The empirical evidences in favor of the hypothesis that the speed of light decreases by a few centimeters per second each year are examined. Lunar laser ranging data are found to be consistent with this hypothesis, which also provides a straightforward explanation for the so-called Pioneer anomaly, that is, a time-dependent blue-shift observed when analyzing radio tracking data from distant spacecrafts, as well as an alternative explanation for both the apparent time-dilation of remote events and the apparent acceleration of the Universe.

Before one can speak about change of c seriously, one must specify precisely what the measurement of speed of light means. In GRT framework speed of light is by definition a constant in local Minkowski coordinates. It seems very difficult to make sense about varying speed of light since c is purely locally defined notion.

- In TGD framework space-time as abstract manifold is replaced by 4-D surface in H=M
^{4}×CP_{2}(forgetting complications due to the hierarchy of Planck constants). This brings in something new: the sub-manifold geometry allowing to look space-time surfaces "from outside", from H-perspective. The shape of the space-time surface appears as new degrees of freedom. This leads to the explanation of standard model symmetries, elementary particle quantum numbers and geometrization of classical fields, the dream of Einstein. Furthermore, CP_{2}length scale provides a universal unit of length and p-adic length scale hypothesis brings in an entire hierarchy of fixed meter sticks defined by p-adic length scales. The presence of imbedding space M^{4}×CP_{2}brings in light-like geodesics of M^{4}for which c is maximal and by a suitable choice of units could be taken c=1. - In TGD framework the operational definition for the speed of light at given space-time sheet is in terms of the time taken for light to propagate from point A to B along space-time sheet. In TGD framework this can occur via several routes because of many-sheeted structure and each sheet gives its own value for c. Even if space-time surface is only warped (no curvature) this time is longer than along light-like geodesic of M
^{4}(×CP_{2}) and the speed of light measured in this manner is reduced from its maximal value. The light-like geodesics of M4 serve as universal comparison standards when one measures speed of light - something which GRT does not provide.

What TGD then predicts?

- TGD inspired cosmology predicts that c measured in this manner increases in cosmological scales, just the opposite for what Louise Riofrio claims. The reason is that strong gravitation makes space-surface strongly curved and it takes more time to travel from A to B during early cosmology. This means that TGD based explanation has different cosmological consequences as that of Riofrio. For instance, Hubble constant depends on the space-time sheet in TGD framework.
- The paradox however disappears since
*local systems*like solar system do not normally participate in cosmic expansion as predicted by TGD. This is known also experimentally. In TGD Universe local systems could however participate cosmic expansion in average sense via phase transitions increasing Planck constant of the appropriate space-time sheet and thus increasing its size. The transition would occur in relatively short time scales: this provides new support for expanding Earth hypothesis needed to explain the fact that continents fit nicely together to form single super continent covering entire Earth if the radius of Earth is by a factor 1/2 smaller than its recent radius (see this). - If one measures the speed of light in local system and uses its cosmic value taken constant by definition (fixing particular coordinate time) then one indeed finds that the speed of light is decreasing locally and the decrease should be expressible in terms of Hubble constant.
- TGD based explanation of Pioneer anomaly can be based on completely analogous reasoning.

** Addition**: I added a videoclip about varying light velocity here.

For background see for instance the chapter TGD and Astrophysics of "p-Adic length Scale Hypothesis and Dark Matter Hierarchy".

## 33 comments:

Before some time I wrote about experimental evidence of variable light speed. Here are many, in fact.

BTW the correct link to ArXiv article.

The point is of course what one precisely means when one speaks about light velocity. My view is that abstract four-manifold geometry of GRT does not allow the addition of variable speed of light to the vocabulary. In many-sheeted space-time rich structure emerges and could also explain the variation of Hubble constant.

The link should be now correct. Thank you very much.

/*..My view is that abstract four-manifold geometry of GRT does not allow the addition of variable speed of light to the vocabulary..*/

I presume, it can be done in rather straightforward way. Constant speed of light is a postulate of special relativity theory, but not general relativity - so in principle general relativity doesn't depend on Lorentz symmetry until someone proves it in explicit way.

Constancy as such is not relevant. Constancy can be achieved always by choosing coordinates suitably by general coordinate invariance. Comparison to a standard is involved with every measurement since dimensionless ratio is what one obtains as outcome. I am unable to see any other manner to achieve this than replacing abstract geometry with sub-manifold geometry. Light-like geodesics of M^4 provide the standard to which light-like geodesics of space-time surface are compared.

