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It is an empirical question whether photons always obey Bose-Einstein statistics, but devising and interpreting experimental tests of photon statistics can be a challenge. The nonrelativistic cross section for Compton scattering illustrates how a small admixture ν of wrong-sign statistics leads to a loss of gauge invariance; there is a large anomalous amplitude for scattering timelike photons. Nevertheless, one can interpret the observed transparency of the solar wind plasma at low frequencies as a bound ν<10−25 if Lorentz symmetry is required. If there is instead a universal preferred frame, the bound is ν<10−14, still strong compared with previous results.

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Altschul, B. (2010). Testing photons’ Bose-Einstein statistics with Compton scattering. Physical Review D, 82(10).

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