Will_Pearson comments on Can You Prove Two Particles Are Identical? - Less Wrong
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If figure 4 and the surrounding theorising is correct: The photons in figure 4 didn't start off identical (they had different momentums). So your experiment made them identical.
I am troubled by your assertion that two photons can interfere with each other, since this slide suggests that even with billions of photons from the same light source, that they only interfere with each other.