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The actual answer is the assumptions which define a self-propagating wave do not apply once the wave leaves a vacuum. When it becomes incident onto some medium, due to the coupling of electrons within the medium to the electromagnetic field, the pure electromagnetic wave gets transformed into a phonon, which is a combination of electromagnetic and mechanical oscillation within the medium (and therefore has speed <c, depending on the particular properties of the medium). When the phonon subsequently leaves the system, those traveling oscillations induce a new self-propagating wave on the other side, sending the light on its way as usual.

What does it mean for something to oscillate electromagnetically and mechanically simultaneously?

Doesn't mechanical oscillation already occupy all three spatial dimensions plus a time dimension?

The phonon oscillates both the electrons and the EM field.

A photon is EM only.

So you’re correct that it occupies all four dimensions, but we’re discussing an excitation in one field (photon) changing to an oscillation in multiple (phonon) and then back to only one field (photon).

Can you explain this in a step by step manner?

I really can't quite grasp how the photon/phonon switches back and forth like this.

1. The photon moves through free space, where only the EM field is disturbed.

2. The photon enters a material, where the disturbance in the EM field couples to the electron waves — creating a phonon.

3. The phonon travels through the material, as an oscillation in both electrons and EM.

4. The phonon reaches the edge of the material, where there are no more electrons and reverts to a wave of just EM — a photon.

5. The photon continues in free space.

The reason this happens is the photon changes the electron behavior, which in turn changes the photon behavior. This is because EM interacts with charged particles like electrons.

For the time it is in a material, a EM wave can’t be separated from the behavior of the electrons present: both and their mutual interaction are required to explain what happens.

That disturbance of both is “coupled” — and called a phonon.

Is this more than a change of terminology? Is it wrong to say that the electromagnetic oscillation is still there in the medium but coupled to a mechanical oscillation, and the coupled system is called a phonon? (I mean there's still an electromagnetic field in the material, it still gets excited, it's not replaced with a new field that fuses the EM and matter fields). Then the question is by which process exactly is the electromagnetic oscillation slowed down, and is the answer much different from the explanations above? I.e. the moving charges due to the mechanical oscillation add perturbations to the EM field such that the net effect is a slower propagating wave.

I'm not sure if this will be satisfying because it is a mathematical explanation rather than an intuitive one. If you combine two of maxwell's equations, you get a wave equation for electric/magnetic fields. However, there is an extra term in there, which is the effect of a time changing current on the magnetic field. In a material, the time changing electric field induces such a current, which in turn has the mathematical effect of reducing the coupling between the electric and magnetic field, creating the equation for a wave that is slower.

Something that might be comforting about light going slower than the speed of light is that the speed of light is not a special property of light, but it is a property of space time. It just so happens that light is the only way we have experience on this magic speed. Light isn't physically bound to go "the speed of light".

I thought that Grant's video did a great job of explaining it was all phase kicks, and how it all depended on resonant frequencies of the medium.

[Edit]In the second video above, he notes that phase kicks don't change the speed of the wave, even though the wavelengths can stretch out, it's still lower than the speed of light in vacuum.

Phase kicks don't change the speed of a wave. If you setup a similar experiment with sound or water where you constructed an interference pattern that kicked back the phase of the wave, the wave wouldn't slow down.

If you want an actual non-layman explanation for why light slows down ib a medium you need to express the light and medium interaction in terms of polaritons. Of course this is incredibly difficult to do so for even simple cases, so alas a whole suite of simplified explanations exist that seek to explain some aspect of the situation while failing to explain others.

https://en.m.wikipedia.org/wiki/Polariton

Could you elaborate please?

So, there no slowdown by phase shift at all? But.. are you sure, because it looks like the phase shift is the real effect and logically speaking result of the phase shift will be the effect that look like slowdown for outside observer.

Also, how can you simulate similar effect in water and sound if there no sound polarization?

The phase shift is dependent on both the resonance frequency of the medium and the incident light. In the case of X-rays, the refractive index can go below 1, resulting in total external reflection for a few tenths of a degree. Even in this case, the speed of the X-ray itself stays below that of C, even though the "wavelength" appears to be longer than in vacuum.

> logically speaking result of the phase shift will be the effect that look like slowdown for outside observer.

If there was a phase shift but no slowdown, wouldn't we expect individual photons to propagate through a 10km loop of fibre optic cable without any slowdown, which would be measurable?

You would certainly see an apparent slowdown due to phase shift if you consider a continuous wave that spans the entire medium, yes for sure and so this explanation and model does have merit, I don't want to dismiss it entirely.

But this model won't be useful for understanding pulses of light through a medium. For example if I emit a very short pulse of light through a medium and measure how long it takes the head of the pulse to traverse the medium, using this model won't work. A phase shift won't move the head of a pulse of light backwards, it will just adjust the amplitude of the head as it propagates through the medium.

You still need a way to explain how it is that the head of the pulse actually takes longer to travel through the medium and that's not something a phase shift can explain.

The understanding of a refractive index only cares about 'phase speed' in steady state. At least, that is what the video claims to be about. For that case, phase kicks are a sufficient explanation no?

I can imagine things get really weird with pulses, but that's out of scope for the video.

> Phase kicks don't change the speed of a wave.

"Phase kicks" explain the phase velocity. The speed of a wave is the group velocity. Phase velocity is omega(k)/k, group velocity is omega'(k). So if "phase kicks" explain phase velocity sufficiently so it's valid for a range of frequencies, then it also explains group velocity by taking the derivative of the dispersion relation.

That's true for a steady-state wave, and hence this model is accurate for a steady-state light wave. But if you were to consider short pulses of light then there is no longer a relationship between the group velocity and phase velocity.

The group velocity of these pulses through a medium will still be lower than the speed of light in a vacuum and phase kicks won't influence the group velocity.

Explaining how the group velocity of light can be slower in a medium than in a vacuum requires analyzing the coupling of photons with electrons to form polariton quasiparticles. You can then calculate the mass of these polaritons which in turn gives you the speed and get the full picture. Doing this, however, is incredibly complex and so it's much easier to consider simplified scenarios like either the steady-state case where you can simply reason about the scenario in terms of interference patterns between the light wave and the electromagnetic waves produced by oscillating electrons, or you can consider some non-steady state scenarios involving photons themselves being absorbed and reemitted by electrons but neither of these explanations fully capture the phenomenon.

A pulse of wave is a superposition of steady-state waves. Group velocity, phase velocity and dispersion relation have one-to-one correspondence.

I agree that the phase-kick classical model is a very simplified material model, which probably breaks down in certain ways. But it does yield a dispersion relation, therefore both phase and group velocities.

visualized well in “Picture Book of Quantum Mechanics” ch 1 (a fairly hardcore physics text that does indeed have many diagrams)