Physics Asked by Sciencemaster on October 12, 2020
If two neutrinos are entangled somehow–say, for instance, by being created in the same reaction–would their flavor (Tau, Muon, Electron) be enangled, including in their oscillations between the three? As such, when one has its state measured, will the other one’s be the same? What reference frame would the collapse of this wave function occur in (i.e. if one neutrino is measured to be in the electron state at a given time would, would the other neutrino be in the same state after the same proper time for it has elapsed in its reference frame, or rather simultaneously collapse to/be in the electron state right when the first neutrino is measured in the observed neutrino’s reference frame)? Just to be sure, there is unvertainty in the elapsed time between neutrinos oscillating between flavors (i.e. Heisenberg uncertainty principle with energy), rather than the oscillations just taking a given amount of proper time that is constant between different oscillations, correct?
Yes, the joint wave function propagates and when one neutrino flavour is determined, that will fix the other one.
There is an analagous situation in decays of the $Upsilon(4S)$ to a pair of $B^0$ and $overline{B^0}$ mesons. These oscillate into each other so after some time both mesons are a superposition of the two states. If one of them decays in a way that tags it as a definite $B^0$ or $overline{B^0}$ - for example $B^0 to D^- pi^+$ or $overline{B^0} to D^+ pi^-$ - then the other one simultaneously collapses to the opposite state. (This is the basis for the CP violation measurements by the BaBar and Belle experiments.)
Answered by RogerJBarlow on October 12, 2020
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