Nonlocality is a problem in space-time definition because in special relativity all physics happens in the nearest surrounding of the observer. This might be solved by quantum field theory. As for entanglement, nonlocality is valid provided there is no transfer of information faster then light. In EPR or teleportation theories, nonlocality is broken through measurements that causes a collapse to the local state.

Dear Abhay Padsala,

Sure, the essence of quantum mechanics is the non-local behavior of particles.

I have a good reason about why we have this behavior in quantum mechanics,

see if you want this paper:

Preprint The theory of disappearance and appearance

especially in section 3.

With best regards.

follow

Quantum mechanics (QM), as of now, is a theory of linear operators in a Hilbert space, although quantum particles are essentially non-local and non-linear objects, as well as are interactions between them. Therefore, there is no rigorous way to account for non-local and non-linear nature of quantum particles and interactions within the framework of QM. Many empirical considerations are added to the theory to account for essentially non-local phenomena (so-called wave-function "collapse" may serve as a great example) understanding of which requires much deeper knowledge of non-classical probability theory and advanced math methods.

Interestingly, classical mechanics, although it works with finite and localized (or even point-wise) classical particles, is essentially non-linear, and its non-linearity helps to account for non-local phenomena. This hints that quantum mechanics may have to be generalized to became a non-linear theory to make it account for non-locality of quantum particles/phenomena and non-linearity of their interactions. Mathematical methods for this generalization may be generalizations, for example, of Feynman's path integral technique. Some other interesting methods are being developed in parametric and functional (I would rather call it functorial) differential geometry.

Yes, non-local phenomena are very much a part of quantum mechanics and quantum theory.

No, non-local phenomena are not limited to cases of entanglement. For example, we see the results of non-local phenomena when an interference pattern emerges after photons are sent, one at a time, through a two slit experiment.

I would say that the two main conditions that lead to measurable displays of non-local phenomena would be, first, when particles are entangled, and second, when it is impossible to know the exact path that particles take. However, these are only the cases where non-local phenomena are measurable and it is likely that non-local phenomena are present in all quantum interactions.

In the first of these two cases, it suggests that the entangled state that is shared by two particles is a state that does not exist in space-time. In the second case, it suggests that when it is possible to know the path that particles take, then those particles will decohere and they will lose their non-local behavior. This suggests that quantum objects that are coherent and have not yet decohered are not fully present in space-time but also exist, at least partially, outside of space-time.

This elucidates the reason why Hilbert space is used in quantum mechanics, because quantum states and wave functions do not fully exist in space-time dimensions except when they are "measured."

There are, of course, other ways of interpreting non-local phenomena. I am just offering answers to your question based on one line of interpretation that ties back closely to quantum formalism.

@Doug Marman has it nearly correct according to the STOE. The STOE suggests if there is one experiment that demonstrates non local phenomena, then all QM phenomena are non-local. The STOE holds particles cause waves in a ether (plenum) which then direct the particle's path (like GR). This uses Bohm interpretation that particles have definite position and momentum at all time - the uncertainty is in the measurement tolerance . See https://www.researchgate.net/project/STOE-photon-diffraction-and-interference

Yes, quantum phenomena can exhibit non-local behavior. This is caused by the use of counterfactual reasoning (the logic condition whose antecedent is or is presumed to be contrary to the fact). When states are entangled, counterfactual reasoning assures a local realism with measurement. However, two other quantum properties (superposition and decoherence) are not inconsistent with counterfactual logic, and, because of these, there are violations of simultaneity, leading to non-local characteristics.

"Quantum nonlocality" and "local realism" are nothing but physical newspeak. As every newspeak, it perverts real meaning.

"Local realism" applies to phenomena that may be described by classical stochastic field theory. Since quantum mechanics may be reformulated in phase space, violation of local realism means quantum phenomena not described by probability theory, and not the impossibility of introducing local physical quantities. And yes, I do realize I am arguing with wording of EPR, but amicus Plato...

"Quantum nonlocality" is a subset of violations of "local realism" involving correlations at space-like intervals. (Such as violation of Bell's inequalities.)

Nonlocality in the true meaning of the word applies to action at a distance, while "quantum nonlocality" - to correlations at a distance.

And so on.

The difficulty is to find local phenomena.

For instance the ionisations in the bubble chamber by charged particles are largely a local phenomenon.

But the micro-wave photons from the big bang radiation are not local.