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Bell's inequality together with the Aspect experiment shows that that we cannot have local realism. But does quantum theory obey locality? and if not how can locality be violated but not special relativity? Can you (if possible) also provide a source with your answer

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Answer to your question

The term "quantum non-locality" refers to the fact that quantum mechanics cannot be described by a local classical hidden variable model. This is the content of Bell's theorem.

In particular, locality is not violated. The statement of the theorem is that if we assume (wrongly) that quantum mechanics is described by a classical hidden variable model, then locality is violated. This doesn't tell us that quantum mechanics violate locality, this tells us that quantum mechanics cannot be described by a local classical model.

An opinionated remark regarding terminology

"Non-locality" is really misleading (although common) terminology. A less confusing term for this might be simply "bell-inequality-violation". A term that describes a broader class of these no-go theorems is "non-classicality", which is also much less misleading.

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