# Is quantum physics nonlocal?

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In which sense can one say that quantum physics is nonlocal (if it is at all)?

asked Nov 3, 2015

## 2 Answers

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There are two significantly different notions of nonlocality in use - the violation of causal locality giving rise to equal-time causal commutation rules and the violation of Bell inequalities and the like. Let me call the former causal nonlocality and the latter Bell nonlocality.

More precisely, causal locality is a condition ensuring that signals, matter, and energy cannot travel faster than light. On the other hand, Bell locality is the assumption that the state of an extended system factors into the states of localized parts of the system. Roughly speaking, this means that complete information about the state of region A and complete information about the state of region B is equivalent to complete information about the union of regions A and B, and this information propagates independently if A and B are disjoint.

The condition characterizing Bell locality is satisfied for classical point particles but not for classical coherent waves extending over the union of A and B. The Maxwell equations in vacuum provide examples of the latter, although they satisfy causal locality. Thus causal locality and Bell locality are two essentially different concepts.

According to our present knowledge, causal nonlocality is not realized in the universe. If it were, it would wreck the basis of all our subatomic quantum field theory. I nowhere claim (or see a claim of) anything that could support causal nonlocality.

On the other hand, Bell nonlocality has been amply demonstrated experimentally for quantum particles (photons, electrons, and even small molecules). It is an intrinsic effect of approximating the analysis experiments whose fundamental description would need quantum field theory by a simpler analysis in terms of a few particle picture. Bell locality applies to particles only and loses its meaning for fields, which are intrinsically Bell nonlocal, even classically.

Thus quantum physics is local in the causal sense but nonlocal in the Bell sense.

answered Nov 3, 2015 by (15,757 points)
edited Nov 22, 2015

I think this needs to be elaborated a little: "Bell locality applies to particles only and loses its meaning for fields, which are intrinsically Bell nonlocal, even classically." I take it you mean a classical stochastic field that has nontrivial fluctuations (and hence has correlations at space-like separation), given that Bell and CHSH inequalities are statistical/probabilistic statements.

@PeterMorgan: This has nothing to do with stochastic fields; it is enough that the detector is stochastic. For example, the photo effect is primarily due to the stochastic nature of the detector, and is present in models where the field is classical, with only tiny quantum corrections for ordinary light.

To be more specific in the present context, experiments with a classical electromagnetic field are able to violate the Bell inequalities in a similar way as experiments with particles.

Your answer raises the question whether general relativity is nonlocal, i.e. whether it allows solutions were neither of your locality conditions are satisfied.

@ThomasKlimpel See my answer

@ArnoldNeumaier 1. Does your answer imply that the nonlocality required to make hidden variables (entities of physical reality) compatible with experiments violating Bell inequalities is of the same sort as coherent states and those described in your last paragraph? 2. According to your answer, entangled states violate Bell locality, right?

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I briefly discuss 9 different notions of (non)locality that are used in the literature, namely, causality or Einstenian locality, microcausality, lagrangian locality, gravitational nonlocality, cluster decomposition principle, nonlocal collapse of the wave function, nonlocal states, entanglement, and local entities of physical reality.

http://physics.stackexchange.com/questions/34650/definitions-locality-vs-causality/34675#34675

answered Dec 2, 2015 by (885 points)

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