[zmgsabst]

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).

[MichaelZuo]

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.

[zmgsabst]

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.