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In classical EM theory, if we have a medium whose dielectric coefficient is independent of wavelengths (suppose we filter the incoming signal to a certain frequency band), then the waveform gets to move through the medium unchanged at a speed lower than the speed of light in vacuum.

How does this look like in a more advanced theory e.g. QFT? The desired result should start from the space filing characteristics (electrons and ions) of the medium that's mostly empty space, and somehow arrive at the conclusion that the overall probability wave on the photon field actually moves at a lower speed despite an individual photon always moves at $c$.

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  • $\begingroup$ The relevant theory is actually condensed matter theories than QFT, though, of course, we could always express any and everything in QFT. The mathematical trickery to get a far faster convergence is to combine phonons and photons into a melded combination of both, so that we can explain why it would be preserving the "one photon particle" identity when it comes back out. And it gains mass, etc, giving rise to the sensible properties. $\endgroup$
    – naturallyInconsistent
    Commented Apr 3 at 2:32
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    $\begingroup$ Does this answer your question? What really causes light/photons to appear slower in media? $\endgroup$
    – Dale
    Commented Apr 3 at 3:01
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/2041/2451 , physics.stackexchange.com/q/466/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Apr 3 at 3:35

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