUATION 164
where sv is the local velocity in excess of the apparent speed of light, c.
At galactic velocities equal to or greater than the apparent speed of light,
the right hand term in Equation 163 becomes meaningless. Without
calculated increase in mass for the protons as they accelerate there is
no basis for the calculation of the velocity which corresponds to the
energy 7 TeV2 energy level.
So, how should the velocity be calculated? The energy content of the
body is not absolute, but is an energy content relative to whatever is
taken as the “stationary” coordinate system. And the mass is, of
course, independent of the choice of reference.
So, the proper interpretation of the 7 TeV energy level imparted to
the protons circulating in the LHC is that all of this is involved with
the increase in kinetic energy, the m0vL2/2 part of Equation 163, and
none of it goes to increasing the mass.
Thus, the ratio of the energies, 7460.52, is attributable solely to the
increase in local velocity, vL.
Les Hardison
234
22 0
20
2 2
0 0
2 12
7460.52
L
L
m vm c
vE
E m c c
. EQUATION 165
Because the proton does not increase in mass,
122.152v c . EQUATION 166
Obviously, the velocity greater than c cannot represent a velocity in
the galactic universe, where an infinite local velocity would appear to
just equal to c. Therefore, it is appropriate to assume that the vL/c
value is a local velocity. .
So, I would say that the mass of the proton remains unchanged as it
accelerates, and the velocity is increased by the addition of energy
without upper limit. Thus the 7 TeV energy level corresponds to the
kinetic, or velocity energy of the protons entirely. The value of the
local velocity increases from 0 at rest to 122.152c when the energy
input to accelerate the proton is 7 TeV.
The calculation of the value of vL is given in Table 6, where all of the
energy imparted to the protons is presumed to contribute to their
velocity.
TABLE 6
RECALCULATION BASED ON LOCAL INTERPRETATION OF
DATA
Symbol Value Units Formula Result
Light in the Local Universe
235
Ep Energy of a
proton Tev 0.00E+00
Ep Energy of a
proton Joules 1.12E-06
c
Apparent
velocity of
light
m/s 2.00+E08
mp0 Rest mass of
proton kg 1.67E-27
mP/mP0 Ratio of
mp/m0p - 1.00E+00
Ekp Kinetic
energy Joules m0PvL
2/2=mPv2 7.46E+03
vL2/c2
Ratio of
vL2/c2
- mp/mp0 1.58E+04
vL/c Ratio of vL/c - sqrt(mp/mp0) 1.22E+02
v/c Ratio of v/c - (vL/c)/(1+vL2/c2) 0.99889
It is apparent that, to achieve the 7 TeV energy level, it is only
necessary for the local velocity to reach a value of approximately 122
times the apparent speed of light. This is, of course, quite phenomenal,
in that ordinary matter cannot be accelerated beyond a fraction of
the apparent speed of light, and likely cannot reach the apparent speed of
light by local measurement, because there is nothing massive in the
universe which is moving at this speed from which it can gather
energy.
It is also apparent that, as only a small amount of the energy used in
accelerating the protons to 122 times the apparent speed of light appears
Les Hardison
236
as an increase in the velocity of the protons by galactic standards, the
only way to account for it is by the appearance that the protons have
become more massive, as was the initial presumption of Special
Relativity. So, although the local observer sees no apparent change
in the mass, it is necessary to indicate a large increase in mass when
converting the data to the galactic plane.
However, it seems that the observations, having been made in the
local universe and with regard to the local timekeeping system, it
would be simpler to avoid the problem by recognizing that, in the
local universe, light really does move from place to place
instantaneously, and does not set a speed limit on anything. Mass is
not a flexible property of matter which varies depending on the
reference system chosen for it, but remains constant as the velocity
changes, and is independent of the motion of the reference system.
With regard to the possibility of sub-atomic particles accelerating to
velocities in excess of the apparent speed of light, it seems possible to
transfer the energy from huge numbers of atoms to the relatively few
circulating protons within the LHC by using the large amounts of
energy to create electrostatic and electromagnetic fields which
transfer energy to a relatively small number of particles, and result in
super c velocities.
The local velocity of 122.152c translates to a true galactic velocity of
0.99188c, rather than the 0.99999999 being used by the CERN
operators.
This is only very slightly slower than their value by the ratio
0.999999991.008
0.99189 , EQUATION 167
or 0.8% less than the value reported. However, there is still a
remarkable difference between the two values, as the CERN value
would require a local velocity of about 10,000,000c, whereas the
calculated value represents a local velocity of 122.152 c. How did we
get such glaringly different results?
Light in the Local Universe
237
Les Hardison
238
THE CERN RESULTS IN LOCAL TERMS
The disparities between the results I derived and those representing
the results reported by the CERN scientists are not difficult to
explain, if one accepts the three premises of this book. That is, the
value c represents the rate of expansion of the universe into a four
dimensional space-time, that the true value of the speed of light in a
vacuum is infinite, and that we are limited to making observations of
any kind to the local universe, where we can actually see objects and
events at the present instant in time.
Let us suppose for the moment that we can actually see the protons
moving around the circular track of the LHC, and that we are able
to measure their velocity, vL, in our local universe.
We would, using Newtonian physics, believe that the total energy of
the proton would be represented by
2
0
2
TT
m vE , EQUATION 168
where ET includes the velocity component in the fourth dimensional
direction, and also the velocity of the matter that is observable in the
three ordinary dimensions in excess of c. The rest mass of matter
used in Special Relativity, m0 is the mass of the proton and it does
not change as the velocity relative to any arbitrary coordinate
changes. The physicists would call it the “rest mass”, but in the local
universe, this is invariant. It is simply the mass, m, and nothing can
change it.
The local velocity has two vector components,
L Lsv v c uur uur r
, EQUATION 169
where LSv is the excess of velocity over c, the velocity of expansion
of the universe. The vL component is the only one we can observe
directly, and represents the velocity of the proton coming toward us
Light in the Local Universe
239
at our observation station along the perimeter of the LHC tube. It is
only the vL, or local spatial component we are going to be able to
measure, so it is only the local kinetic energy we will be dealing with,
2 22
22 2
L LL
mv vmcE
c
. EQUATION 170
Similarly, the kinetic energy of the proton in the LHC, when
translated to galactic coordinates, should be
2
22 2
22 2
1
K
v
cmv mcE
v
c
. EQUATION 171
The condition that the kinetic energy of a moving object is a
property of the object, and should be the same in both systems, if
calculated relative to the same observation point is
2
220
1
1
Lvm
m v v
c
. EQUATION 172
22
22
0
11
1
L Lvm v
m v cv
c
. Equation 173
This equation satisfies most of our prejudices with regard to the
appearance of the mass increase with increased velocity when viewed
as though the measurements had all been made in the galactic
reference system. When the velocity in the galactic system is zero,
the mass is m0, the rest mass. When it is accelerated, it moves faster,
but the velocity cannot appear to exceed c, so the mass increases to
account for the energy by the object in excess of the inherent rest
Les Hardison
240
energy, mc2/2, which is due to the expansion of the universe at
velocity c.
When the local velocity, vL, reaches c, the galactic velocity is c/2, etc.
and at a local velocity of 2c, the galactic velocity would be 2/3c. For
the galactic velocity to reach c, the local velocity would have to be
infinite.
Because the relationship between mass and velocity in the galactic
system does not agree with the values given in Equation 172, it seems
that the translation between the two systems is not handled properly
in Special Relativity (or, of course, I could be wrong, and the
remainder of the world right!)
But, if we consider for a moment what sort of correction would have
to be applied to the Special Relativity formulary if all of the
measurements were made in the local universe, which is the only
place they can be measured, and then treated as though they were
made in the galactic universe, the velocities would be in error by the
factor F, which is
2
2
1
1
Fv
c
. EQUATION 174
From this,
2 1
1 1
LvF
v v v
c c
, EQUATION 175
or
LvF
v . EQUATION 176
Light in the Local Universe
241
How does the F factor enter into Einstein’s equation for the increase
in mass with velocity?
Apparently, in all of the other instances in which the value of c, the
apparent speed of light, plays a role, it is really the actual speed of the
universe in the fourth dimensional direction. But the relationship
holds well even though the physical meaning of the value was not
what wa supposed. However, in the mass-energy relationship, c
actually signifies the velocity of light through a vacuum. The whole
purpose of this equation is to keep anything, including light, of
course, from moving faster than the actual speed of light. So, in this
case, the proper interpretation of the speed of light is that it is not
the value 300,000 /c kM Sec , but is, rather, infinite.
So, it is a different F that is used in equation 176; one where c is
infinitely large, and
20
2
11
1
m
m v
c
, EQUATION 177
for the value of c taken as infinite.
The velocity shrinkage, and that of the distance and time shrinkages
are, like the mass increase with velocity, artifacts of the mistaken use
of the local system for making measurements, and of the galactic
system for applying them.
But, of course, we really knew that to begin with. This is basically
what I derived in Chapter 7, when I pointed out that the result of
using measurements in the local system as though they had been
taken in the galactic system should be the appearance of the factor
F, where
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242
2 2
2 2
11 1
11 1
A A L
L
vt t t cF
vt t t v vcc c
.
EQUATION 178
So, my conclusion is that it would be better to stop trying to fit all
of the observed data (which was necessarily observed from the
viewpoint of a local observer) into the galactic reference system,
where it produces anomalous results when high velocities are
involved.
The basic energy equation of Special Relativity,
2
2
21
mcE
v
c
, EQUATION 179
should be replaced with
22
21
2
LvE mc
c
. EQUATION 180
The mass stays constant with acceleration, Newtonian physics seems
to hold for masses and accelerations. My lunch pail continues to have
two pounds of mass regardless of the motion of your reference
system, and it doesn’t get smaller if I move very fast relative to your
position.
