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My understanding is that Michelson-Morley experiment really proves that phase velocity of light is constant, but does not directly address its group velocity, i.e., the velocity with which the information propagates.

Of course, if we accept the Maxwell equations, the two velocities are equal in vacuum, and therefore the group velocity is limited to $c$. However, I wonder, if any experiments tried to prove directly that the group velocity of light (or any signal) cannot exceed $c$ (in my understanding, this would require analyzing transient behavior, rather than merely an interference pattern - e.g., by using a pulsed light source.)

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  • $\begingroup$ IIRC, there had been cases whereby people forced group velocity to exceed c, but then the information carrying capability of that light dissipates. Becomes noisy messes. $\endgroup$
    – naturallyInconsistent
    Commented Sep 25 at 9:59
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    $\begingroup$ Isn't that equivalent to saying the phase and group velocities are the same, and that in turn is equivalent to saying the propagation of light in a vacuum is non-dispersive? And we know propagation is non-dispersive from observations of distant supernovae. Indeed, trying to detect dispersion in a vacuum is a significant measurement since it could be evidence for quantum gravity. $\endgroup$
    – John Rennie
    Commented Sep 25 at 10:15
  • $\begingroup$ @JohnRennie If vacuum is non-dispersive, then $v_g$ and $v_{ph}$ are equal. But in my opinion MM experiment does not show that... or perhaps shows in some more extended version than the one I am familiar with. If you could expand your remarks about supernovae and quantum gravity in an answer, it would be a pleasure to read. $\endgroup$
    – Roger V.
    Commented Sep 25 at 10:54
  • $\begingroup$ @RogerV. Done!! $\endgroup$
    – John Rennie
    Commented Sep 25 at 11:32

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Given that we know the phase velocity of light is constant the statement that the group velocity is constant is equivalent to saying the phase and group velocities are the same. This is in turn equivalent to saying light transmission through the vacuum is non-dispersive. So if we had experimental observations that the speed of light in vacuum is independent of wavelength this would address your question.

And we do have such evidence, because various theories of quantum gravity suggest that spacetime becomes ill defined at distances approaching the Planck length, and this is expected to affect the propagation of EM waves. Specifically shorter wavelengths are more affected than longer wavelengths and would propagate at different speeds. See for example Experimental bounds on Lorentz-violating dispersion relation.

Exactly what would happen depends on what theory of quantum gravity you prefer, though for all theories we expect the difference to be very small since the shortest wavelengths we can detect are still many orders of magnitude larger than the Planck length. However if you have a very long path length, e.g. the distance to a remote gamma ray burst, the difference might be enough to produce a measurable delay between the arrival times of photons with different wavelengths.

This measurement is described in A limit on the variation of the speed of light arising from quantum gravity effects, and the result was that no dispersion was measured.

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