### Changing Light Speed

Thanks to Carl Brannen for pointing out a new paper by Sanejouand, Empirical evidences in favor of a varying speed of light. The paper summarises results from lunar laser ranging, the Pioneer anomaly, supernovae redshifts and the known fixed constants, namely fine structure and Rydberg. He finds that the varying speed of light hypothesis is (a) consistent with all these results and (b) explains the results that the Dark Force cannot.

Assuming fine structure, Rydberg and electron charge to be truly constant, one must have constants

$\epsilon \hbar c$ and $\frac{m_e c^{2}}{\hbar}$.

There are then two natural alternatives to consider under the varying $c$ hypothesis. First, if the electron mass is constant in cosmic time, we find that

$\frac{c^{2}}{\hbar}$

must be constant, forcing $\hbar$ to vary, but not as in the usual description of Louise Riofrio's cosmology. Because $\hbar c$ cannot then be constant, fine structure depends on a variation in $\epsilon$. Secondly however, if we assume that $\hbar c$ is constant, it follows that the electron mass $m_e$ must go as $\hbar^{3}$. That is, electron mass starts out at zero and grows larger with Riofrio's cosmological law $M = t$. This is also reminiscent of Penrose's thermodynamic cosmology.

Note that the latter alternative would not prevent, in principle, the computation of local mass relations; only the computation of absolute scales. Such a cosmology, at least initially, therefore relies on precisely one parameter, which is a measure of our epoch.

Assuming fine structure, Rydberg and electron charge to be truly constant, one must have constants

$\epsilon \hbar c$ and $\frac{m_e c^{2}}{\hbar}$.

There are then two natural alternatives to consider under the varying $c$ hypothesis. First, if the electron mass is constant in cosmic time, we find that

$\frac{c^{2}}{\hbar}$

must be constant, forcing $\hbar$ to vary, but not as in the usual description of Louise Riofrio's cosmology. Because $\hbar c$ cannot then be constant, fine structure depends on a variation in $\epsilon$. Secondly however, if we assume that $\hbar c$ is constant, it follows that the electron mass $m_e$ must go as $\hbar^{3}$. That is, electron mass starts out at zero and grows larger with Riofrio's cosmological law $M = t$. This is also reminiscent of Penrose's thermodynamic cosmology.

Note that the latter alternative would not prevent, in principle, the computation of local mass relations; only the computation of absolute scales. Such a cosmology, at least initially, therefore relies on precisely one parameter, which is a measure of our epoch.

## 15 Comments:

Can I ask what you mean when you say "cosmic time"? I'm guessing it's something non-standard...

And a minor comment: let's all remember that only dimensionless quantities are physically meaningful. Discussion about these sorts of issues often seems confused due to a failure to acknowledge this point.

Kea, want a shock? Look at equation (21) in Two knees and the Evasion of Greisen-Zatsepin-Kuz'min Cutoff in Cosmic Ray Spectrum -- Are Neutrinos the Tachyons? Guang-Jiong Ni, Zhi-Qiang Shi, hep-ph/0605058. For those who don't recognize it, compare with (11) in Sheppeard and Brannen. And by the way, how come I couldn't find our paper on Vixra?

It's on vixra at vixra:0907.0011

By the way there is now an RSS feed at http://vixra.org/feed/rss.xml

Rhys, you cannot be serious. The speed of light is

dimensionful. It is something we can measure. I fail to see how it cannot bephysically meaningful.We have all heard the pathetic arguments against variation of dimensionful parameters. It is somewhat analogous to saying that planetary orbits can only be circles. The simplest, and most

naturalway, of explaining things just does not keep constants constant."The speed of light is dimensionful. It is something we can measure."

I don't know of any way of measuring a dimensionful quantity which doesn't boil down to comparing it with another quantity of the same dimensions. In other words, it seems to me that we only measure dimensionless ratios. If you can demonstrate that that is wrong, I'm willing to listen.

And I'd still like to know what you mean by "cosmic time"! I'm guessing it's the 't' appearing in various equations, and if so it seems important...

All right, Rhys, but I don't feel it is necessary to point these things out.

The argument that "change in fundamental constants is impossible by definition" is an old and tired one.

"Earth's position in the centre of the universe is fixed by definition! Arguing that it changes is nonsense!"

"The argument that "change in fundamental constants is impossible by definition" is an old and tired one."

Seems strange to bring it up then...

I looked at the article of Sanjouand. To me it seems ok.

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.

a) In TGD framework space-time as abstract manifold is replaced by 4-D surface in H=M^4xCP_2 (forgetting hierarchy of Planck constants) and this brings in something new: the sub-manifold geometry allowing to look space-time surfaces from H-perspective. CP_2 length scale as universal unit of length is one element. p-Adic length scale hypothesis actually brings in an entire hierarchy of fixed meter sticks defined by p-adic length scales. The presence of imbedding space M^4xCP_2 brings in light-like geodesics of M^4 for which c is maximal and by definition could be taken c=1.

b) In TGD framework the operational definition for the speed of light at given space-time sheet is in terms of time taken for light to propagate from point A to B at space-time surface. 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(xCP_2) and the speed of light measured in this manner is reduced from its maximal value.

What TGD then predicts?

a) TGD inspired cosmology predicts that c measured in this manner *increases* in cosmological scales, just the opposite for what 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.

b) The paradox however disappears that *local systems* like solar system do not not normally participate in cosmic expansion as predicted by TGD. This is known also experimentally. [The expansion would however occur in average sense via phase transitions increasing Planck constant and occurring 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].

c) 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.

d) TGD based explanation of Pioneer anomaly is based on completely analogous reasoning.

Matti, I see that you mentioned the expanding earth again here.

Off topic remark: the best evidence against a continual cosmological growth of Earth is the paleomagnetic data. The abstract starts:

New estimates of the palaeoradius of the Earth for the past 400 Myr from palaeomagnetic data limit possible expansion to less than 0.8% ...Now 400 Myr is roughly 3% of the current cosmic age, and reducing to radius could drop this to about 1%, but the data does seem to rule out a naive expansion. I realise that you are actually in favour of discrete jumps, which are not ruled out this way, but this scenario is less predictive.

I think, given the even younger age of the ocean floors, that one must accept the evidence for subduction, possibly along with an earlier phase transition or two. But this is starting to look ugly.

The alternative, with regard to continual mass growth, is to conclude that the density also increases cosmologically. Even a small increase in density could allow <0.8% radius shift over 400 Myr, in line with observation. I prefer this idea, which has the advantage of predicting precisely that growth should be measurable by future paleomagnetic data.

There are also connections with biology. The fast expansion by a factor of two explains the sudden appearance of highly developed life forms as water from undergound seas bursted to the surface of Earth (similar water reservoirs seem to exist also in Mars whose radius is by the way just one half of that for Earth). Already Darwin regarded Cambrian explosion as a main argument against his theory of evolution.

Also the the oxidation of atmosphere caused by the emergence of seas interacting with solar light implying splitting of water to oxygen and hydrogen can be understood as well as the development of very large life forms due to the gradual weakening of surface gravity (and emergence of oxygen rich atmosphere).

The idea that electron mass has increased linearly with time is to my opinion unrealistic.

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

Zephir, Louise published papers on an elegant varying speed of light cosmology before blogging was even invented - something you could easily have checked yourself.

Wow that got a little out of hand. Re the theory that the earth is expanding; the easiest explanation for the reduction in surface units is folding and subsistence. It makes it very difficult to estimate what size stuff was long ago.

OK, I've cleaned up the mess. In all the years this blog has been running, that is the first time I have had to delete so many posts.

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