We know that a charged particle moving at uniform speed does not radiate. However, when travelling sufficiently fast in a medium, the build up of wavefronts cause a shockwave to form, which we observe as Cherenkov radiation. As the name suggests, the waves in the Cherenkov radiation radiate away to infinity.

Everytime the particle 'enters a new position in space', its electromagnetic influence propagates outwards in a wave-like manner. At subluminal speeds, there is no radiation field.

At superluminal speeds, I'd expect the picture to be similar, except that the wavefronts build up along a line forming a shock wave. Since Maxwell's theory is a linear one, I am inclined to think that this shockwave, being a superposition of 'circular waves', is non radiative. Yet we have the phenomenon of radiation. This seems a bit contradictory.

Am I thinking about this correctly, or is it plain wrong to think of drawing this analogy for electromagnetic wave to acoustic waves?

  • $\begingroup$ There are shock waves in plasmas, which are electromagnetic in nature. Not all electromagnetic waves are free modes propagating at the speed of light. A shock wave is a medium's response to some piston/driver moving faster than the medium can properly/linearly respond. I've tried thinking of Cerenkov radiation (in the specific form to which you refer) as a sort of shock wave, but I am not convinced it is appropriate. $\endgroup$ – honeste_vivere Apr 3 at 15:12

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