|MadSci Network: Physics|
These are really tough questions that I confess, I do not have the level of expertise needed to answer effectively. What I will say is that I have searched for any reference in the literature and the WWW that suggest the possibility of such phenomena, and I have found none. It seems to me that in order for photons to be compressed as we would think about a sound compression wave for example, that the photons within the "wave" would necessarily have to take on different quantum characteristics or localized properties. As this is strictly forbidden I see no way to describe a true photon compression wave using quantum mechanics or special relativity. Einstein's work showed that there must be an assumption that photons are rigorously identical and that it implied a "mysterious non-local interaction", now understood as the requirement for a symmetric quantum mechanical state. The difference in local photon properties for compressed photon waves would necessarily render this assumption false.  Einstein, A. (1924). "Quantentheorie des einatomigen idealen Gases". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalisch-mathematische Klasse 1924: 261–267. (German)  Einstein, A. (1925). "Quantentheorie des einatomigen idealen Gases, Zweite Abhandlung". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalisch-mathematische Klasse 1925: 3–14.
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