Hauser Smaller Than Planck

7/29/2019 Hauser Smaller Than Planck

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1. Transparent time

If there is a theory which allows you to makea computer based simulation of physicalprocesses, then according to Church-Turingthesis there are many other representationsof physical objects together with othersimulations which lead exactly to the samepredictions. There is a difference however,the different amounts of computing time.Computational scientist often try to find acomputer simulation, which can do asimulation as fast as possible. Lets supposethere are two theories with two simulationprograms S1 and S2. In time interval T1 it isS1 which is the faster program. In timeinterval T2 it is S2 which is the faster, and inT3 again S1 is faster. Now it is a good idea

to use first S1, then transform the data to therepresentation of theory 2, run S2 for theinterval T2, and transform back for S3.

Simulation S1(T1)

Transformation S1 -> S2

Simulation S2(T2)

Transformation S1


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Fig 1: Two optimal "theories" or histories.One theory (left) with 2 timetransformations (green) and 7 time steps

(orange), and one theory with 4transformations and 5 time steps.

Let me call the time complexity which isconsumed by the transformations atransparent time. Is transparent time a usefulconcept with real world consequences?Does the internal representation matter?Could it be that the time differenceexperienced by the twins in the twin paradoxis a difference in transparent time? I

hypothesize that the answer to these threequestions is yes. More about transparenttime you find here, in section 2 and 11 and inTab 1. Sections 3 to 10 are independent ofthis idea.

Unnoticeable transformations by a systemlead to transparent time.

There is this famous twin paradox, whereone of the twins sits on the sofa while theother is travelling to the fridge to fetch two

beers. After returning they meet at the sofa,and surprisingly the one who did thetravelling has aged less. To make the effectmore dramatic the fridge is usually located inanother star system or so. Transparent Timeis system dependent. It is not unique.

2. Global time

Global time is the sum of ordinary time plustransparent time.

Global time = time + transparent time

The twins in the twin paradox do not agreeon the time which has passed. However, Iargue, they should agree on the global time.

Hypotheses: Everything you observe orexperience at an instant does have equalglobal complexity or equal global complexity

bound.Global time is a computational timecomplexity measure for the simulation of acausal cycle as in John Cramer'sTransactional interpretation1.

3. Underlying time

What Cramer calls pseudo time, I would liketo call underlying time. I consider this type of

time as more fundamental than our ordinarytime from previous sections. Contrary toCramer I consider this ordinary time as akind of pseudo time. It does not determinethe causal order of the universe. To avoidfurther confusion I will avoid the termpseudotime in this essay except when referring toCramer's terminology as Cramer's pseudotime.

4. Final or intermediate equilibrium

An observation by an observer may be either

1. a final equilibrium, or

2. an intermediate equilibrium

of physical processes happening inunderlying time.

The first of these two Hypotheses finalequilibrium is sometimes claimed inconnection with the Block universe. Thesecond intermediate equilibrium could becompared to a modified block universe view.

The immediate equilibrium view versioncould be compared, instead to a frozen river,to a melting glazier. The glazier is growingfaster on one end than it is melting on itsopposite end. That is what glaziers indeedsometimes do, when it is getting colder, andan ice age is approaching.

5. Equilibrium with the past

There is an equilibrium with the past, or to be

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Underlying time (Ordinary) timeor internal time

Transparent timeor external time

Global time

Known in Implicitly assumedin manyargumentationssuch as time travel

Part of space timein GeneralRelativity

Time difference intwin paradoxequals thedifference of

external time

Coincidence oftwo events onlyif identical globaltime

Similar to JohnCramer's pseudotime

Suggestedinterpreta-tion

Fundamental(ontological) time.Complies withcausal order ofinstances of objects.

Internal complexitycomponent of object collections.

External complexitycomponents ofobject collections.Complexity of general covariancetransformation.

Sum of ordinarytime + externaltime.

Properties Not unique, butobserverdependent.

Not unique, butobserverdependent.

Unique

Filmproductionanalogy:

Film productiontime. The timewhich passes whilethe film crew,producer, actorsand computerscreate ever

improved versionsof all parts of themovie. Analternativeanalogy would bethe movie versionnumber.

The story time.The time acomparse withartificialintelligence mayexperience or atleast claims to

experience in adigital animationmovie.

