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I've read the article Quantum Entanglement, which is a summary of the basics of non-locality, as well a claim for the first "real" proof of its existence. I also have some background from self-studying QFT and reading Matt Strassler's blog.

My question is: is it logical to assume that, if elementary particles are treated as excitations of a underlying field, that non-locality might imply instantaneous propagation "through" the fields?

I appreciate that both the field and the particles should be treated as purely mathematical in nature, but that the particle has more "reality" because we can perform experimental work on it. (And that as far as I want to go regarding any naïve philosophical aspect to physics.)

If we can (mathematically) treat a positron as an electron travelling backwards in time, is it as valid to treat non-locality as an instantaneous propagation in the field?

Qmechanic
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    related: Locality in QFT vs “non-local” in QM. – AccidentalFourierTransform Jun 22 '18 at 17:49
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    I don't know ow the answer from a QFT perspective, but some interesting points: the instantaneous nature of entanglement is one of the things that Einstein used to reject QM initially (until entanglement was actually demonstrated). Yet one cannot use entanglement to propogate a signal faster than the speed of light. On the other hand, recall in Coulomb Gauge in classical electrodynamics the scalar potential "propagates instantaneously". But this is purely mathematical and does not reflect any physical transmission of information. The physical EM field does not propagate instantaneously. – Kai Jun 22 '18 at 19:25
  • Thanks for that, (which I kinda knew, sorry :), but what I was really after was more of an elaboration of why QFT prefers treating some situations as going backwards in time rather than occuring instantaneously, (both of which are obviously not realistic physically) but I need to read more into the preservation of causality. Your comment gave me a chance to spell that out hopefully. –  Jun 22 '18 at 19:34
  • @kai thank you, didn't see all your comment, sorry –  Jun 22 '18 at 19:39
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    QFT is a subtle topic, unfortunately my knowledge is not far beyond graduate courses. Antiparticles propagating backwards in time are a useful way to interpret the results of the mathematics in Feynman diagrams. But remember Feynman diagrams and the particle picture, while intuitively powerful, are not perfect. Feynman diagrams arise from perturbative expansions, which do not capture all of the physics. In any case it may be helpful to give some specific examples of nonlocality which you would like to clarify. – Kai Jun 22 '18 at 21:48

2 Answers2

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Quantum mechanics is based on equations in which no field can travel faster than light. All predictions of quantum mechanics, including quantum entanglement, are therefore in agreement with causality.

my2cts
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Both QM and QFT are local. Bell's theorem does not imply non-locality. It implies that any theory that reproduces the predictions of quantum mechanics is non-local if that theory represents the state of a system before a measurement by a stochastic variable, i.e. - a single number that is chosen from a set of possible outcomes with some probability.

There is a local description of the evolution of any given quantum system in terms of its Heisenberg picture observables, which are represented by operators not single numbers. The observables change only when the system changes by itself or through a local interaction with another system.

Entanglement and teleportation can be explained by quantum information being transported locally through decoherent channels. The information is contained in the observables of the channels, but it does not affect their expectation values: locally inaccessible information. This locally inaccessible information can only be unlocked by using it in conjunction with information from the other entangled system:

http://arxiv.org/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223

This treatment has been extended to quantum field theory too, see

https://arxiv.org/abs/quant-ph/0103079

alanf
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  • "if that theory represents the state of a sytem after a measurement by a stochastic variable" - I think you mean -before- the measurement. The essence of 'hidden local variables' is that they are intended to represent hidden properties (not described by standard QM) that determine the outcome of future measurements.

    Also the last paragraph of this answer is a bit confusing, or at least very non-standard.

     – user34722 May 29 '21 at 04:17
  • I have made the edit you suggested. I admit that working the implications of quantum theory consistently without qualification and applying them to understanding experiments is non-standard. I regard this as a criticism of standard ideas. Also, the paragraph isn't meant to be a complete explanation since the explanation is provided in the linked papers. – alanf May 30 '21 at 07:48