And, the protons circulating around the track at Geneva Switzerland
don’t really get as heavy as butterflies. However, they have, when
moving at a velocity of 122 times the apparent speed of light, the same
impact a butterfly would have if he were moving at just the apparent
speed of light.
Light in the Local Universe
243
HOW DOES THE CERN LHC FUNCITION?
Surely, if there is a very great difference between the design velocities
for the LHC and the velocities actually achieved, there would be
problems in the operation that have not, presumably, surfaced.
One of these is the design of the superconducting magnet system
used to provide the magnetic field which bends the path of the
rapidly moving protons into the precise circular orbit they must
follow in order to stay within the vacuum tube in which they travel.
Another lies in keeping count of the number of bunches of protons
which pass a given detection station per unit time. If the velocity, in
terms of local time, is 122c instead of .98856c, would one not expect
the number of counts to be off by a factor of 122?
Each of these problems will be considered in the next few
paragraphs. There are, of course, many other such problems which
I am not aware of, but would be interested in learning about.
MAGNETIC FIELD STRENGTH
In order to make the protons follow a roughly circular path around
the 27 Km circumference of the LHC, rather than moving in a
straight line, a strong magnetic field must be present, with the poles
above and below the proton path. The field strength must be set
precisely to bring about the right amount of acceleration of the
protons toward the center of the Collider.
How, if both the values for both the mass and the velocity of the
protons are in error by a large factor, can the magnetic field strength
be anywhere near correct?
This is easily explained. The magnetic field exerts a force on the
particles which is equal to
MF qv B uur r ur
, EQUATION 181
Les Hardison
244
where:
q = proton charge
v= proton velocity
B=magnetic field strength,
and the v and B are both vector quantities. The cross product is equal
to the product of their magnitudes when they are at right angles to
each other, and is directed at right angles to both of them. In this
case, the force tends to bend them toward the center of the circular
orbit. This force must just equal the centrifugal force which tends to
keep them going straight, or outward from the center of the orbit.
The centrifugal force on the protons is proportional to the mass
times the velocity squared, divided by the radius of curvature of the
path
2
c
mvF
r . EQUATION 182
A stable circular path requires that these two forces be equal, so,
mvr
qB . EQUATION 183
Thus, for the known electrical charge on the proton, and radius of
the circular path, the momentum, mv, must be set correctly.
One would suppose that if the values of m and v were other than
they appear to the observer to bs, the magnetic field strength would
be set incorrectly at CERN, and the protons would follow a circular
path of the wrong radius. So, how can it be that the design actually
functions properly if the mass and velocity are both perceived
incorrectly?
I believe that the physical laws involved were all worked out on the
basis of experiments done before it was technologically possible to
accelerate particles to velocities greater than the apparent speed of light.
Light in the Local Universe
245
What the experimenters did was to make measurements of distance
and velocity in the local universe and attribute the values of local
velocity to the galactic universe without correction. Thus, the
development of Faraday’s l
Law, from which the force acting to bend the path of the proton
toward the center of the circular path, was based on measurements
made in the local universe, and was accurately defined by Equation
181 when the uncorrected rest mass was used with the local velocity,
0r
M LF qv B uur uur ur
, EQUATION 184
and
2
0 Lc
m vF
r . EQUATION 185
Thus the proper calculation of the magnetic field strength would
require
0 Lm vB
r . EQUATION 186
Because this simply doesn’t work if one uses the local velocity and
the rest mass, it is necessary to “correct” the rest mass upward by
the factor
2
2
1
1
Fv
c
, EQUATION 187
to compensate for the fact that the observed local velocity has been
“corrected’’ downward by this ratio.
The development of Faraday’s Law, and many of the other physical
laws was done at a time when it was not understood that the universe
Les Hardison
246
was expanding in a fourth dimensional direction, and that the
physical measurements being made were all relative to a different
coordinate system than they were actually using. A coordinate
system in which light moved from place to place at infinite velocity,
according to a consistent definition of the universe they were
observing.
The same appears to be the case for Newton’s laws of motion, and
for many other physical constants. They were developed using
observations relative to a local coordinate system, but using the
measurements of distance and time as though they had been
measured in reference to a coordinate system contained within the
galactic universe.
COUNTING THE PROTONS
Another seemingly puzzling problem about the difference between
the ordinary, galactic scheme for measuring times and velocities
involves the problem of how one could make a mistake in counting
the number of protons passing a particular observation station along
the perimeter of the LHC. On the one hand, the velocity is taken as
essentially c, and the time it takes to make a circuit is 88.9
microseconds. However, if one supposes that the velocity is 122c,
the time required for a full circuit is less than one microsecond.
This will take a bit of explaining, as one is used to physicists
reporting results accurate to one part in a billion when they are
measuring things, and not at all used to the idea that they might be
off by a large factor --- 122 in this case.
It all boils down, as I have repeated many times, to the concept of
how one regards the passage of time, and whether one makes
measurements in the local universe and presumes that they are,
instead, made in the galactic universe. .
Light in the Local Universe
247
FIGURE 57
SCHEMATIC OF CERN LARGE HADRON COLLIDER, SHOWING
THE UNIVERSE EXPANDING IN TO THE FOURTH DIMENSION
In Figure 57, it is apparent that the protons move around
substantially in a circle in the x – y plane in which the tubular ring is
located, and is shown as the lower perimeter of the vertical cylinder.
While the collider is located within this plane, the plane itself, along
with the rest of our entire universe, is moving in the vertical T
direction without limit as time passes. The cross sections of the
vertical cylinder represent the subsequent positions of the x – y plane
during each instant of time.
As photons move around the circular channel in the x – y plane, they
are following a helical path as the x – y plane moves in the T direction
at the velocity c. The protons move in bunches each containing
many protons. However, we can think of a single one of these
protons as being representative of one of a bunch.
Les Hardison
248
According to the example in table 6, with the protons moving at
very, very nearly the apparent speed of light, c, it takes about 0.09
seconds, or 90,000 nanoseconds for the proton to complete the
roughly 27 Km circuit. So, each proton should pass our checkpoint
about 11,245 times per second. However, there are 3705 bunches of
protons circulating in the ring, so the frequency of passage is 11,245
x 3705 = 41,670,000 sec-1, or a frequency of 41.67 MegaHz,
according to the time-clock of the galactic observer.
The local observer, on the other hand, has two times to deal with.
He has his local clock, which agrees at every instant with the galactic
timekeeper’s clock. However, he has his own local time clock, which
says that the time everywhere reads exactly the same along the 45
degree lines which are defined by the path radiant energy takes from
one point to another. His calculations of velocity, momentum and
energy are all based on the reading of his local clock.
Up until now, we have regarded the path of light as being in the local
time cone only, and therefore moving only in straight lines relative
to the observer who receives them. However, this is in the simplified
world of Special Relativity, where there are no gravitational, or
electrostatic and electromagnetic forces. In this world, protons
would also move in straight lines only.
What we must take into consideration is the enormously powerful
magnetic field in which the protons are moving in the LHC, in order
to force them to move in a circle when going at enormously high
velocities. These velocities lie completely outside the range of
comprehension.
It is my contention that the magnetic field warps the shape of the
galactic universe (and the historic picture of it we see in the local
universe) such that the cylinder pictured in Figure 57 represents a
segment of x - T space, which would ordinarily be a vertical flat
plane, wrapped around to form the cylindrical domain in which the
protons are circling. In this circular domain, light also would be bent
into a helical path through space-time, just as the protons are.
Light in the Local Universe
249
Our ordinary picture of the local universe could be examined by
unrolling the cylinder and laying it out flat, like a strip chart, where
the width of the chart represents the length of the proton’s path in
x – y space, and the vertical dimension represents the T dimension,
which stretches on far into the future.
The critical point here is that the observations on which the laws of
motion were formulated by Newton, were based on observations
made entirely within the local universe as he saw it. Because this
universe has been warped from the flat vertical plane, which would
represent the x – T universe with y = z = 0, into the shape of a
cylinder by the magnetic fields which cause the protons to follow a
cylindrical path, light would also follow the same cylindrical path.
The direction of the passage of time has been changed from a
straight vertical arrow pointing in the T direction to a helical curve,
pointing in a very nearly 45 degree angle to the galactic plane as
shown in Figure 58.
If we are to look at the protons from the standpoint of a real
observer, in his local universe, we can do so most easily by unrolling
the cylinder and laying the resulting strip chart out flat. This is akin
to unrolling a roll of toilet paper, where each square sheet width
represents the length of the circumference of the cylinder, and each
equal vertical distance represents an increment in the T Axis also
numerically equal to the circumference.
Les Hardison
250
FIGURE 58
CERN DIAGRAM WITH TWO CYCLES SHOWN
In Figure 58 the cylinder is shown with two complete orbits taking
place at essentially velocity c from the standpoint of the galactic
observer, so both the vertical and horizontal dimensions of the
unrolled sheet represent two orbits. It should be apparent that we
could unroll as many sheets as desired, so long as we kept the
diagram square, because as the protons moved around the cylinder
and from one sheet to the next in the horizontal direction, they
would also be passing upward in the T direction by the same
distance.
Light in the Local Universe
251
FIGURE 59
DEVELOPED SURFACE OF THE PROTON PATH
Figure 59 shows the developed surface, which contains the path of
the proton as it moves through two complete orbits and
simultaneously moves through the same physical distance in the
fourth, T dimension, as time passes.
