7/29/2019 A Problem in Astronomy - The age of galaxies - Science
- Subramanian A
1/3
A PROBLEM IN ASTRONOMY
The age of a galaxy, from which, if a light ray takes 10000
light years to reach the earth is assumed to
be 10000 years.
On a deeper analysis, this seems to be incorrect on the
following lines. If a light ray from a star takes
5 light years to reach the earth, the age of the star cannot be
5 light years for the following reason(s):-
Look at the following figure:- A
oo
o
B
Let us for a moment remember the fact that the universe has been
created out of a big bang. Let us
further assume that the Centre of the Big Bang is at point
O.
We know that the universe is expanding. Let us assume that the
universe is expanding like an
expanding balloon. Let us take that A and B are two material
points of this universal balloon which
are lying inside, diametrically opposite to each other. Let us
suppose that A is travelling at a velocity
V1 and B is travelling at the rate of V2 away from the Centre
O.
Now, let us imagine that there is a light emitting source at A,
emitting light at regular intervals. Let
us presume that the Source emitted light after t seconds from
the occurrence of Big Bang. Let us
calculate the time that the light from the source takes to reach
the material point B.
Distance travelled by point A from the Centre O before it
emitted light, travelling at a velocity V1 is
V1xt.
Distance travelled by point B from the Centre O for the same
time t = V2xt.
7/29/2019 A Problem in Astronomy - The age of galaxies - Science
- Subramanian A
2/3
While the light which is emitted by A from a distance of V1t
reaches the material point B, B would
have travelled further away by a factor V2xt1, where t1 is the
time taken by the light to reach B.
Equating distances, we get,
V1xt + V2xt + V2xt1 = Cxt1
Where C is the velocity of light.
t (V1 + V2) = t1 (C V2)
i.e. t = t1 (C V2)/ (V1 + V2).
T1 is the observed time. What is t?
t is the time lapse after the Big Bang according to our
assumption. By such a computation, we are
arriving at the age of the material point A when it did emit
light. It is clear that t1 can be equal to t
only when
V1 = V2 = 1/3 C.
Otherwise, we cannot take the observed time in light-years as
the age of the material point A in years.
(The very concept of diametrically opposite points has no sense
in the Astronomical volume of things
but I have chosen this in an arbitrary sense. After all, where
is the Centre point of this Big Bang?)
Another fact to be noted here is that we can compute only V1 +
V2 and not V1 and V2 separately,
because we havent in the Astronomical scale a third referential
static point which can tell us at what
velocities A and b are moving with reference to the static
point. When we say that one galaxy is
receding from us, we cannot directly say whether that galaxy is
static and our own moving away from
it. Only, in a relativistic manner can we say that the other
galaxy is moving away from us. It can be
that our own galaxy is moving away and the other one remains
stationary. Absolute velocities can be
computed only with reference to a static point. When we say that
the Galaxy A is moving away from
Galaxy B, we presume that Galaxy B is stationary or moving
rather very slow. At the Astronomical
scale we can find velocities only in a compounded manner. That
is, when we say that the velocity of
recession of Galaxy is x, it need not be the absolute velocity
of the Galaxy since the measuring
instrument on our Galaxy which is not stationary has got the
velocity of our Galaxy.
Now, the picture is clearer. Time is related to the concept of
velocity rather change and
displacement and distance and compounded velocities give rise to
one kind of notion of time
whereas Absolute velocities give rise to another kind of notion
of time. This is my view.
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Note:- The above article has been reproduced from my notes
titled Magic Moments with
Mathematics which happens to be a compilation of my works done
in Mathematics. This article is
undated and I cant now recall what exactly had prompted me to
explore this particular one.
