In Vol. III, Ch. 4 (Identical Particles) of his lectures, Feynman talks about the probability of detecting a boson/fermion when two particles are involved. He introduces the idea of computing detection amplitudes as a sum of two terms, with a plus or minus sign for cases with swapped particles.(adsbygoogle = window.adsbygoogle || []).push({});

Link: http://www.feynmanlectures.caltech.edu/III_04.html

I am wondering how literally true this is, particularly for photons. Is this one of those notions that we have to unlearn (or seriously modify) as we go along?

For example, consider the diagram in Sec. 4.2, image url is here : http://www.feynmanlectures.caltech.edu/img/FLP_III/f04-03/f04-03_tc_big.svgz

http://www.feynmanlectures.caltech.edu/img/FLP_III/f04-03/f04-03_tc_big.svgz

Here the probaiblity of detection at 1 is computed from this amplitude:

⟨1|a⟩⟨2|b⟩+⟨2|a⟩⟨1|b⟩.

Now if we add an arbitrary phase shift to source b, then both the terms are affected equally because |b⟩ has a multiplicative effect on both tems. This means that the interference pattern is unaffected by the phase of source b. This in turn implies "no temporal beat frequency at any given detector". However, interference and beat frequences between independent, mutually locked lasers is well established experimentally, and it is hard to believe that the phase of one source would have no physical significance.

So my two questions:

[1] How does this stuff translate into the rigorous theory for photons

[2] How does it translate into rigorous theory for Helium-type bosons?

Re. Question 2, can you see beat frequencies between two beams of He bosons?

[Sorry, the image url does not display directly here so I have pasted it as a link]

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# Unlearning / Relearning Feynman's 2-Boson Stuff?

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