Here the path of a proton moving around the circular CERN track
is indicated by the 45 degree line, which corresponds with a galactic
velocity essentially equal to c. However, the observations must be
made by a stationary observer, who has no visible communication
with the proton, and can only sense the location as the proton passes
the sensor in very close proximity. The 45 degree diagonal line
represents a galactic velocity of exactly c, the rate of expansion of
the universe in the T direction. Several other proton speeds are also
shown for reference. The sloping lines to the left of the 45 degree
line are the paths which would be followed by protons moving at
3c/4, c/2, c/4, c/8 and c/16, by galactic measure.
Les Hardison
252
However, the 45 degree line represents a velocity which corresponds
to c in the galactic system, where the vertical distance is the period
of rotation, to the local observer would involve the passage of no
time at all, and would correspond to an infinite velocity.
The proton, moving at 122.15c in local terms, or 0.99181c in terms
of the galactic reference system, would arrive at the second location
of the observer on his next cycle only a minute fraction of a cycle
later than would a light beam traversing the same distance. It is
apparent that the closer to the value of c the speed becomes, the
closer to the exact 45 degree path the trajectory becomes.
Now, the observer, located at the origin, is also moving in the x – y
plane as it moves upward in the T direction, and in which the proton
is moving according to the galactic frame of reference. However, the
observer cannot sense the location of the proton while it moves away
from his position. He can only tell where it has been, and sense the
velocity as it approaches. So, for each cycle, the observer must look
at the velocity as it approaches him from the left, and can never see
it as departing on the right, as it passes out of his sight at the moment
it passes his position.
It should also be apparent that the local observer is moving upward
in the T direction as the proton moves away from his position at, or
directly above the origin, but that it will begin to approach the
observer as it passes the point opposite the origin, as shown in
Figure 60.
However the observer will no longer be at the origin, as he was
moving in the T direction during the period of the cycle. As the
proton begins to approach the observer again, it will be as the
observer approaches, not point B in the diagram, but point B’.
Light in the Local Universe
253
.
FIGURE 60
THE DEVELOPED SURFACE FROM THE LOCAL OBSERVER’S
STANDPOINT
While the positions of the observer moves from Point A to Point B
to Point C as the universe moves in the T direction, Points A’, B’
and C’, and Points A’’, B’’ and C’’ also represent these same points
in spaced time. It is obvious that point A senses the passing of the
proton as it goes through the origin, at the beginning of the cycle,
while point B’ experiences the passing at the end of this cycle and
the beginning of the next one, while point C’’ experiences the third
passing,
Because the cycles are identical (or nearly so, if there is no further
acceleration or deceleration of the protons) the path from A to B’ to
C’’ could also be represented by a parallel path of the same electron
through points B and C’, and between A’ and B’’.
The number of crossings shown on the diagram will be exactly the
same as were presented on the diagram where the local observations
were attributed to the galactic coordinate system. However, the
difference is in the time assigned to the points. Points A, B’ and C’’
are all three in what an observer at C’’ would call the same local
Les Hardison
254
present. That is, he would see essentially no passage of local time
having taken place at all between the events recorded at A, B’ and
C’’. He would say that the protons were moving at near-infinite
velocity, just as light passing along this path would be moving at
infinite velocity according to a local observer.
The local observer at C’’ would presume that these events were
simultaneous if the galactic velocity were exactly c, and would
perceive that they were almost simultaneous, but not quite, if the
galactic velocity were, in fact, 0.99 times the apparent speed of light. In
fact, the local observer would report the velocity of the proton to be
121.15c, and the energy commensurate with that higher velocity,
with no change in the mass of the protons as they increase in speed.
Light in the Local Universe
255
CHAPTER 11 DO NEUTRINOS MOVE
FASTER THAN LIGHT?
No, they don’t. Not in the galactic reference system the physicists
are using.
Early in September, 2011, the OPERA Scientists announced that
they had measured the speed of neutrinos along a path between the
source at CERN and a receptor located about 725 Km away. I
immediately concluded that they must be mistaken, because,
according to my theory, light really moves at infinite speed, and only
appears to move at the apparent speed of light when the data are
incorrectly attributed to the wrong frame of reference. So, it really
is impossible for anything to exceed the apparent speed of light. That is
what “infinite” looks like the way physicists keep track of things.
There are two ways of looking at why neutrinos don’t move faster
than light, without bothering to go into the several ways in which the
experimenters could have been in error. I will start with these, and,
hopefully, convince you that they were in error because it is simply
not possible that their conclusion was correct.
The first, and simplest way is to convince you that the speed of light
is infinite, at least when measured by experiments conducted by
humans in the real world, which I have described as the local
universe. That is, light travels from place to place in zero time
without moving through the space between the source and the
receptor. In order for anything to go faster than that, it would have
to arrive at its destination at an earlier time than it left. In my picture
of the local universe, this is not possible.
The second way is to find some fatal flaw in their experiment which
would lead them to believe they had measured a velocity faster than
they actually did, granting that their measurements are made in the
local universe, as I have described, and used without correction in
their idealized galactic universe.
Les Hardison
256
I do have an idea of where the error might have been made, and also
a radical suggestion about the nature of neutrinos. I hit upon this
possibility a few days after the experimental results were announced,
and submitted my critique on the Vixra blog under High Energy
Particle Physics on September 26, 2011. Although I thought at the
time that my comment was far short of the typical high end physics
and mathematical comments which were being made, that I had
found the flaw in their experimental technique.
I got absolutely no comment of any sort on this submission, and
thought it appropriate to repeat it here, as long as I was already
making radical comments about relativistic physics.
THE FASTER THAN LIGHT NEUTRINO ERROR
Here is my critique of the Sasso experiments which indicated that
the speed of neutrinos passing through the earth had been observed
to traverse the distance between CERN and Gran Sasso slightly
faster than the apparent speed of light. It was made only a few days after
the popular media had broken the story, and before the
experimenters had published their paper detailing the results.
The news made quite a splash, and then died down. I had not had a
chance to read the original paper on which the story was based, but
I was convinced they were in error on general principles, as I don’t
think anything can be observed to go faster than the apparent speed of
light so long as the physicists use a coordinate system which I think
is incompatible with the measurements they make.
So, I was just taking a guess as to where they might have gone wrong,
based on the assumption that they had gone wrong somewhere.
I have since studied their paper, and have not found anything in it
to indicate that they took the problem I pointed out into account.
But they are a very big, very brainy group, and it seems likely that
they did make the correction for the shorter path length the
Light in the Local Universe
257
neutrinos took, as compared with light going through a fiberglass
cable, etc.
Anyway, here is my commentary, untouched since the initial
publication on the Vixra Blog Site11, which is specifically designed
for receiving just such comments.
September 26, 2011 at 2:50 pm
I think the experimenters might have used the wrong distance for
clocking the speed of the neutrinos.
Given that their distance measurement was quite precise, it was
done, according to reports, using GPS.
As a pilot, I know that the GPS does not give the linear distance
between two points, but rather the great circle distance connecting
them. That is, the distance as it would be measured by a tape measure
along the surface of the earth at sea level.
Neutrinos, reputedly, do not follow this curved path, but instead go
straight through the earth between the two points, which is a
significantly shorter distance. In this particular case, instead of 725
Km approximately, the chord of the arc distance is about 723. 8
11 Vixra Blog Site http”//www.vixra.com
Les Hardison
258
Km, using the mean radius of the earth as 6471 Km.
FIGURE 61
PROPOSED PATH LENGTH ERROR
Using the shorter distance and the roughly 60 nanoseconds sooner
arrival than light speed gave me a calculated speed of 299,638,769
m/sec, rather than 299,792,458 m/sec, or a velocity of about
0.99948735 times the speed of light.
Light in the Local Universe
259
ARE NEUTRINOS A FORM OF HIGH ENERGY
RADIATION?
If the experimenters did, in fact, neglect to correct the path length
in this way, it would not only leave the “laws of physics as we know
them” intact, but would also suggest some interesting things about
the nature of neutrinos. For example, consider that they might, like
photons, not really be particles, but rather attributes of a particular
kind of radiation.
That is, they would travel through Space just as light does, at the
“apparent speed of light” (when using the galactic coordinate
system) or at infinite speed (when using the local coordinate system),
but travel through matter more slowly, just as light does.
They would be to x-rays what x-rays are to visible light, passing
through all but the most energetic atoms of ordinary matter without
interaction, except for an occasional head-on collision with an
electron or proton. This is because only very heavy atoms can have
the inner electron pair so tightly bound by the electric field around
the nucleus to allow very high energy levels to exist.
This would account for the observation that the large flow of
neutrinos which seem to originate in space and pass through the
earth continuously comes from the interior of the sun, from super
novae, etc., all places where the energy levels are very high.
If this is the case, what the Sasso experimenters did was to measure
the refractive index of the radiation we describe as neutrinos through
dirt/rock/etc.
It would not, of course, be the first time radiation got mistaken for
particulate matter. In my opinion, exactly the same kind of error was
made in making up the photon to account for the quantum nature
of light. I do not believe there is any such thing as photons.
Les Hardison
260
THE OPERA EXPERIMENT PAPER
The following is a complete copy of the paper released by the
experimenters working at Gran Sasso Laboratories in Italy to
determine the velocity of a stream of artificially created neutrinos
passing between the source at the CERN Large Hadron Collider in
Geneva, Switzerland, and their detector installation at Sasso.
The paper is reprinted here in its entirety, as I think it may provide
some support for my arguments in favor of the apparent speed of light
being, in reality, the speed of expansion of the universe into a fourth
dimension which we cannot sense directly.
I invite the reader to look at:
1. My proposed explanation of the measurements of
velocity exceeding the apparent speed of light, and see
if it has any merit.
2. The possibility that the use of the conventional local
coordinate system for the interpretation of the
measurements is supported by these experiments, and
3. The suggestion that neutrinos are not particles at all, but
are instead, ultra high energy transfer events, much as
ordinary light is a transfer of energy from atom to atom,
rather than a stream of photons.