If you can give me a precise prescription how to make the speed of light variable in GRT context without giving up general coordinate invariance, I am ready to listen.

The variation of light velocity in the sense as it is define in measurements is of fundamental importance for the entire world view. Unfortunately particle physics colleagues regard this as physics of eighteenth century and could not care less.

The refined mathematical methodology of recent day theoretical physics is useless if the theoretician is not sensitive to the messages carried by these tiny irritating anomalies. Sadly, anomalies are put under the rug completely routinely one after another since real world is abstracted to a low energy limit of some TOE expressible in terms of Einstein-YM action for some gauge group allowing symmetry breaking to standard model gauge group. At the same time colleagues are passively waiting for LHC as a Messiah bringing the light.

This attitude is the tragedy of modern physics and landscape farce will be seen as the symbol of ultimate blind alley.

/*..if the theoretician is not sensitive to the messages carried by these tiny irritating anomalies..*/

This is an inherent property of most of theoreticians. They developed theory as a subject of belief, just because they spent a lotta time with them. No wonder, they tend adopt reality to their theories - not vice-versa.

Albert Einstein: "If the facts don't fit the theory, change the facts."

In this way, if such theoretician falls into black hole, he can still consider path of light straight and space-time curved, even at the moment, when he is revolving black hole "at place". From his strictly local perspective is still everything in perfect agreement with relativity - while everybody can see, path of light is curved heavily.

These connections are quite easy to understand - but from the above follows, general relativity has nothing to say about gravitational lensing and relativistic aberrations, because these effects are quantum gravity effects in fact.

/*..i am unable to see any other manner to achieve this than replacing abstract geometry with sub-manifold geometry...*/

Providing the fact, general relativity is able to describe the curvature of space of whatever complexity, I can imagine, GR can describe nested foam in pure geometrodynamics way. You can imagine, how general relativity describes complex gravity field between stars with many overlapping Lagrange points. In this way it would be possible to emulate submanifold geometry and solve it in numeric way, at least conceptually.

Of course we can use a nested manifold approach (like Bekenstein has used), but its a simplification of real problem, i.e. a replacement of complex problem by more complex approach. This doesn't say, TGD framework is uselles - on the contrary - but the true appearance of vacuum is a nested foam composed of density fluctuations, formed by many nested curvatures of space (which are itself formed in simmilar way).

Every formal model of such hypercomplex system is just a high level approximation of it. If you cannot see it, then it's just you, who is in position of theorist, who cannot see tiny divergences of your model by now.

Therefore do believe, the only universal approach is to simulate it by particle collisions in simmilar way, like we can model turbulent solution of Navier-Stokes equations by particle simulation in much easier, stable and general way.

Dear Zephir,

it seems that you are confusing the notions of geometry and sub-manifold geometry and badly misinterpreting what TGD really is.

The emulation of sub-manifold geometry is impossible in GRT framework because the very notion of sub-manifold geometry brings in a rich variety of new structure which abstract four-manifold does not possess. The habitant of flatland cannot experience what it is to be a habitant of 3-D space.

A unique choice of imbedding space gives rise to exact conservation laws of energy and momentum and explains standard model quantum numbers. You can geometrize classical gauge fields in terms of induced spinor connection. Baryon and lepton number conservation follow automatically, etc, etc... This is something which you simply cannot get out from GRT.

The anomaly discussed here is just a one representative of a plethora of anomalies directly demonstrating the signatures of sub-manifold geometry and put under the rug.

From above it should be clear that TGD is not some exotic approximation of GRT but a completely new theory which fuses special relativity and general relativity and also generalizes string models by replacing strings with light-like 3-surfaces and in this manner generalizes the super-conformal symmetries of string models.

Can you illustrate some simplest possible connection to observable reality of your theory?

This depends on the person with whom I am trying to communicate.

The 7 books of basic TGD where practically whole physics have been gone through should be more than enough. Combined with 8 books about quantum biology and consciousness they should give quite a detailed view about connections with reality.

Reader must however have rather strong background in mathematics and physics in order to understand. Theoretical physics at fundamental level is really hard science nowadays and there are no free lunches. Good luck!

