Eliezer_Yudkowsky comments on Can You Prove Two Particles Are Identical? - Less Wrong
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My best guess is that the slide is just wrong. I can't think of any reason for each photon to interfere only with itself under those conditions.
Photons certainly can all amplitude-add with each other in principle. That's how a laser works in the first place.
Any physicists want to chime in?
See also e.g. Wikipedia on Identical Particles, though rest assured, I'm not getting all my information from Wikipedia.