Light in the Local Universe
261
Measurement of the neutrino velocity
with the OPERA detector in the CNGS
beam
T. Adama
, N. Agafonovab
, A. Aleksandrovc,1
, O. Altinokd
, P.
Alvarez Sancheze
, S. Aokif
,
A. Arigag
, T. Arigag
, D. Autieroh
, A. Badertscheri
, A. Ben
Dhahbig
, A. Bertolinj
, C. Bozzak
,
T. Brugièreh
, F. Brunetl
, G. Brunettih,m,2
, S. Buontempoc
, F.
Cavannan
, A. Cazesh
, L. Chaussardh
,
M. Chernyavskiyo
, V. Chiarellap
, A. Chukanovq
, G. Colosimor
,
M. Crespir
, N. D’Ambrosios
,
Y. Déclaish
, P. del Amo Sanchezl
, G. De Lellist,c
, M. De Seriou
,
F. Di Capuac
, F. Cavannap
,
A. Di Crescenzot,c
, D. Di Ferdinandov
, N. Di Marcos
, S.
Dmitrievskyq
, M. Dracosa
,
D. Duchesneaul
, S. Dusinij
, J. Ebertw
, I. Eftimiopolouse
, O.
Egorovx
, A. Ereditatog
, L.S. Espositoi
,
J. Favierl
, T. Ferberw
, R.A. Finiu
, T. Fukuday
, A. Garfagniniz,j
,
G. Giacomellim,v
, C. Girerdh
,
M. Giorginim,v,3
, M. Giovannozzie
, J. Goldbergaa
, C. Göllnitzw
,
L. Goncharovao
, Y. Gornushkinq
,
G. Grellak
, F. Griantiab,p
, E. Gschewentnere
, C. Guerinh
, A.M.
Gulerd
, C. Gustavinoac
,
K. Hamadaad
, T. Haraf
, M. Hierholzerw
, A. Hollnagelw
, M.
Ievau
, H. Ishiday
, K. Ishiguroad
,
K. Jakovcicae
, C. Jolleta
, M. Jonese
, F. Jugetg
, M. Kamiscioglud
,
J. Kawadag
, S.H. Kimaf,4
,
M. Kimuray
, N. Kitagawaad
, B. Klicekae
, J. Knueselg
, K.
Les Hardison
262
Kodamaag
, M. Komatsuad
, U. Kosej
,
I. Kreslog
, C. Lazzaroi
, J. Lenkeitw
, A. Ljubicicae
, A. Longhinp
,
A. Malginb
, G. Mandrioliv
,
J. Marteauh
, T. Matsuoy
, N. Maurip
, A. Mazzonir
, E.
Medinaceliz,j
, F. Meiselg
, A. Meregagliaa
,
P. Migliozzic
, S. Mikadoy
, D. Missiaene
, K. Morishimaad
, U.
Moserg
, M.T. Muciacciaah,u
,
N. Naganawaad
, T. Nakaad
, M. Nakamuraad
, T. Nakanoad
, Y.
Nakatsukaad
, D. Naumovq
,
V. Nikitinaai
, S. Ogaway
, N. Okatevao
, A. Olchevskys
, O.
Palamaras
, A. Paolonip
, B.D. Parkaf,5
,
Parkaf
, A. Pastoreag,u
, L. Patriziiv
, E. Pennacchioh
, H.
Pessardl
, C. Pistillog
,
Polukhinao
, M. Pozzatom,v
, K. Pretzlg
, F. Pupillis
, R.
Rescignok
, T. Roganovaai
, H. Rokujof
,
Rosaaj,ac
, I. Rostovtsevax
, A. Rubbiai
, A. Russoc
, O.
Satoad
, Y. Satoak
, A. Schembris
, J. Schulera
,
Scotto Lavinag,6
, J. Serranoe
, A. Sheshukovq
, H.
Shibuyay
, G. Shoziyoevai
, S. Simoneah,u
,
Siolim,v
, C. Sirignanos
, G. Sirriv
, J.S. Songaf
, M.
Spinettip
, N. Starkovo
, M. Stellaccik
,
Stipcevicae
, T. Straussg
, P. Strolint,c
, S. Takahashif
, M.
Tentim,v,h
, F. Terranovap
, I. Tezukaak
,
Tioukovc
, P. Tolund
, T. Tranh
, S. Tufanlig
, P. Vilainal
,
M. Vladimirovo
, L. Votanop
, J.-L. Vuilleumierg
, G. Wilquetal
,
B. Wonsakw
, J. Wurtza
, C.S. Yoonaf
, J. Yoshidaad
, Y. Zaitsevx
,
Zemskovaq
, A. Zghichel
1 On leave of absence from LPI-Lebedev Physical Institute of
the Russian Academy of Sciences, 119991 Moscow, Russia 2
Now at Albert Einstein Center for Fundamental Physics,
Laboratory for High Energy Physics (LHEP), University of
Light in the Local Universe
263
Bern, CH-3012 Bern, Switzerland 3 Now at INAF/IASF,
Sezione di Milano, I-20133 Milano, Italy 4 Now at Pusan
National University, Geumjeong-Gu, Busan 609-735,
Republic of Korea 5 Now at Asian Medical Center, 388-1
Pungnap-2 Dong, Songpa-Gu, Seoul 138-736, Republic of
Korea 6 Now at SUBATECH, CNRS/IN2P3, F-44307
Nantes, France a
IPHC, Université de Strasbourg,
CNRS/IN2P3, F-67037 Strasbourg, France b
INR-Institute for
Nuclear Research of the Russian Academy of Sciences, RUS-
327312 Moscow, Russia c
INFN Sezione di Napoli, I-80125
Napoli, Italy d
METU-Middle East Technical University, TR-
06532 Ankara, Turkey e
European Organization for Nuclear
Research (CERN), Geneva, Switzerland f
Kobe University, J-
657-8501 Kobe, Japan g
Albert Einstein Center for
Fundamental Physics, Laboratory for High Energy Physics
(LHEP), University of Bern, CH-3012 Bern, Switzerlandh
IPNL, Université Claude Bernard Lyon I, CNRS/IN2P3, F-
69622 Villeurbanne, France i
ETH Zurich, Institute for
Particle Physics, CH-8093 Zurich, Switzerland j
INFN
Sezione di Padova, I-35131 Padova, Italy k
Dipartimento di
Fisica dell’Università di Salerno and INFN ”Gruppo
Collegato di Salerno”, I-84084 Fisciano, Salerno, Italyl
LAPP,
Université de Savoie, CNRS/IN2P3, F-74941 Annecy-le-
Vieux, France m
Dipartimento di Fisica dell’Università di
Bologna, I-40127 Bologna, Italy n
Dipartimento di Fisica
dell’Università dell’Aquila and INFN ”Gruppo Collegato de
L’Aquila”, I-67100 L’Aquila, Italy
Les Hardison
264
o
LPI-Lebedev Physical Institute of the Russian Academy of
Science, RUS-119991 Moscow, Russia p
INFN - Laboratori
Nazionali di Frascati, I-00044 Frascati (Roma), Italy q
JINR-
Joint Institute for Nuclear Research, RUS-141980 Dubna,
Russia r
Area di Geodesia e Geomatica, Dipartimento di
Ingegneria Civile Edile e Ambientale dell’Università di Roma
Sapienza, I-00185 Roma, Italy s
INFN - Laboratori Nazionali
del Gran Sasso, I-67010 Assergi (L’Aquila), Italy t
Dipartimento di Scienze Fisiche dell’Università Federico II di
Napoli, I-80125 Napoli, Italy u
INFN Sezione di Bari, I-70126
Bari, Italy v
INFN Sezione di Bologna, I-40127 Bologna, Italy w
Hamburg University, D-22761 Hamburg, Germany x
ITEP-
Institute for Theoretical and Experimental Physics 317259
Moscow, Russia y
Toho University, J-274-8510 Funabashi,
Japan z
Dipartimento di Fisica dell’Università di Padova,
35131 I-Padova, Italy aa
Department of Physics, Technion, IL-
32000 Haifa, Israel ab
Università degli Studi di Urbino ”Carlo
Bo”, I-61029 Urbino - Italy ac
INFN Sezione di Roma , I-
00185 Roma, Italy ad
Nagoya University, J-464-8602 Nagoya,
Japan ae
IRB-Rudjer Boskovic Institute, HR-10002 Zagreb,
Croatia af
Gyeongsang National University, ROK-900 Gazwa-
dong, Jinju 660-300, Korea ag
Aichi University of Education,
J-448-8542 Kariya (Aichi-Ken), Japan ah
Dipartimento di
Fisica dell’Università di Bari, I-70126 Bari, Italy ai
(MSU
SINP) Lomonosov Moscow State University Skobeltsyn
Institute of Nuclear Physics, RUS119992 Moscow, Russia aj
Dipartimento di Fisica dell’Università di Roma Sapienza, I-
00185 Roma, Italy ak
Utsunomiya University, J-321-8505
Utsunomiya, Japan al
IIHE, Université Libre de Bruxelles, B-
1050 Brussels, Belgium
Light in the Local Universe
265
Abstract
The OPERA neutrino experiment at the underground
Gran Sasso Laboratory has measured the velocity of neutrinos
from the CERN CNGS beam over a baseline of about 730 Km
with much higher accuracy than previous studies conducted with
accelerator neutrinos. The measurement is based on high-statistics
data taken by OPERA in the years 2009, 2010 and 2011.