Look, in discussion here I predicted/explained by using of few sentences here, why and how AWT model of vacuum predicts

1) foamy structure of vacuum

2) why observable Universe is of limited age and size

3) why vacuum is the most vast space-time observed

4) why vacuum exhibits dispersion for gamma rays

5) why such dispersion isn't observable for visible light

6) why huge gamma ray flares doesn't exhibit a dispersion

7) the observation of Hubble red shift and Big Bang model

8) Why string theory cannot predict it in compare to LQG

9) Why both these theories converging into foam model

10) Why string theory has no observatory evidence, although they're many of them, in fact

11) Why only objects with positive surface curvature can be observed

12) Why only objects with positive curvature have zero rest mass

13) Why causual creatures see the foamy structure only but not longitudinal waves

14) Quantization of energy spreading in vacuum

15) Why light is the highest speed observable form of energy, which can propagate through it.

...etc.

Until you prove, by using of AWT we can derive different conclusions, my explanations remains valid and testable. So...

Can your theory explain/predict at least something from the above? Are you really trying to find simplest possible explanation of reality by Occam's razor criterion?

As far I know, you developed a nice formal model of something - but can you compute/predict at least something testable by using it? Can you propose such formula?

Do you really understand, what your model does? Isn't it more abstract and difficult, then the reality itself? Isn't your theory just another version of string theory fantasy?

Hi Matti, ( If I may be so presumptuous )

I hope this is not too far off-topic but it does have to do with the Universe, if not please forgive me for not waiting for the right post.

I presented some of my premise below to Mahndisa Rigmaiden and she though it was worth running by you and so here it is. As I told her I hoped that it would not be laughed at and said that she found it very interesting and worth running by you.

I formulated this idea many years ago when I first heard of the big bang and also before I ever heard of a White Hole. And it began with the following thoughts:

There must be opposition to everything in order for there to be Free Will and choice. For example, Matter/Anti Matter, Positive/Negative, Up/Down, Left/Right, etc.

So, if the Yen and Yang are just as true in Physics as everything else, well therefore..... A Black Hole must mean there is a "White Hole".

I think that there is a Multi-Verse, where there are a myriad of Black Holes that are gateways to other universes and that Black Holes are the way in which Universes are Created? Kinda like a really big bubble with smaller bubbles attached through a black hole as the gateway.

For example, what if a Black Hole in another Universe gathered matter until critical mass and out of the other side of the Black Hole came a White Hole or in other words a "Big Bang" and voila, a new universe?

Meaning if a Black Hole "sucks in matter" and turns it into energy, then the other side of a Black Hole might "explode" with energy, which becomes matter. Kind of fulfilling the cycle of energy-to-matter and then matter-to-energy.

This would then mean that all matter has always existed and it would futher mean that the statement “nothing can neither be created nor destroyed” takes on new meaning.

As it is I believe I have read that many think that the “Big Bang” means that the Universe was created from nothing, (and/or that God was the cause that made the effect of the big bang), and this premise of mine would certainly be an interesting counter argument to that premise.

Anyway….your thoughts?

Gary (FreeAgencyRules)

P.S.

I forgot to add, that our Universe expands until it becomes the really big bubble with smaller bubbles creating other universes.

I see there is a big crisis in the nowadays physics and Einstein

soon probably wiil be lynched.

One person asked me to promote

his work:

http://www.gpofr.com/default.aspx

What about it?

To Gary:

I have not thought white holes from TGD point of work. White holes can be regarded as time reversals of black holes. Both attract matter but the initial conditions at horizon are different so that the flow of matter is outwards.

One speculation is that the throats of wormhole like object behave as black and white hole respectively and the matter flows between two universes through the wormhole.

Also I speak about wormhole contacts and wormhole throats but in different sense. TGD wormhole contacts have very small size of order 10^4 Planck lengths). They are light-like 3-surfaces as are also horizons. The interpretation is however as gauge bosons. The region between throats has Euclidian signature of induced metric and also this is something totally new. These light-like surfaces do not expand unlike light-like surfaces in 4-D Minkowski space.

To Anonymous: I agree about crisis but not about the fate of Einstein. In fact, when space-time is regarded as a 4-D surface the real power of Poincare invariance, General Coordinate Invariance, and Equivalence Principle becomes manifest. For instance, Einstein's geometrization program of physics finds elegant realization in both classical and quantum sense and classical physics becomes exact part of quantum theory and space-time surfaces are analogous to Bohr orbits.

What is in crisis is the naive GUT type view about generalization of standard model and string models which rely on this vision and recent view about supersymmetry. Also the naive reductionistic view about reduction of physics to Planck length scale must be given up if we want to make progress.

Colleagues must sooner or later return to the roots and start doing TGD but this will take time since I have no intention to die within decade or two;)! Be patient: the progress begins immediately when the flow of postings to my blog has ceased!

