Exploring Variable Speed of Light Theories

[Einstein's Cat]

I was researching variable speed of light theories as alternatives to inflation theory; from Wikipedia I cam across this:

"The idea from Moffat and the team Albrecht–Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the expanding universe have had time to interact at the beginning of the universe.

There is no known way to solve the horizon problem with variation of the fine-structure constant, because its variation does not change the causal structure of spacetime. To do so would require modifying gravity by varying Newton's constant or redefining special relativity."

My questions are why is this theory not mainstream and could the second paragraph please be explained more vigorously?

 

[Chronos]

It's not mainstream because there is no observational evidence supporting VSL. For those interested the paper discussed in the Wiki article is http://arxiv.org/abs/astro-ph/9811018, A time varying speed of light as a solution to cosmological puzzles. Magueijo's appears to clarify his views on VSL in this paper http://arxiv.org/abs/0705.4507, Comments on "Note on varying speed of light theories"..

 

[newjerseyrunner]

Wouldn't we be able to see different speeds of light in the early universe by gravitational lensing? When we have multiple images of the same galaxy, they're usually offset in time too since the light had to travel different distances. If light traveled much faster in the past, the images from further away should show less deltas between different projections of the same image. I would think this would seriously skew any attempt to map dark matter in the distant universe.

 

[Chalnoth]

Wouldn't we be able to see different speeds of light in the early universe by gravitational lensing? When we have multiple images of the same galaxy, they're usually offset in time too since the light had to travel different distances. If light traveled much faster in the past, the images from further away should show less deltas between different projections of the same image. I would think this would seriously skew any attempt to map dark matter in the distant universe.

From what I recall, this idea only has a chance of working if the speed of light only changes in the very early universe, as in long before the CMB was emitted. In effect, they're considering a scenario where the inflationary epoch is replaced by a high-speed-of-light epoch.

 

[Garth]

The conceptual question behind VSL is how are are time and space measured?

A natural consequence of SR's assumtion that there is a space-time continuum is to set c as the conversion factor between time units and distance units; its value depending on whatever arbitrary system of units you choose to use, and a natural choice would be to set c at unity and define a time unit, seconds, years, or whatever, measured by a clock and then measuring distance by the distance light travels in that time in light-seconds or light-years or 'light-whatever'.

An equivalent alternative to VSL is a conformal transformation of the metric.

In such a transformation mass, length and time units are changed.

If the mass of an atom should increase then its size would shrink and atomic frequencies speed up, i.e. steel rulers would shrink and atomic clocks would speed up proportionally so the speed of light c, as measured in the new units would be unchanged, it is invariant under the conformal transformation.

In this way rather than explain the connection of distant regions in the early universe by a 10⁶⁰ expansion rate of Inflation, or the same factor increase in c it might also be explained by a 10⁶⁰ increase in particle masses and hence shrinking of atomic diameters.

Thus Inflation would be seen not as an 'explosive' expansion of space but as an 'explosive' shrinking of the rulers used to measure space.

The reason why atoms and rulers might shrink in this way might be that the Inflation epoch was caused by the Higgs field, which suddenly gave particles their inertial mass.

Garth

 

[PeterDonis]

An equivalent alternative to VSL is a conformal transformation of the metric.

In such a transformation mass, length and time units are changed.

I agree that a conformal transformation would change the length and time units (while keeping their ratio, the speed of light, constant). But why would it change the mass unit?

The reason why atoms and rulers might shrink in this way might be that the Inflation epoch was caused by the Higgs field, which suddenly gave particles their inertial mass.

It would be nice to have a reference for this statement (not the Higgs mechanism itself, that's well established, but the additional idea that atoms and rulers might shrink when the electroweak phase transition happened). Please bear in mind the PF rules about personal theories.

One obvious question about this speculation: if the particles were massless before the transition, then the "ratio of sizes of atoms" (really a misnomer since there were no atoms this early in the universe, but we could finesse that) before and after would not be $10^{60}$ or any finite number; it would be infinity (zero mass to nonzero mass). So I'm not sure how this mechanism could explain a very large but finite change in the natural size scale of fundamental objects. Again, a reference would be nice so we would have a more concrete (if speculative) model to discuss. (Such a discussion, with proper references, should also be spun off to a new "A" thread, since this is a "B" thread.)

 

[Garth]

I agree that a conformal transformation would change the length and time units (while keeping their ratio, the speed of light, constant). But why would it change the mass unit?

The standard formula for mass transformation under a conformal transformation:
${g*}_{{\mu}{\nu}} = \Omega ^2 g_{{\mu}{\nu}}$ is ${m}* = \Omega^{-1} m$. See for example Cosmological Models in a Conformally Invariant Gravitational Thgeory

Garth said: The reason why atoms and rulers might shrink in this way might be that the Inflation epoch was caused by the Higgs field, which suddenly gave particles their inertial mass.

It would be nice to have a reference for this statement (not the Higgs mechanism itself, that's well established, but the additional idea that atoms and rulers might shrink when the electroweak phase transition happened). Please bear in mind the PF rules about personal theories.

Its just basic physics, the Bohr radius of an atom being inversely proportional to their mass.

One obvious question about this speculation: if the particles were massless before the transition, then the "ratio of sizes of atoms" (really a misnomer since there were no atoms this early in the universe, but we could finesse that) before and after would not be $10^{60}$ or any finite number; it would be infinity (zero mass to nonzero mass). So I'm not sure how this mechanism could explain a very large but finite change in the natural size scale of fundamental objects. Again, a reference would be nice so we would have a more concrete (if speculative) model to discuss. (Such a discussion, with proper references, should also be spun off to a new "A" thread, since this is a "B" thread.)

I thought the Higgs mechanism did not impart all the particle's mass but required a tiny seed to act on? I agree it is speculative, just as speculative as a VSL theory, but IMHO I find it more resonable to think of shrinking atoms during the Higgs epoch rather than a 10⁶⁰ explosive expansion of the universe during the Inflation epoch. I would like to continue this dicussion but I am going away now so I'll sign in again in about a week's time!
Garth

 

[windy miller]

I agree the main reason is that inflation seems confirmed by observers. Maybe the observation of varying alpha could be taken as some evidence for varying c ? http://arxiv.org/abs/1008.3907 but this observation in itself is controversial so much caution should be given to it.
Im also wondering how much priority in time comes into these things. Inflation explained the many puzzles of the big bang ( horizon, flatness etc) first. VSL came along after. I suspect that has some role to play as well. Although please note my opening statement the observational evidence is paramount.

 

[PeterDonis]

I thought the Higgs mechanism did not impart all the particle's mass but required a tiny seed to act on?

Not as I understand it. As I understand it, prior to electroweak symmetry breaking all of the fermions in the Standard Model are exactly massless.