The question is in the context of Cerenkov radiation, where a coherent wavefront is formed when a particle which is moving faster than speed of light in a dielectric medium, (v>c/n, where n is refractive index of the medium). In my opinion, for the formation of coherent wavefront, all the molecules that get polarized by the passing particle, should return to unpolarized state in the same instant when they are polarized, because if there is a non-fixed time lag between excitation and de-excitation, then different molecules can take different amount of time(w.r.t the instant when they were polarized) to get de-excited and then the wavefront will not be coherent. If there is a fixed time gap between excitation and de-excitation, in that case, coherent wavefront will be formed. I want to know what is the reality. Is the excitation and de-excitation instantaneous or is there a fixed time gap for all molecules?
1 Answer
Your reasoning is with classical electrodynamics which you are using for systems of molecules.
if there is a non-fixed time lag between excitation and de-excitation, then different molecules can take different amount of time(w.r.t the instant when they were polarized) to get de-excited and then the wavefront will not be coherent.
Molecules are quantum mechanical entities, they will emit photons and only the probability of the time the photon emission happens is calculable with QM, i.e.accumulation of many events.
If you search "quantum field theory cherenkov radiation" you will see several quantum calculations for specific problems.
Single photon wavefunctions can add coherently to produce a classical wave depending on the boundary conditions of the problem. In my view, the difference between individual photons and the classical light wave becomes clear with this experiment I discuss here..
Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.
On the left, the photons seem random, in the accumukation the classical wavefront behavior becomes clear.
In a similar way, I hand wave, the geometrical constraints of the problem "charged particle faster than light in medium" allow for the "random" photons from the molecular activity to add up to a coherent wave.
