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Happiness
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For the case of an electron passing through a double slit, there will be an interference pattern if it is indistinguishable which slit the electron passes through. If we put a light source behind the slits to measure which slit the electron passes through, the interference pattern is destroyed.
So by the same logic, since there is interference in an interferometer, it must be indistinguishable which of the two paths the light takes or a photon takes.
So by the same logic, since there is interference in an interferometer, it must be indistinguishable which of the two paths the light takes or a photon takes.