So was thinking if we construct 2 levels of double slit experiments where in the first we know whichway information, and then the same photons pass through a second double slit experiment, will they form an interference pattern if we do not know whichway information in the second double slit? Once the wave collapses does it stay collapsed?
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2 Answers
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That is a really good question. The simple answer is "Yes, a second double-slit interferometer downstream from a first one will act just the same as the first." But of course there is more to be said.
In the usual double-slit interferometer, doing anything that tells you which slit the photon goes through will prevent interference. The reason is that the photon wavefunction needs to go through both slits in order to interfere.
But if you put a second double-slit interferometer downstream, in a place where photons from only one slit in the upstream interferometer can reach the downstream interferometer's slits, the photons will interfere just the same as they would if the first interferometer weren't there. You know that any photons that make it through the second interferometer's slits must have passed through that one slit in the upstream interferometer, but you will still get interference on a screen beyond the second interferometer. Do anything that determines which slit the photon goes through in the second interferometer, though, and there will be no interference visible on the screen.
The crucial thing is simply the fact that interference in a double-slit interferometer only occurs on the screen or camera if the wavefunction travels through both slits and all the way to the screen or camera before it is detected.
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The experiment you refer to has been done with electrons but not with photons, i.e. you can't detect a photon without collapsing it so there would be no more photon to continue on to the screen. In the case of electrons, when detected, the detection alters its wave function so that it is no longer is effected by the slit(s) alone, its path to the screen is a new wavefunction. Another interpretation of the dual slit experiment is from single photon experiments where the pattern still builds up. An explanation (Feynman) is that photons need to travel in integer multiples of their wavelength. Thus the "interference" pattern is visible because of allowed paths and disallowed paths (dark spots). This path explanation aligns with the photon wave function theory of light, the photon wave function helps to explain more advanced photon phenomenon like the Mach-Zender interferometer and the quantum eraser experiments.
answered Mar 31, 2019 at 12:56