Dear Mário,

I looked at your astro-ph/0301085 of 6 Jan 2003. I believe I understand your point and agree with you that c  is a constant. However, "the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential", says Einstein in Ann. Physik 38, 1059 (1912), quoted by Asher Peres in gr-qc/0210066. Asher also has a very speculative and yet interesting argument supporting Davis et al. (Ref. [5] in your astro-ph/0301085). See

A. Peres, Variability of Fundamental Constants,
http://xxx.lanl.gov/abs/quant-ph/0209114

"We must therefore have a closer look at  c . In general relativity, all four coordinates may have different dimensions and the constant  c  does not appear in the fundamental equations (it may appear in particular solutions, once sources that are not generally covariant have been specified with arbitrary units). In the early universe, where background radiation cannot be ignored, Lorentz invariance does not hold. There is a preferred frame. It is then plausible that, in such an environment, the "vacuum" behaves as a dielectric medium where the speed of light acquires a factor (XX). It thus appears that a variable c  is the most reasonable conclusion to be drawn from a variation of the fine structure constant. However this phenomenon is not yet fully understood and more work is clearly needed."

So, we have three intermingled animals: the fine-structure constant [alfa], the gravitational constant [G], and the speed of light in a vacuum [c]. Regarding [alfa] and the conjecture that it had been smaller in the distant past than it is now, see

J. K. Webb et al., Further Evidence for Cosmological Evolution of the Fine Structure Constant. Phys. Rev. Lett. 87, 091301 (print issue of 27 August 2001)

and

Peter Weiss, Constant Changes, Science News, October 6, 2001,
http://www.sciencenews.org/20011006/bob16.asp

"As an example, Turner points out the accepted theoretical claim that elementary particles known as the W boson and the Z boson had no mass when the universe first exploded into being. Modern accelerator experiments have shown, however, that both are very massive today. Even so, physicists have not concluded that the laws of physics have changed. Instead, they envision that as the universe evolved according to the steady laws of physics, the inherent possibility for W and Z  bosons to become massive was realized. Something similar may be behind the apparent discrepancy between ancient and modern values of alpha."

"Constants are invented by man to help him describe the natural world that he sees. You have to keep that in mind," points out Barry N. Taylor. See at the end the letter by Gregory Kusnick, too.

After all this mess, you may ask, why do I agree with you that  c  is a constant?

Because my hypothesis about a global mode of spacetime, in which the quantum waves and gravitational waves "propagate", allows me to say that at *all instants* of the local mode of time, as measured with a physical clock, [alfa], [G], and [c] are "fundamental" constants.

They may, however, vary w.r.t. the global mode of spacetime. Do you remember the old joke from Martin Gardner about two people whose ship sank and were left on an island for many years, and one day they found a big Coca-Cola bottle (they know only the small ones), and one of them said to the other "Holy shit, we got shrunken!" To find out whether or not they got shrunken, they have to compare two parallel causal histories: their history on the island with the one at the Coca-Cola factory. No problem, since the two parallel causal histories have evolved along the same cosmological time.

Not so in our case. Relative to our epoch (strictly speaking: any instant 'now'), the three constants *might* have evolved from their initial values at some distant cosmological past. But if we place ourselves in that same distant cosmological past, there is no way we would find out that [alfa], [G], and [c] are different than those of today. They will be ever again constants w.r.t. the given instant 'now'.

In order to compare the *numerical* values of [alfa], [G], and [c] and give an ultimate answer of their evolution, we have to stay "outside" the local mode of time, say, in the atemporal 'hand-shaking' medium of Cramer's transactional interpretation of QM. Then we would be able to keep track of the changes of these three variables as they evolve in this absolute time. Thank God, that's impossible, so we say that they are fundamental constants w.r.t. any given instant 'now'.

That's all I can say. Hope to hear from you regarding the Fibunacci story and the quarks.
 

Best regards,

Dimi