Cthugha
Science Advisor
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Fredrik said:I don't think this is a problem for the path integral description. I'd say it's the exact opposite of a problem!
Oh, I never intended to say, that it is a problem for the path integral formalism. Putting such a detector in just makes the whole experiment uninteresting by destroying any interference pattern. Path integrals are fine as a model although they are nasty and unpractical when it actually comes to calculate stuff.
Robert Noel said:Also, in the case of the first image I posted, where it looks as though an interference pattern is formed after both exit ports of the recombining beamsplitters (I really wish I hadn't posted that image, but rather, only the second image in post #41), when we block the long-path beam, I'm now picturing the interference pattern being diminished before we block the beam rather than completely erased, until 5ns after we block the path, and then it is completely erased. After all, only the subject photons would stop interfering, while the photons taking the long path (of their 2-path journey) before we block the long path would keep interfering. That is, we make the short path "subject" photons distinguishable at the detector while the older photons taking the long path (or their 2-path journey) still interfere because they are still indistinguishable...?
No matter which image I look at (though I much prefer the second image), I still see effect preceding cause, unless photons are interfering with other photons and not themselves, which counters everything I've read in books on the subject...sigh!
Ok, letme at first comment on the first image.
Where exactly do you think, that different photons interfere? You can't really say, that photons taking one path keep interfering, while those taking the other path don't. The key to interference is, that you can't distinguish photons taking the short path from photons taking the long path. So in fact the photon taking the long path and the photon taking the short path are the same single photon, which produces the interference pattern. Although this seems counterintuitive, one must keep in mind, that we have a coherent state. The key property of a coherent state is, that the uncertainty of the moment, when one certain photon is emitted is roughly the order of the coherence time. So it is this one single photon, which interferes with itself. It takes the long path and is emitted early or it takes the short path and is emitted later. As long as those paths (or better realizations or histories) are indistinguishable, there will be interference. Just to stress it, you do not need one older photon traveling the long path and one newer photon traveling the short path, but just one photon, which could have taken both paths and could have been emitted at both times with equal probability.
The second image does not change anything in principle.