The claim of the page that you refer is that Jupiter's rest mass equals to electron charge. This makes no sense to me. The quantities in question have different dimensions and by choosing the units suitably you can make any dimensional quantities numerically identical.

To Zephir,

concerning predictions of TGD I can repeat my suggestion: perhaps you might read what I have written in the books at my homepage and also in previous responses;-).

[You could perhaps start from p-adic mass calculations reported in one of the books.]

It seems that you have not bothered to do this yet: probably because you do not want to lose your prejudices so essential for ego conservation. You are in a good company in this respect;-).

I have no intention to die within decade or two;)! Be patient: the progress begins immediately when the flow of postings to my blog has ceased!

Happy to hear the first, but why the second? Is it so hard to communicate?

To Anynymous:

Bohr said once that a new idea makes breakthrough only after the proponents of the old idea are dead.

Bohr did not say all. On basis of my experiences I have become fully convinced that my colleagues do not allow me to experience the day when breakthrough comes. The progress in physics ceases for a few decades but the joy of revenge more than compensates the loss.

This has also much to do with a very special feature of finnish society. Some time ago both Finnish peace Nobelist Ahtisaari and Ollila - the former leader of Nokia - regretted this special feature. In Finland we do not tolerate someone raising above the average and the Dear Brother net - a form of corruption very characteristic to Finnish society - successfully isolates this kind of people from community. I have been doing 30 years TGD: PhD 1982 after John Wheeler had evaluated my first published article and regarded the work as brilliant. After that I have done an enormous amount of work materialized in 15 online books. Despite this I have never got a job as researcher and not a single grant. Beware of Dear Brothers!

Ever thought of leaving Finland? ;D

Best wishes,

André

To Andre K:

When I was younger, yes.

Finland is something as Austria,

this is my notion about it.

You know Matti, I read this morning one old article

Dark Matter Chemistry For Mind

and it flashed me. Everything

with this critical point in the

human evolution, predicted even

in a mathematical way for the next

years is connected with the jump

onto a new level of awareness.

But I wanted to ask you how do you see the lateralisation of the

functions of the brain(mind) from

the POV of your theory.

It seems that dark matter based vision about biology is rapidly diffusing from my homepage;-). As a rule, the people seem to forget where they saw the idea in the first place;-).

Right brain sings- left brain talks metaphor might be a useful starting point if one wants to understand right-left brain duality (I do not know how generally this duality is accepted nowadays). Brain hemispheres could build different kinds of cognitive representation of sensory input and communicate them to the respective magnetic bodies. Function and its Fourier transform could be the mathematical correlate for the left-right duality.

Right brain could abstract patterns in frequency space and therefore represent holistic aspects of temporal patterns. Frequencies associated with Fourier transforms of correlation functions for temporal pattern instead of pattern as such could be in question.

Left brain could abstract short time scale temporal patterns such as rhythm in music. This would be the correlate for left brain as analyzer interested in precise details.

This kind of division of labor could occur in all time scales and also inside brain hemispheres. Left-right brain division could represent only one particular time scale.

You are maybe right, but there is

something more ontologically. And when the the talking is not

corresponding to the singing one

can say: "There is left me only one soul." Why people say so.

Aren’t physical and metaphysical

conjugating at the continuum.

I think there is a place in us

of a full accordance. That’s why the children’s reminescences are

so bright not only because of the

ontogenesis and even in the words

said(talking).

Excuse me Matti, I forgot to ask

you what do you think about the

time of Kozyrev. I saw your name

somewhere on the Russian sites

next to his and maybe you are

known with his investigations.

To Anonymous:

sorry, I did not get the meaning of "There is left me only one soul" and cannot answer.

Kozyrev claims that he has detected three kinds of signals from distant astrophysical objects, at distance L. One normal and representing object as it was time t=L/c earlier, second time t=L/c in future, and one more or less instantaneous signal. This would be what zero energy ontology predicts.

Phase conjugate photons (and phase conjugate counterparts of all kinds of particles) would represent negative energy signals propagating to geometric past.

Here it is essential to distinguish between experienced time and geometric time: otherwise what I have said sounds pure nonsense.

If the effect is real it would have interesting consequences. Consider only predicting catastrophic events by receiving signals from the geometric future!

I will comment Kozyrev's time density concept in second posting.

