
#1
Apr1212, 12:09 PM

P: 2

If you get an electron going faster than the local speed of light i know that it starts emitting light, but why does it do this?, furthermore, In a theoretical material with an infinite index of defraction (a.k.a light is stopped within it), wouldn't that cause the system to quickly go to near absolute zero?




#2
Apr1212, 01:02 PM

P: 136

Have you looked at http://en.wikipedia.org/wiki/%C4%8Cerenkov_radiation?




#3
Apr1212, 05:24 PM

P: 4,664

The best derivation of Cerenkov radiation by a fast charged particle I have seen is the semiclassical derivation in Schilff Quantum Mechanics (2nd Edition) pages 267271. Schiff derives the classical E and H fields, and the resulting Poynting vector P = E X H. He then gets the number of quanta radiated per unit path length in frequency interval ω to ω+dω:
[tex] dN=\frac{1}{137}\left(1\frac{c^2}{n^2v^2} \right)\frac{d\omega}{c} \text{ photons per unit length}[/tex] which becomes for infinite index of refraction [tex] dN=\frac{1}{137}\frac{d\omega}{c} \text{ photons per unit length}[/tex] So the total number of quanta depends on wnat interval the frequency interval dω covers. Normally, the index of refraction is n ≤1 for wavelengths less than ~ 1000 Angstroms (UV). 


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