Another puzzle for mixing quantum mechanical and classical notions. Let a nucleus decays amitting, say, electrons. It is surrounded with detectors. There is a flight time \tau. One of the detectors fires at last. At this moment the direction of the recoil becomes known.
Interestingly, if there is a double slit on the path of electron, there should be an interference pattern in the recoil as well.
Absolutely NOT!
If the electron is entangled with the nucleus recoil you won't get a clear interference pattern. For each direction of recoil you'd get a separated set of interference fringes, but the sum of all these sets is likely to produce an unclear picture.
Igor, your puzzle is very close to the ghost interference effect (in fact is modification of it). GIE is when we have an entangled pair of electrons and one is send tru 2 slit. The second electron also shows interference.
If Alice measures electrons and Bob nuclei, the no-communication theorem says that whatever Alice does should not affect what Bob gets.
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