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Unlearning / Relearning Feynman's 2-Boson Stuff?

  1. Jul 1, 2015 #1
    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.

    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]
     
    Last edited: Jul 2, 2015
  2. jcsd
  3. Jul 2, 2015 #2

    e.bar.goum

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    Unfortunately the link to the picture doesn't seem to work either, but I think I see the one you're talking about. You can absolutely see beats in the angular distributions of the scattering of identical particles in nuclear physics. Here's an example for different carbon isotopes (homework question: why does 12C scattering look different to 13C scattering?):
    Screenshot from 2015-07-02 18:46:00.png

    From Plattner and Sick, EPJ 2 (1981) p. 109 iopscience.iop.org/0143-0807/2/2/008

    Though my favourite example is 58Ni + 58Ni.
    Screenshot from 2015-07-02 18:43:42.png
    From Hinde et. al. Phys. Rev. C 76 (2007)
     
  4. Jul 2, 2015 #3
    Thank you. That means that the phase of each source has some physical meaning, and if we change the phase of any one beam the interference pattern will shift? And how about temporal (as opposed to spatial) beats, where we plot the intensity at one point as a function of time?
     
  5. Jul 2, 2015 #4

    e.bar.goum

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    I suggest you read this. https://www.ikp.uni-koeln.de/students/fp/download/AnleitungVers19eng.pdf or http://www2.ph.ed.ac.uk/~gja/qp/qp13.pdf or https://people.nscl.msu.edu/~nunes/phy982/phy982-isospin.pdf

    (I rather like the first and third treatments).
    To be honest, I'm not sure what you're getting at here. The beam doesn't have a well defined phase that you can change, nor would there be a temporal beat.
     
  6. Jul 2, 2015 #5
    I see that now. I misunderstood what is happening in there.
     
  7. Jul 2, 2015 #6

    e.bar.goum

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    Cool. I hope my links helped. Scattering of identical particles totally blew my mind when I learned about it. There's even a measurement of 208Pb + 208Pb scattering. Awesome experiment.
     
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