Dear Anonymous,

I have not really understood Kozyrev's notion of time density but in the model explaining the arrow of subjective time and the localization of contents of sensory experience to a short time interval I ended up with a picture which might have something to do with Kozyrev's view.

a) Fractal hierarchy of 8-D causal diamonds (CDs) defined as Cartesian products of intersections of future and past direct light-cones of Minkowski space with CP_2 represents imbedding space correlates for selves (one can consider also space-time sheets as these correlates).

b) The conventional view about time would suggest that these CDs would move towards geometric future: each quantum jump would shift them to either direction in time of 8-D imbedding space M^4xCP_2 and in average sense to future. This was my original view but with space-time sheets serving as correlates of selves. One cannot exclude that also this kind of process takes place.

c) My recent view is however different since it explains in terms of consciousness theory why arrow of time emerges.

CDs would not move anywhere. Rather, each quantum jump would shift the quantum superposition of space-time surfaces representing the system towards geometric past. Self would be like audience sitting in 4-D movie theater and seeing the film coming from geometric future. The theorizing self would develop the illusion that it is movie theater which is moving towards geometric future.

The basic questions are why the arrow of time emerges and why the sensory experience (but not memories) are sharply localized in time.

a) The answer is basically that selves are curious! What is unknown to self is represented by the regions of space-time surfaces outside the CD and self intentionally induces quantum jumps shifting the quantum superposition of space-times so that this region enters to the field of perception represented by CD.

b) The unknown and interesting regions of space-time sheets are above and below the future and past directed light-cones representing the boundaries of CD definign the 4-D perceptive field of self.

Self must select either of them. The selection of the direction in which film runs represents spontaneous symmetry breaking and kind of domino effect implies that all selves make the same choice. The breaking of time reversal (T) equivalent breaking of CP invariance might be involved with the selection.

By the way, during my great experience about 25 years ago, I had direct and very frightening experience of what it feels when the arrow of experienced time changes temporarily. Also one of my childhood friends had had the same experience.

c) One must also understand why sensory input is not from the entire CD but mostly from either light-like boundary of CD (light-cone)- which could be called the "future"/"upper" boundary. The localization of the sensory input to a small time interval - the duration of subjectively experience moment of time (about .1 seconds for humans)- could mean that the sensory mental images representing sub-selves populate the region near the upper light-light boundary of CD. The population of sensory mental images -sub-CDs-live here because in this manner news emerge to CD there and create mental images-subselves!

d) Memories would represent sub-selves- mental images populating the other regions of CD. Childhood memories are very lively creatures and often survive when other memories are lost. Maybe these memories represent sub-selves hanging around the lower boundary of CD.

The density of these subselves (mental images,sub-CDs) concentrated near the upper boundary of CD might have something to do with Kozyrev's time density. The density would also measure also the intensity of a particular kind of consciousness: that with sharp experience about time. In some meditative states subselves might tend to populate entire CD (also the view about time of aboriginals comes in mind here).

The time is a geometrical

quantization of the possible

jumps and transitons in all

scales, isn’t it. Excuse me

if I’m naive and inexact in

the words. This can explain

the results of Kozyrev and

the time anomalies on the

places of landing of the UFOs.

Changing the possibilities

can influence the time measured

or perceived.

Well, today I realize I was

carried away by the time to

explain it. I have to read more.

But there is something like

this mentioned higher up. It downed on me spontaneously,

thinking and summarizing some events. The results of Kozirev are surely true, but they are caused of something else and

not of the time as a substance.

You know when I was drowning

at 6 the time had stopped.

/*..concerning predictions of TGD I can repeat my suggestion..*/

Why I should read your books, if you cannot give me such trivial prediction after years of writting them? Such approach has no meaning for me..

BTW Matti, where is your essay about the time. I couldn’t find

it. As I saw from the winners I’m

not so far from the thruth. There

is something like a closed reality

between mathematicians and physicists, which is changing

every day and every minute, but

people stay in the Newton’s world

and you too. When people will learn to fly.

Zephir, did you have difficulties in understanding written text? If you don't like it there is no "have to". It is all free will. Completely unnecessary to be rude. It harms nobody else than yourself.

Excuse me Matti, I have forgotten,

I have seen About the Nature of Time. It is maybe your essay for the contest.

To Anynomous: About the Nature of Time should be in fQXI page. It is also at my homepage.

To Zephir:

you have been quite active recently. If you goal has been to generate with your silly comments deep disgust in people wishing having genuine interest to discuss, you have managed. If you do not stop sending this idiotic spam I will delete your messages from now on.

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