Dedicated upgrades of the CNGS timing system and of the
OPERA detector, as well as a high precision geodesy campaign
for the measurement of the neutrino baseline, allowed reaching
comparable systematic and statistical accuracies. An early arrival
time of CNGS muon neutrinos with respect to the one computed
assuming the speed of light in vacuum of (60.7 ± 6.9 (stat.) ± 7.4
(sys.)) ns was measured. This anomaly corresponds to a relative
difference of the muon neutrino velocity with respect to the speed
of light (v-c)/c = (2.48 ± 0.28 (stat.) ±
0.30 (sys.)) ×10-5
.
1. Introduction
The OPERA neutrino experiment [1] at the
underground Gran Sasso Laboratory (LNGS) was designed to
perform the first detection of neutrino oscillations in direct
appearance mode in the νµ→ν
τ channel, the signature being the
identification of the τ−
lepton created by its charged current
(CC) interaction [2].
In addition to its main goal, the experiment is well
suited to determine the neutrino velocity with high accuracy
through the measurement of the time of flight and the distance
between the source of the CNGS neutrino beam at CERN
(CERN Neutrino beam to Gran Sasso)
[3] and the OPERA detector at LNGS. For CNGS neutrino
energies, <Eν> = 17 GeV, the relative deviation from the speed
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266
of light c of the neutrino velocity due to its finite rest mass is
expected to be smaller than 10-19
, even assuming the mass of the
heaviest neutrino eigenstate to be as large as 2 eV [4]. Hence,
a larger deviation of the neutrino velocity from c would be a
striking result pointing to new physics in the neutrino sector.
So far, no established deviation has been observed by any
experiment.
In the past, a high energy (Eν > 30 GeV) and short
baseline experiment has been able to test deviations down to |v-
c|/c <4×10-5
[5]. With a baseline analogous to that of OPERA
but at lower neutrino energies (Eν peaking at ~3 GeV with a tail
extending above 100 GeV), the MINOS experiment reported a
measurement of (v-c)/c = 5.1 ± 2.9×10-5
[6]. At much lower
energy, in the 10 MeV range, a stringent limit of |v-c|/c <2×
10-9
was set by the observation of (anti) neutrinos emitted by the
SN1987A supernova [7].
In this paper we report on the precision determination
of the neutrino velocity, defined as the ratio of the precisely
measured distance from CERN to OPERA to the time of flight
of neutrinos travelling through the Earth’s crust. We used the
high-statistics data taken by OPERA in the years 2009, 2010
and 2011. Dedicated upgrades of the timing systems for the
time tagging of the CNGS beam at CERN and of the OPERA
detector at LNGS resulted in a reduction of the systematic
uncertainties down to the level of the statistical error. The
measurement also relies on a high-accuracy geodesy campaign
that allowed measuring the 730 Km CNGS baseline with a
precision of 20 cm.
Light in the Local Universe
267
2. The OPERA detector and the CNGS neutrino beam
The OPERA neutrino detector at LNGS is composed of
two identical Super Modules, each consisting of an
instrumented target section with a mass of about 625 tons
followed by a magnetic muon spectrometer. Each section is a
succession of walls filled with emulsion film/lead units
interleaved with pairs of 6.7 × 6.7 m2
planes of 256 horizontal
and vertical scintillator strips composing the Target Tracker
(TT). The TT allows the location of neutrino interactions in the
target. This detector is also used to measure the arrival time of
neutrinos. The scintillating strips are read out on both sides
through WLS Kuraray Y11 fibres coupled to 4-channel
Hamamatsu H7546 photomultipliers [8]. Extensive
information on the OPERA experiment is given in [1] and in
particular for the TT in [9].
Fig. 1: Artistic view of the SPS/CNGS layout.
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The CNGS beam is produced by accelerating protons
to 400 GeV/c with the CERN Super Proton Synchrotron
(SPS). These protons are ejected with a kicker magnet
towards a 2 m long graphite neutrino production target in two
extractions, each lasting 10.5 µs and separated by 50 ms. Each
CNGS cycle in the SPS is 6 s long. Secondary charged
mesons are focused by two magnetic horns, each followed by
a helium bag to minimise the interaction probability of the
mesons. Mesons decay in flight into neutrinos in a 1000 m
long vacuum tunnel. The SPS/CNGS layout is shown in Fig.
1. The different components of the CNGS beam are shown in
Fig.2.
Fig.2: Layout of the CNGS beam line.
The distance between the neutrino target and the OPERA
detector is about 730 km. The CNGS beam is an almost pure νµ
beam with an average energy of 17 GeV, optimised for νµ→ν
τ appearance oscillation studies. In terms of interactions in the
detector, the ⎯νµ
contamination is 2.1%, while νe and ⎯νe
contaminations are together smaller than 1%. The FWHM of the neutrino beam at the OPERA location is 2.8 km.
The kicker magnet trigger-signal for the proton
extraction from the SPS is UTC (Coordinated Universal Time)
time-stamped with a Symmetricom Xli GPS receiver [10]. The
schematic of the SPS/CNGS timing system is shown in Fig. 3.
The determination of the delays shown in Fig. 3 is described in
Light in the Local Universe
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Section 6.
The proton beam time-structure is accurately measured
by a fast Beam Current Transformer (BCT) detector [11]
(BFCTI400344) located (743.391 ± 0.002) m upstream of the
centre of the graphite target and read out by a 1 GS/s Wave
Form Digitizer (WFD) Acqiris DP110 [12]. The BCT consists
of toroidal transformers coaxial to the proton beam providing a
signal proportional to the beam current instantaneously
transiting through it, with a few hundred MHz bandwidth. The
start of the digitisation window of the WFD is triggered as well
by the magnet kicker signal. The waveforms recorded for each
extraction by the WFD are stamped with the UTC and stored
in the CNGS database.
The proton beam has a coarse bunch structure
corresponding to the 500 kHz of the CERN Proton Synchrotron
(PS) (left part of Fig. 4), on which the fine structure due to the
200 MHz SPS radiofrequency is superimposed, which is
actually resolved by the BCT measurement, as seen in the right
part of Fig. 4.
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Fig. 3: Schematic of the CERN SPS/CNGS timing system. Green boxes
indicate detector time-response. Orange boxes refer to elements of the
CNGS-OPERA synchronisation system. Details on the various elements
are given in Section 6.
Fig. 4: Example of a proton extraction waveform measured with the BCT
detector BFCTI400344. The five-peak structure reflects the continuous
PS turn extraction mechanism. A zoom of the waveform (right plot)
allows resolving the 200 MHz SPS radiofrequency.
Light in the Local Universe
271
3. Principle of the neutrino time of flight measurement
A schematic description of the principle of the time of
flight measurement is shown in Fig.
5. The time of flight of CNGS neutrinos (TOFν) cannot be
precisely measured at the single interaction level since any
proton in the 10.5 µs extraction time may produce the neutrino
detected by OPERA. However, by measuring the time
distributions of protons for each extraction for which neutrino
interactions are observed in the detector, and summing them
together, after proper normalisation one obtains the probability
density function (PDF) of the time of emission of the neutrinos
within the duration of extraction. Each proton waveform is
UTC time-stamped as well as the events detected by OPERA.
The two time-stamps are related by TOFc, the expected time of
flight assuming the speed of light [13]. It is worth stressing that
this measurement does not rely on the difference between a
start (t0) and a stop signal but on the comparison of two event
time distributions.
The PDF distribution can then be compared with the
time distribution of the interactions detected in OPERA, in
order to measure TOFν. The deviation δt = TOFc -TOF
ν is
obtained by a maximum likelihood analysis of the time tags of
the OPERA events with respect to the PDF, as a function of δt.
The individual measurement of the waveforms reflecting the
time structure of the extraction reduces systematic effects
related to time variations of the beam compared to the case
where the beam time structure is measured on average, e.g. by
a near neutrino detector without using proton waveforms.
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Fig. 5: Schematic of the time of flight measurement.
The total statistics used for the analysis reported in this paper
is of 16111 events detected in OPERA, corresponding to about
1020
protons on target collected during the 2009, 2010 and 2011
CNGS runs. This allowed estimating δt with a small statistical
uncertainty, presently comparable to the total systematic
uncertainty.
The point where the parent meson produces a neutrino
in the decay tunnel is unknown. However, this introduces a
negligible inaccuracy in the neutrino time of flight
measurement, because the produced mesons are also travelling
with nearly the speed of light. By a full FLUKA based
simulation of the CNGS beam [14] it was shown that the time
difference computed assuming a particle moving at the speed
of light from the neutrino production target down to LNGS,
with respect to the value derived by taking into account the
speed of the relativistic parent meson down to its decay point
is less than 0.2 ns. Similar arguments apply to muons produced
in muon neutrino CC interactions occurring in the rock in front
Light in the Local Universe
273
of the OPERA detector and seen in the apparatus (external
events). With a full GEANT simulation of external events it is
shown that ignoring the position of the interaction point in the
rock introduces a bias smaller than 2 ns with respect to those
events occurring in the target (internal events), provided that
external interactions are selected by requiring identified muons
in OPERA. More details on the muon identification procedure
are given in [15].
Fig. 6: Schematic of the OPERA timing system at LNGS. Blue delays
include elements of the time-stamp distribution; increasing delays
decrease the value of δt. Green delays indicate detector time-response;
increasing delays increase the value of δt. Orange boxes refer to
elements of the CNGS-OPERA synchronisation system.
A key feature of the neutrino velocity measurement is the
accuracy of the relative time tagging at CERN and at the
OPERA detector. The standard GPS receivers formerly
installed at CERN and LNGS would feature an insufficient
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~100 ns accuracy for the TOFν measurement. Thus, in 2008,
two identical systems, composed of a GPS receiver for time-
transfer applications Septentrio PolaRx2e [16] operating in
“common-view” mode [17] and a Cs atomic clock
Symmetricom Cs4000 [18], were installed at CERN and
LNGS (see Figs. 3, 5 and 6).
