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?
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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 Sep 12, 2020 at 7:59
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$\begingroup$ Good answer. One nit-pick: the wording "simultaneously collapses to the opposite state" could be replaced by something like "is guaranteed to be found in the opposite state when measured," as recommended (for example) by Conway and Kochen on page 16 in "The Free Will Theorem" (arxiv.org/abs/quant-ph/0604079). That wording avoids suggesting any dubious interpetations of quantum theory, and it also avoids suggesting that measurement has any faster-than-light effects. Doesn't change the point of the answer, of course, just a less presumptuous way of wording that one detail. $\endgroup$ Commented Sep 12, 2020 at 13:18
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$\begingroup$ First off, just to clarify, what is Y(4S)? Second, I find it interesting that you bring up CP violation experiments, because the thought that led to this question was about the symmetry violation caused by the differences (i.e. in time intervals) between oscillations between different states (i.e. tau to electron is different from electron to muon). Finally, when you say that the state of the other particle collapses "simultaneously", in which reference frame are you referring to? Do we (meaning the scientific community) know the answer? Does it have physical meaning? $\endgroup$ Commented Sep 12, 2020 at 18:50
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$\begingroup$ Also, how do we know that neutrino states (and thus the oscillations between them) can be entangled? Is it through empirical evidence, or something else? Also, How can they be entangled? Is is just when two neutrinos are created together, or is there something more (or other methods)? $\endgroup$ Commented Sep 13, 2020 at 0:33