Delays from localproblems. Possibleproblems areincompatiblelanguages of actors,incompatible video

data formats,replacement ofbroken computer,swap file to small.

The film framenumber.Alternatively, thetime the viewerof a strictlychronologicalmovie

experiences,unless he goesto fetch a beer.

Relations (Ordinary) time + Transparent time = Global time

Underlying timeat which a final

or intermediateequilibrium isreached or lostis related to ...

Global time

Tab 1: Comparing different types of time


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more precise, with the current version of thehistory. Viewed in underlying time the past isconstantly adapted to the new present. Pastand Present are in equilibrium. Thedecreasing of the size of phase space whengoing back in time is compensated by agrowing number operators of higher order.

Or could we say by a growing number ofparallel universes?

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Fig 2: The Block universe growing whileunderlying time proceeds. It is thenstable.

Global complexity

Fig 3: The Block universe in the pictureof the glazier which is melting on oneend and growing on the other end while

underlying time proceeds. Theinformation may survive by moving intodomains of higher tensor order, lying atthe same time.


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Fig 4: Time epochs of paths with critical times such as Planck time. This is a snapshot of theuniverse at a particular point of underlying time. For the classes C1, C2, C4, C6, C8, C12and C16 the critical times are indicated. Approximate times are given not in seconds, just inpure numbers (underlying Planck units). Paths do start at the left hand side of this graphicand pass through several of the indicated epochs. Class Ci indicates that tensors of order iare present and tensors of the order (i/2) have reached an intermediate equilibrium. The rightpart of the graphics is based on the excellent graphics of NASA / WMAP Science Team(http://wmap.gsfc.nasa.gov/), but I have changed the type of projection to show anotheraspect, the uniform expansion of the universe, according to logical (operator) space. Varyingratio between time and transparent time may be responsible for perceived acceleration ofexpansion of the universe. In this space all the laws of physics plus the universe(s)

themselves, become united in a single space.

10120

C4

Age of

universe

10480

C1

1060

C8

Planck

time

1080

C6

Space time

1040

C12

Boson

Particle

index

1030

C16

Graviton

Particle

sub-

component

index

Particle

type

index

World

Index

?

Particle

path

10240

C2

Sketch


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6. Paths through space time andthrough other domains.

A fundamental object does contain one ormore path objects. A scalar object maycontain a single path object, a vector twopath objects and tensor objects contain nobjects if the order is n. Each path objects iscomposed of several path epochs (seeFig. 4). Only the Space time -epochactually corresponds to traditional paths inphysics. If there is an intermediateequilibrium from the present with the currentversion of the past, we get from entropiebased considerations:

(ti )(i/k) >= t2

Where I did set k=2. The tensor order ofobjects which are in intermediate equilibriumat time ti is i/k with k=2. Then the number ofpath objects per object equals the tensororder i/k. Now we get complexity classes Ci,where i denotes the tensor order of thosetypes of objects where at least some arepresent.

This gives you a tower of uncertaintyprinciples, one principle for every possiblevalue of i. To each of these complexity

classes C1, C2, C3, corresponds a criticaltime ti =

i

t22

=i

h2 and each of thetimes t1, t2, t3 in this decreasing seriesmarks the beginning of a new domain ofphysics. Each domain has got its ownversion of an uncertainty principle. You arriveat an at least partly convincing picture forexample when t8 corresponds to Plancktime. Then Planck time is not the smallestcritical time. Its value here is 1060. Most ofthe critical times are smaller.

The Heisenberg Uncertainty Principle can bemade plausible by the fact that a physicalparticle consists of a large number ofsubcomponents. The number of particles isrelated to the size of the particlesubcomponent exchange equivalence class.Carl Adam Petri the inventor of Petri nets,has suggested that propagation physicalparticles is realized through a network ofexchanges from momentum into positionand vice versa. Of course the Schrdingerequation also shows momentum - position

oscillations. This information may help to

identify the particle subcomponent exchangeclass. It may be C6. In the above examplethat equivalence class does have the size of10^80.