The Cs4000 oscillator provides the reference frequency
to the PolaRx2e receiver, which is able to time-tag its “One
Pulse Per Second” output (1PPS) with respect to the individual
GPS satellite observations. The latter are processed offline by
using the CGGTTS format [19]. The two systems feature a
technology commonly used for high-accuracy time transfer
applications [20]. They were calibrated by the Swiss Metrology
Institute (METAS) [21] and established a permanent time link
between two reference points (tCERN and tLNGS) of the timing
chains of CERN and OPERA at the nanosecond level. This
time link between CERN and OPERA was independently
verified by the German Metrology Institute PTB (Physikalisch-
Technische Bundesanstalt) [22] by taking data at CERN and
LNGS with a portable time-transfer device [23]. The difference
between the time base of the CERN and OPERA PolaRx2e
receivers was measured to be (2.3 ± 0.9) ns [22]. This
correction was taken into account in the application of the time
link.
All the other elements of the timing distribution chains
of CERN and OPERA were accurately calibrated by using
different techniques, further described in the following, in
order to reach a comparable level of accuracy.
4. Measurement of the neutrino baseline
The other fundamental ingredient for the neutrino
velocity measurement is the knowledge of the distance between
Light in the Local Universe
275
the point where the proton time-structure is measured at CERN
and the origin of the underground OPERA detector reference
frame at LNGS. The relative positions of the elements of the
CNGS beam line are known with millimetre accuracy. When
these coordinates are transformed into the global geodesy
reference frame ETRF2000 [24] by relating them to external
GPS benchmarks, they are known within 2 cm accuracy.
The analysis of the GPS benchmark positions was first
done by extrapolating measurements taken at different periods
via geodynamical models [25], and then by comparing
simultaneous measurements taken in the same reference frame.
The two methods yielded the same result within 2 cm [26]. The
travel path of protons from the BCT to the focal point of the
CNGS target is also known with millimetre accuracy.
The distance between the target focal point and the
OPERA reference frame was precisely measured in 2010
following a dedicated geodesy campaign. The coordinates of
the origin of the OPERA reference frame were measured by
establishing GPS benchmarks at the two sides of the ~10 Km
long Gran Sasso highway tunnel and by transporting their
positions with a terrestrial traverse down to the OPERA
detector. A common analysis in the ETRF2000 reference frame
of the 3D coordinates of the OPERA origin and of the target
focal point allowed the determination of this distance to be
Les Hardison
276
730534.61 ± 0.20) m [26].The 20 cm uncertainty is dominated
by the long underground link between the outdoors GPS
benchmarks and the benchmark at the OPERA detector [26].
Fig. 7: Monitoring of the PolaRx2e GPS antenna position at
LNGS, showing the slow earth crust drift and the fault displacement due
to the 2009 earthquake in the L’Aquila region. Units for the horizontal
(vertical) Axis are years (meters).
The high-accuracy time-transfer GPS receiver allows to
continuously monitor tiny movements of the Earth’s crust, such
as continental drift that shows up as a smooth variation of less
than 1 cm/year, and the detection of slightly larger effects due
to earthquakes. The April 2009 earthquake in the region of
LNGS, in particular, produced a sudden displacement of about
7 cm, as seen in Fig. 7. All mentioned effects are within the
Light in the Local Universe
277
accuracy of the baseline determination. Tidal effects are
negligible as well. The baseline considered for the
measurement of the neutrino velocity is then the sum of the
(730534.61 ± 0.20) m between the CNGS target focal point and
the origin of the OPERA detector reference frame, and the
(743.391 ± 0.002) between the BCT and the focal point, i.e.
(731278.0 ± 0.2) .
5. Data selection
The OPERA data acquisition system (DAQ) time-tags
the detector TT hits with 10 ns quantization with respect to the
UTC [27]. The time of a neutrino interaction is defined as that
of the earliest hit in the TT. CNGS events are preselected by
requiring that they fall within a window of ± 20 µs with respect
to the SPS kicker magnet trigger-signal, delayed by the
neutrino time of flight assuming the speed of light and
corrected for the various delays of the timing systems at CERN
and OPERA. The relative fraction of cosmic-ray events
accidentally falling in this window is 10-4
, and it is therefore
negligible [1, 28].
Since TOFc is computed with respect to the origin of
the OPERA reference frame, located beneath the most
upstream spectrometer magnet, the time of the earliest hit for
each event is corrected for its distance along the beam line from
this point, assuming a time propagation according to the speed
of light. The UTC time of each event is also individually
corrected for the instantaneous value of the time link
correlating the CERN and OPERA timing systems.
The total statistics used for this analysis consists of
7586 internal (charged and neutral current interactions) and
8525 external (charged current) events. Internal events,
preselected by the electronic detectors with the same procedure
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278
used for neutrino oscillation studies [29], constitute a
subsample of the entire OPERA statistics (about 70%) for
which both time transfer systems at CERN and LNGS were
operational, as well as the database-logging of the proton
waveforms. As mentioned before, external events, in addition,
are requested to have a muon identified in the detector.
6. Neutrino event timing
The schematic of the SPS/CNGS timing system is
shown in Fig. 3. A general-purpose timing receiver “Control
Timing Receiver” (CTRI) at CERN [30] logs every second the
difference in time between the 1PPS outputs of the Xli and of
the more precise PolaRx2e GPS receivers, with 0.1 ns
resolution. The Xli 1PPS output represents the reference point
of the time link to OPERA. This point is also the source of the
“General Machine Timing” chain (GMT) serving the CERN
accelerator complex [31].
The GPS devices are located in the CERN Prevessin
Central Control Room (CCR). The time information is
transmitted via the GMT to a remote CTRI device in Hall
HCA442 (former UA2 experiment counting room) used to
UTC time-stamp the kicker magnet signal. This CTRI also
produces a delayed replica of the kicker magnet signal, which
is sent to the adjacent WFD module. The UTC time-stamp
marks the start of the digitization window of the BCT signal.
The latter signal is brought via a coaxial cable to the WFD at a
distance of 100 m. Three delays characterise the CERN timing
chain:
a) The propagation delay through the GMT of the time
base of the CTRI module logging the PolaRx2e 1PPS output to
the CTRI module used to time-tag the kicker pulse ΔtUTC =
(10085 ± 2) ns;
Light in the Local Universe
279
b) The delay to produce the replica of the kicker magnet
signal from the CTRI to start the WFD Δttrigger = (30
± 1) ns;
c) The delay from the time the protons cross the BCT to the
time a signal arrives to the WFD ΔtBCT = (580 ± 5) ns.
The kicker signal is just used as a pre-trigger and as an
arbitrary time origin. The measurement of the TOFν is based
instead on the BCT waveforms, which are tagged with respect
to the UTC.
The measurement of ΔtUTC was performed by means of
a portable Cs4000 oscillator. Its 1PPS output, stable to better
than 1ns over a few hour scale, was input to the CTRI used to
log the Xli 1PPs signal at the CERN CCR. The same signal was
then input to the CTRI that timestamps the kicker signal at the
HCA442 location. The two measurements allowed the
determination of the delay between the time bases of the two
CTRI, and to relate the kicker timestamp to the Xli output. The
measurements were repeated three times during the last two
years and yielded the same results within 2 ns. This delay was
also determined by performing a two-way timing measurement
with optical fibres. The Cs clock and the two-way
measurements also agree within 2 ns.
The two-way measurement is a technique used several
times in this analysis for the determination of delays.
Measuring the delay tA in propagating a signal to a far device
consists in sending the same signal via an optical fibre B to the
far device location in parallel to its direct path A. At this site
the time difference tA-tB between the signals following the two
paths is measured. A second measurement is performed by
taking the signal arriving at the far location via its direct path A
and sending it back to the origin with the optical fibre B. At the
origin the time difference between the production and receiving
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280
time of the signal corresponds to tA+tB. In this procedure the
optoelectronic chain used for the fibre transmission of the two
measurements is kept identical by simply swapping the
receiver and the transmitter between the two locations. The two
combined measurements allow determining tA and tB [32].
Δttrigger was estimated by an accurate oscilloscope
measurement. The determination of ΔtBCT was first performed
by measuring the 1PPS output of the Cs4000 oscillator with a
digital oscilloscope and comparing to a CTRI signal at the point
where the BCT signal arrives at the WFD. This was compared
to similar measurement where the Cs4000 1PPS signal was
injected into the calibration input of the BCT. The time
difference of the 1PPS signals in the two configurations led to
the measurement of ΔtBCT = (581 ± 10) ns.
Since the above determination through the calibration
input of the BCT might not be representative of the internal
delay of the BCT with respect to the transit of the protons, a
more sophisticated method was then applied. The proton transit
time was tagged upstream of the BCT by two fast beam pick-
ups BPK400099 and BPK400207 with a time response of ~1
ns [33]. From the relative positions of the three detectors (the
pick-ups and the BCT) along the beam line and the signals from
the two pick-ups one determines the time the protons cross the
BCT and the time delay at the level of the WFD. In order to
achieve an accurate determination of the delay between the
BCT and the BPK signals, a measurement was performed in
the particularly clean experimental condition of the SPS proton
injection to the Large Hadron Collider (LHC) machine of 12
bunches with 50 ns spacing, passing through the BCT and the
two pick-up detectors. This measurement was performed
simultaneously for the 12 bunches and yielded ΔtBCT = (580 ±
5 (sys.)) ns.
Light in the Local Universe
281
The schematic of the OPERA timing system at LNGS
is shown in Fig. 6. The official UTC time source at LNGS is
provided by a GPS system ESAT 2000 [34, 35] operating at the
surface laboratory. The 1PPS output of the ESAT is logged
with a CTRI module every second with respect to the 1PPS of
the PolaRx2e, in order to establish a high-accuracy time link
with CERN. Every millisecond a pulse synchronously derived
from the 1PPS of the ESAT (PPmS) is transmitted to the
underground laboratory via an 8.3 Km long optical fibre. The
delay of this transmission with respect to the ESAT 1PPS
output down to the OPERA master clock output was measured
with a two-way fibre procedure and amounts to (40996 ± 1) ns.
