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Is quantum entanglement affected by time dilation? Let's say one of the entangled pair is accelerated to very high speed. When both the entangled particles are observed at the same time, will they have the opposite spin?

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    $\begingroup$ A word to those who voted to close this question: If you do not have solid knowledge that truly justifies a close vote, can you please refrain from the "guilt and shame" approach. It's frivolous, ridiculous, and getting to the point where it detracts severely from the value of this site. The problem of relativistic effects on entanglement and quantum communication is non-trivial enough to warrant a host of papers, plus Master and PhD theses, see for instance lanl.arxiv.org/pdf/1003.1874v1, lanl.arxiv.org/abs/1306.4853, lanl.arxiv.org/abs/1309.4419, and refs. therein. $\endgroup$
    – udrv
    Commented Nov 20, 2016 at 7:14
  • $\begingroup$ At least a down-voter should explain why this question is ill phrased or why it is not acceptable by him. I am no expert on this field, but the question seems fine. If there is a phrasing problem of clarity a comment on the OP could help him, other users and the site. Also, if someone knows that the answer to this question is negative, one should try an answer or at least a comment and not downvote. $\endgroup$ Commented Nov 20, 2016 at 9:27
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    $\begingroup$ I am not a downvoter, but I would like to say that the question phrasing is rather sloppy. Notably, the idea of observing both particles at the same time does not make sense in such a relativistic setting. This is surprisingly overlooked considering that the question title explicitely mentions time dilation. $\endgroup$ Commented Nov 20, 2016 at 15:19
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    $\begingroup$ The OP's sloppiness about what "the same time" means in this context is not at all unfixable. It warrants quizzing via a comment, editing perhaps, or the odd downvote , but not closing. And the rest is a valid question. $\endgroup$
    – udrv
    Commented Nov 20, 2016 at 17:40
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    $\begingroup$ @udrv Why should closing only be justified for unfixable problems?? Also, why should downvotes be more justified in such a case? I would rather think the opposite. Note that also the "opposite spin" is only vaguely related to entanglement (it depends on the state and the measurement basis, for the very least). $\endgroup$ Commented Nov 20, 2016 at 21:46

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A relativistic boost entails a momentum-dependent Wigner rotation that changes the spin direction by an angle dependent on the qubit's momentum, see https://arxiv.org/abs/quant-ph/0203051. If the qubit is not initially in a momentum eigenstate, which practically is always the case, the Wigner rotation will "entangle" its spin and momentum degrees of freedom. The result is that the qubit's spin state, obtained after averaging out the momentum part, will show an apparent "decoherence".

In this sense the answer to the question is negative: if one qubit of an entangled pair is boosted to some relativistic velocity, a simultaneous spin measurement in one reference frame, along the original spin polarization direction, may not produce the expected correlation or anti-correlation.

The problem can be avoided either by adjusting the measured spin direction(s), or better, by redefining the "qubit spin" as a projection of the helicity along an eigendirection of the boost, see https://arxiv.org/abs/quant-ph/0312040. In any case, since a Wigner rotation amounts to a unitary transformation on the overall state space, a boost to another inertial frame, and with it the corresponding time dilation, does not affect overall spin-momentum entanglement.

On the other hand, boosting to a non-inertial frame poses much more serious problems of potential entanglement loss through the Unruh effect.

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