7. Tower of uncertainty principles

The series of uncertainty principles, if h =10240, are as follows:

Tensororder

i ti

1 Time with no objectsyet

>= 10480

1 2 Planck constant,Age of future sketch

universe

>= 10240

2 4 (Age of universe)2 >= 10240

4 8 (Planck time)4 >= 10240

3 6 x . p >= 10240

= h

... 10240

Tab 2: All values are in underlyingPlanck units

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Planck time is therefore not the minimalinterval of time. Two of the series ofuncertainty principles determine the age ofthe universe and the Planck time. A third isidentical to the well known Heisenberguncertainty principle. At this point we haveenough equations to fix units such as kg,meter, seconds.

Gravitational G constant turns out to beidentical to the age of the universe. Thismeans that G will grow at the same rate as

the universe as Dirac had anticipated. Sucha strong growth is supposed to becontradicting with experiments. But here Iactually assume that the past does getchanged. Therefore when we observe thepast, we might see an effective Gravitationalconstant which has already partly reached itspresent value.

Further equations and their associatedclasses are expected to correspond to otherknown and yet unknown physical

components.

8. A digital principle instead of generalcovariance

General covariance (also known asdiffeomorphism covariance or generalinvariance) is the invariance of the form ofphysical laws under arbitrary differentiablecoordinate transformations.(http://en.wikipedia.org/wiki/Diffeomorphism_invariance). If we believe that the universe isdiscrete or digital, this principle is notapplicable, since then nothing isdifferentiable. Is there an correspondingprinciple to the covariance principle in thedigital world. I would like to suggest a strongbut simple digital extension of the principle. Itassumes that the universe consists of amultiset of objects which are operators. Theproposed digital principle then states thatevery operator is the immediate future of anyother operator.

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Fig 5: Snapshot of the block universe at a fixed point of underlying time, in otherwords the current version of the history. While time traveling (at an instant ofunderlying time) back in (global) time to the left hand side you are getting in domainswith tensors of higher and higher tensor order. Each additional order introduces alsoa new global time: second, third, forth... global time. The maximum of the sum of allglobal times is always given by the global complexity. Global complexity is related tounderlying time. The yellow global time arrows are just three examples.

C1

C2

C8

C6

C4

C3

3. Global

time

Global time

S

econd

G

lobaltime

Globaltime

GlobalComplexity

87. 6. 5. 4.


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Everything is immediate future of everything

If X and Y are objects in the universe (notnecessarily distinct), then Y is immediate futureof X.

Here immediate future stands for direct

causal consequence. If X and Y are objectsin the universe, then Y is immediate future ofX. From this it also follows that X isimmediate future of Y and we get a causalloop. John Cramer has suggested suchcausal loops while explaining hisTransactional Interpretation of QuantumMechanics. They occur at specific points inthe universe where waves are emitted orabsorbed, when a Transaction is formed.This is impossible to happen in ordinarytime. The loop is supposed to be passedthrough in another type of time, whichCramer calls pseudo time. These loops helpto explain entangled quantum mechanicalstates. Above mentioned Digital principleleads also to such loops, to tiny transactionsif you like, but unlike in Cramer's case wherethey occur only between specific points, theyoccur between any pair of space time pointsin the (history of the) universe. Theimportance of particular loops may beextremely low in most cases though.

However the existence of them is important.This is similar to Quantum Mechanics whereit is in principal necessary to include allpossible paths including incredibleimprobable ones, like those, which make thecup of coffee suddenly jump up one meter.

9. Discretization of tensor fields

One natural way to discretize tensors whichtransform tensors into tensors is by meansof operators which substitute substitution

operators by substitution operators. They dohave the form of binary trees.

10. Discretization of differentialequations.

It is a mathematical theorem that differentialequations in physics are equivalent tovariational principles. Thus if you have asystem where all variations are actuallyhappening and wait until the system gets intoan equilibrium, this could means that thevariational principle is automatically fulfilled.

The equilibrium condition automatically iscompliant with the corresponding variationalprinciple. I did not prove this. Max Tegmarkamong others has suggested theories whichinclude all of mathematics.

11. Time travelling and inter-universaltravel

Unnoticeable transformation between timesor maybe even between universes does just,as any other unnoticeable transformation,introduce a transparent time which may bethe cause for perceiving acceleratedexpansion of the universe.

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1 The Transactional Interpretation of Quantum Mechanics, John G. Cramer

http://www.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html

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Hauser Smaller Than Planck