Assumptions behind Maxwell's equations for constant speed

[giulio_hep]

I need some help in defining what are the assumptions needed to derive a constant speed of light from Maxwell equations.
Is it correct to say that this result applies to a sinusoidal wave as an assumption? In my understanding that is _{(more or less)} equivalent to planar waves in vacuum: is it another way to define the context of this derivation?
Sorry, a final doubt: I've read that Maxwell equations say nothing about other frames of observation, so the invariance of speed from this point of view is a postulate of special relativity, not a consequence of Maxwell equations... my question is: have there been any new _{(more modern)} experimental tests related to this postulate in the last couple of years? _{(found some recent articles in the web about CMB and variable speed of light theories)}

 

[Dale]

I need some help in defining what are the assumptions needed to derive a constant speed of light from Maxwell equations.

You just need to assume vacuum.

Is it correct to say that this result applies to a sinusoidal wave as an assumption?

No, sinusoidal waves are convenient, not required.

 

[giulio_hep]

And what about different deductions of the Lorentz-like transformations without resorting to the light postulate? Are there modern formulations of the relativity principle, in which the maximal speed is not specific to the light and the derivation of the Lorentz transformations depends on the properties of the space-time?

 

[Dale]

Are there modern formulations of the relativity principle, in which the maximal speed is not specific to the light and the derivation of the Lorentz transformations depends on the properties of the space-time?

Yes. In fact I think that most modern treatments do not make it specific to light. The modern approach is to start with symmetry. If you merely assume homogeneity, Isotropy, and the principle of relativity then you are left with only two possible transformations between inertial frames. One is the Galilean transform in which the invariant speed is infinite, or the Lorentz transform in which the invariant speed is finite. It is then a simple matter of experiment to determine that speed.

 

[giulio_hep]

Thanks again, could you please point me to a suggested one of these modern treatments (hopefully online)? How (if ever) does this correlate to CMB and variable speed of light theories. So do you believe that such a theory could soon be put to the test?

 

[Battlemage!]

Thanks again, could you please point me to a suggested one of these modern treatments (hopefully online)? How (if ever) does this correlate to CMB and variable speed of light theories. So do you believe that such a theory could soon be put to the test?

Based on your link, this particular variable speed of light theory does not say that there was at one point NOT a universal speed limit, just that it's value was different. If that is the case, you'd still have special relativity, just with a different number for c. But then, your article doesn't really go into any details.

 

[giulio_hep]

Based on your link, this particular variable speed of light theory does not say that there was at one point NOT a universal speed limit, just that it's value was different. If that is the case, you'd still have special relativity, just with a different number for c. But then, your article doesn't really go into any details.

The question is:

• does the special relativity allow the universal speed to vary with time?

I'd say no.

Moreover I was kindly asking for a reference of the modern formulations of the relativity principle... while the article was only a marginal example _{(btw the article correctly quotes the Journal Reference 10.1103/PhysRevD.94.101301 with all the details, but they're too complex... I've notice also a free archiv version in the web)} to say something also about the experimental side