Measurements with a transportable Cs clock were also
performed yielding the same result. The OPERA master clock
is disciplined by a high-stability oscillator Vectron OC-050
with an Allan deviation of 2×10-12
/s. This oscillator keeps the
local time in between two external synchronisations given by
the PPmS signals coming from the external GPS.
The time base of the OPERA master clock is
transmitted to the frontend cards of the TT. This delay (Δtclock)
was also measured with two techniques, namely by the two-
way fibres method and by transporting the Cs4000 clock to the
two points. Both measurements provided the same result of
(4263 ± 1) ns. The frontend card time-stamp is performed in a
FPGA (Field Programmable Gate Arrays) by incrementing a
coarse counter every 0.6 s and a fine counter with a frequency
of 100 MHz. At the occurrence of a trigger the content of the
two counters provides a measure of the arrival time. The fine
counter is reset every 0.6 s by the arrival of the master clock
signal that also increments the coarse counter. The internal
delay of the FPGA processing the master clock signal to reset
the fine counter was determined by a parallel measurement of
trigger and clock signals with the DAQ and a digital
oscilloscope. The measured delay amounts to (24.5 ± 1.0) ns.
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This takes into account the 10 ns quantization effect due to the
clock period.
The delays in producing the Target Tracker signal
including the scintillator response, the propagation of the
signals in the WLS fibres, the transit time of the
photomultiplier [8], and the time response of the OPERA
analogue frontend readout chip (ROC) [36] were overall
calibrated by exciting the scintillator strips at known positions
by a UV picosecond laser [37]. The arrival time distribution of
the photons to the photocathode and the time walk due to the
discriminator threshold in the analogue frontend chip as a
function of the signal pulse height were accurately
parameterized in laboratory measurements and included in the
detector simulation. The total time elapsed from the moment
photons reach the photocathode, a trigger is issued by the ROC
analogue frontend chip, and the trigger arrives at the FPGA,
where it is time-stamped, was determined to be (50.2 ± 2.3) ns.
Since the time response to neutrino interactions
depends on the position of the hits in the detector and on their
pulse height, the average TT delay was evaluated by computing
the difference between the exact interaction time and the time-
stamp of the earliest hit for a sample of fully simulated neutrino
interactions. Starting from the position at which photons are
generated in each strip, the simulation takes into account all the
effects parametrized from laboratory measurements including
the arrival time distribution of the photons for a given
production position, the time-walk of the ROC chip, and the
measured delays from the photocathode to the FPGA. This TT
delay has an average value of 59.6 ns with a RMS of 7.3 ns,
reflecting the transverse event distribution inside the detector.
The 59.6 ns represent the overall delay of the TT response
down to the FPGA and they include the above-mentioned delay
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of 50.2 ns. A systematic error of 3 ns was estimated due to the
simulation procedure. Several checks were performed by
comparing data and simulated events, as far as the earliest TT
hit timing is concerned. Data and simulations agree within the
Monte Carlo systematic uncertainty of 3 ns for both the time
difference between the earliest and the following hits, and for
the difference between the earliest hit and the average hit
timing of muon tracks.
More details on the neutrino timing as well as on the
geodesy measurement procedures can be found in [38].
7. Data analysis
The data analysis was performed blindly by
deliberately assuming the setup configuration of 2006. In
particular, important calibrations were not available at all that
time, such as the BCT delay ΔtBCT, the trigger delay Δttrigger and
the improved estimate of the UTC delay ΔtUTC. Also TOFc was
not expressed with respect to the BCT position but referred to
another conventional point upstream in the beam line. DAQ
and detector delays were not taken into account either. This led
by construction to an unrealistically large deviation from TOFc,
much larger than the individual calibration contributions. The
precisely calibrated corrections applied to TOFν and yielding
the final δt value are summarized in Table 1.
For each neutrino interaction measured in the OPERA
detector the analysis procedure used the corresponding proton
extraction waveform. These were summed up and properly
normalised in order to build a PDF w(t). The WFD is triggered
by the magnet kicker pulse, but the time of the proton pulses
with respect to the kicker trigger is different for the two
extractions. The kicker trigger is just related to the pulsing of
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the kicker magnet. The exact timing of the proton pulses stays
within this large window of the pulse.
A separate maximum likelihood procedure was then
carried out for the two proton extractions. The likelihood
function to be maximised for each extraction is a function of
the single variable δt to be added to the time tags tj of the
OPERA events. These are expressed in the time reference of
the proton waveform digitizer assuming neutrinos travelling at
the speed of light, such that their distribution best coincides
with the corresponding PDF:
Near the maximum the likelihood function can be
approximated by a Gaussian function, whose variance is a
measure of the statistical uncertainty on δt (Fig. 8). As seen in
Fig. 9, the PDF representing the time-structure of the proton
extraction is not flat but exhibits a series of peaks and valleys,
reflecting the features and the inefficiencies of the proton
extraction from the PS to the SPS via the Continuous Turn
mechanism [39]. Such structures may well change with time.
The way the PDF are built automatically accounts for the beam
conditions corresponding to the neutrino interactions detected
by OPERA. The result of the maximum likelihood analysis of
δt for the two proton extractions for the years 2009, 2010 and
2011 are compared in Fig. 10. They are compatible with each
other.
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Data were also grouped in arbitrary subsamples to look
for possible systematic dependences. For example, by
computing δt separately for events taken during day and night
hours, the absolute difference between the two bins is (17.1 ±
15.5) ns providing no indication for a systematic effect. A
similar result was obtained for a possible summer vs spring +
fall dependence, which yielded (11.3 ± 14.5) ns.
The maximum likelihood procedure was checked with
a Monte Carlo simulation. Starting from the experimental
PDF, an ensemble of 100 data sets of OPERA neutrino
interactions was simulated. Simulated data were shifted in
time by a constant quantity, hence faking a time of flight
deviation. Each sample underwent the same maximum
likelihood procedure as applied to real data. The analysis
yielded a result accounting for the statistical fluctuations of
the sample that are reflected in the different central values and
their uncertainties.
The average of the central values from this ensemble
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of simulated OPERA experiments reproduces well the time
shift applied to the simulation (at the 0.3 ns level). The
average statistical error extracted from the likelihood analysis
also reproduces within 1 ns the RMS distribution of the mean
values with respect to the true values.
.
Fig. 8: Log-likelihood distributions for both extractions as a
function of δt, shown close to the maximum and fitted with a parabolic
shape for the determination of the central value and of its uncertainty
The result of the blind analysis shows an earlier arrival
time of the neutrino with respect to the one computed by
assuming the speed of light δt (blind) = TOFc -TOFν = (1048.5
± 6.9 (stat.)) ns. As a check, the same analysis was repeated
considering only internal events. The result is δt (blind) =
Light in the Local Universe
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(1047.4 ± 11.2 (stat.)) ns, compatible with the systematic error
of 2 ns due to the inclusion of external events. The agreement
between the proton PDF and the neutrino time distribution
obtained after shifting by δt (blind) is illustrated in Fig. 11. The
χ2
/ndf is 1.06 for the first extraction and 1.12 for the second
one. Fig. 12 shows a zoom of the leading and trailing edges of
the distributions given in the bottom of Fig. 11.
Fig. 9: Summed proton waveforms of the OPERA events corresponding
to the two SPS extractions for the 2009, 2010 and 2011 data samples.
Fig.
10: Results of the maximum likelihood analysis for δt corresponding to
the two SPS extractions for the 2009, 2010 and 2011 data samples.
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Fig. 11: Comparison of the measured neutrino interaction time
distributions (data points) and the proton PDF (red line) for the two SPS
extractions before (top) and after (bottom) correcting for δt (blind)
resulting from the maximum likelihood analysis.
The 17.4 ns correction in Table 1 takes into account all
the effects related to DAQ and TT delays, as well as the
difference between the value of Δtclock determined in 2006 from
a test-bench measurement and the one obtained on-site with the
procedure previously described. The 353 ns relative to the 2006
calibration assume the relative synchronisation of the CERN
and LNGS GPS systems prior to the installation of the two
high-accuracy systems operating in common-view mode. One
Light in the Local Universe
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then obtains:
δt = TOFc –TOFν = 1048.5 ns – 987.8 ns = (60.7 ± 6.9 (stat.))
ns
The above result is also affected by an overall systematic
uncertainty of 7.4 ns coming from the quadratic sum of the
different terms previously discussed in the text and summarised
in Table 2. The dominant contribution is due to the calibration
of the BCT time response. The error in the CNGS-OPERA GPS
synchronisation has been computed by adding in quadrature the
uncertainties on the calibration performed by the PTB and the
internal uncertainties of the two high-accuracy GPS systems.
The final result of the measurement is (Fig. 13):
δt = TOFc -TOFν = (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns.
We cannot explain the observed effect in terms of
presently known systematic uncertainties. Therefore, the
measurement indicates an early arrival time of CNGS muon
neutrinos with respect to the one computed assuming the speed
of light in vacuum. The relative difference of the muon neutrino
velocity with respect to the speed of light is:
(v-c)/c = δt /(TOF’c -δt) = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×
10-5
,
with 6.0 σ significance. In performing this last calculation a
baseline of 730.085 Km was used, and TOF’c corresponds to
this effective neutrino baseline starting from the average decay
point in the CNGS tunnel as determined by simulations.
Actually, the δt value is measured over the distance from the
BCT to the OPERA reference frame, and it is only determined
by neutrinos and not by protons and pions, which introduce
negligible delays.
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Fig. 12: Zoom of the leading (left plots) and trailing edges (right plots)
of the measured neutrino interaction time distributions (data points) and
the proton PDF (red line) for the two SPS extractions after correcting for
δt (blind).
A possible neutrino energy dependence of δt was
studied in order to investigate the physics origin of the early
arrival time of CNGS neutrinos. For this analysis the data set
was limited to νµ CC interactions occurring in the OPERA target
(5489 events), for which the neutrino energy can be measured
by adding the muon momentum to the hadronic energy. Details
on the energy reconstruction in the OPERA detector are
available in [15]. A first measurement was performed by
considering all νµ CC internal events. We obtained δt = (60.3 ±
13.1 (stat.) ± 7.4 (sys.)) ns, for an average neutrino energy of
28.1 GeV.
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Table 2:
Contribution to the overall systematic uncertainty on the
measurement of δt.
Data were then split into two bins of nearly equal
statistics, including events of energy lower or higher than 20
GeV. The mean energies of the two samples are 13.9 and 42.9
GeV. The result for the low-and high-energy data sets are,
respectively, δt = (53.1 ± 18.8 (stat.) ± 7.4 (sys.)) ns and (67.1
± 18.2 (stat.) ± 7.4 (sys.)) ns. The above result was checked
against a full Monte Carlo simulation of the OPERA events.
The same procedure used for real data was applied to νµ CC
simulated interactions in the OPERA target. The comparison
between the two data sets indicates no energy dependence, with
a difference of ~1 ns. The simulation does not indicate any
instrumental effects on δt possibly caused by an energy
dependent time response of the detector. Therefore, the
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systematic uncertainties of the two measurements tend to
cancel each other out regarding the difference of the two
values, which amounts to (14.0 ± 26.2) ns. This result,
illustrated in Fig. 13, provides no clues on a possible energy
dependence of δt in the domain explored by OPERA, within
the statistical accuracy of the measurement.
Fig. 13: Summary of the results for the measurement of δt. The left plot
shows δt as a function of the energy for νµ CC internal events.
The errors attributed to the two points are just statistical in
order to make their relative comparison easier since the
systematic error (represented by a band around the no-effect
line) cancels out. The right plot shows the global result of the
analysis including both internal and external events (for the
latter the energy cannot be measured). The error bar includes
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statistical and systematic uncertainties added in quadrature.
Conclusions
The OPERA detector at LNGS, designed for the study
of neutrino oscillations in appearance mode, has provided a
precision measurement of the neutrino velocity over the 730
Km baseline of the CNGS neutrino beam sent from CERN to
LNGS through the Earth’s crust. A time of flight measurement
with small systematic uncertainties was made possible by a
series of accurate metrology techniques. The data analysis took
also advantage of a large sample of about 16000 neutrino
interaction events detected by OPERA.
The analysis of internal neutral current and charged
current events, and external νµ CC interactions from the 2009,
2010 and 2011 CNGS data was carried out to measure the
neutrino velocity. The sensitivity of the measurement of (v-c)/c
is about one order of magnitude better than previous accelerator
neutrino experiments.
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The results of the study indicate for CNGS muon
neutrinos with an average energy of 17 GeV an early neutrino
arrival time with respect to the one computed by assuming the
speed of light in vacuum:
δt = (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns.
The corresponding relative difference of the muon
neutrino velocity and the speed of light is:
(v-c)/c = δt /(TOF’c -δt) = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×
10-5
.
with an overall significance of 6.0 σ.
The dependence of δt on the neutrino energy was also
investigated. For this analysis the data set was limited to the
5489 νµ CC interactions occurring in the OPERA target. A
measurement performed by considering all νµ CC internal
events yielded δt = (60.3 ± 13.1 (stat.) ± 7.4 (sys.)) ns, for an
average neutrino energy of 28.1 GeV. The sample was then
split into two bins of nearly equal statistics, taking events of
energy higher or lower than 20 GeV. The results for the low-
and high-energy samples are, respectively, δt = (53.1 ± 18.8
(stat.).) ± 7.4 (sys.)) ns and (67.1 ± 18.2 (stat.).) ± 7.4 (sys.))
ns. This provides no clues on a possible energy dependence of
δt in the domain explored by OPERA within the accuracy of
the measurement.
Despite the large significance of the measurement
reported here and the stability of the analysis, the potentially
great impact of the result motivates the continuation of our
studies in order to investigate possible still unknown
systematic effects that could explain the observed anomaly.
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We deliberately do not attempt any theoretical or
phenomenological interpretation of the results.
Acknowledgements
We thank CERN for the successful operation and
INFN for the continuous support given to the experiment
during the construction, installation and commissioning
phases through its LNGS laboratory. We are indebted to F.
Riguzzi of the Italian National Institute of Geophysics and
Volcanology for her help in geodynamical analysis of the
high-frequency PolaRx2e data. We warmly acknowledge
funding from our national agencies: Fonds de la Recherche
Scientifique FNRS and Institut Interuniversitaire des Sciences
Nucléaires for Belgium; MoSES for Croatia; CNRS and
IN2P3 for France; BMBF for Germany; INFN for Italy; JSPS
(Japan Society for the Promotion of Science), MEXT
(Ministry of Education, Culture, Sports, Science and
Technology), QFPU (Global COE program of Nagoya
University, ”Quest for Fundamental Principles in the
Universe” supported by JSPS and MEXT) and Promotion and
Mutual Aid Corporation for Private Schools of Japan for
Japan; The Swiss National Science Foundation (SNF), the
University of Bern and ETH Zurich for Switzerland; the
Russian Foundation for Basic Research (grant 09-02-00300
a), the Programs of the Presidium of the Russian Academy of
Sciences ”Neutrino Physics” and ”Experimental and
theoretical researches of fundamental interactions connected
with work on the accelerator of CERN”, the Programs of
support of leading schools (grant 3517.2010.2), and the
Ministry of Education and Science of the Russian Federation
for Russia; the Korea Research Foundation Grant (KRF-2008-
313-C00201) for Korea; and TUBITAK The Scientific and
Technological Research Council of Turkey, for Turkey. We
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are also indebted to INFN for providing fellowships and
grants to non-Italian researchers. We thank the IN2P3
Computing Centre (CC-IN2P3) for providing computing
resources for the analysis and hosting the central database for
the OPERA experiment. We are indebted to our technical
collaborators for the excellent quality of their work over many
years of design, prototyping and construction of the detector
and of its facilities.
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CHAPTER 12 CONCLUSIONS
My conclusions from the analysis made here are very simple. The
world we live in, and the measurements we, and physicists, make are
all tied to what we see in the world when we look around us. The
measurements are dependent on light, or other forms of radiation as
they are perceived in our own local universe.
Prior to the beginning of the 20th century, the world was a simpler
place, where things moved relatively slowly, compared to the speed
of light, and we could well believe that what we were seeing was the
world as it really existed at that moment in time. Relationships
between the velocity of objects, their mass and the change in velocity
resulting from the application of some kind of force, seemed to be
straightforward and irrevocable.
But, physicists were experimenting with the only thing that moved
really fast --- light itself. And they were surprised to find that light
did not follow the rules that had been defined by Isaac Newton for
the relationship between velocities. When the speed of light was
measured accurately by a “stationary” apparatus, it came out the
same as it did when measured by a moving apparatus. That didn’t
seem right, but there was no way to deny the accuracy of the
experimenters who measured the velocity.
Albert Einstein was the first one to put the experimental data into a
framework which seemed to explain everything. He did it without
doing any experimentation at all, by simply applying some of the
mathematical techniques which were available to describe a model
of the universe in which a beam of light would appear to be moving
at the same speed if two observers moving relative to each other
measured it and got the same answer.
There were, of course, some complications. These included some
peculiar properties of time, which everyone had considered to be
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absolute and independent of anything else. Time had to be allowed
to expand, so that clocks would run more slowly if they were moving
with respect to the stationary observer. This, in turn, required that
the space had to appear differently to moving observers than to
stationary ones, and that physical objects had to get shorter as their
velocities increased. In terms of the equations of Special Relativity,
nothing could go faster than the apparent speed of light.
Finally, the coup de grace was that masses of objects had to increase
as they accelerated to higher velocities in order to avoid reaching
velocities which would exceed c, the apparent speed of light.
I have proposed that the experimenters who measured the apparent
speed of light from both “moving” and “stationary” vantage points
were, in fact, measuring the rate at which the universe is expanding
into a fourth spatial dimension. We are unaware of anything beyond
our normal three dimensions; although vaguely aware that time has
some properties like a fourth dimension.
If, in fact, they were measuring the a constant velocity at which we
(everyone and everything in the universe) are moving in this
direction, it would it would explain why light seems to be moving at
this rate, when it is actually being transferred from a source to a
receptor instantaneously.
This simple change in viewpoint would make much of the
complexity of the physical world as it is commonly regarded by
physical scientists go away. There would no longer be a limitation on
the speed at which material objects can travel. They wouldn’t get
shorter and become more massive as their velocity increases relative
to any fixed reference system. And, matter and energy are no longer
necessarily interchangeable.
Newton’s laws of motion would, once again, work and relativistic
correction factors would only have to be used if one chose to use
the particular galactic playing field in which most scientific
experiments are erroneously presumed to be conducted. Time
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would, once again, be the same everywhere, but the measurement of
time would have to be done realistically, taking into account that o
These conclusions are of no consequence whatever to any of us in
the conduct of our ordinary lives. The people to whom this might
have some significant meaning are the scientists who are cooperating
on the biggest scientific project the world has even known, the
CERN Large Hadron Collider. I would be surprised but pleased if
any one of them showed sufficient interest to prove me wrong.