A question about quantum entanglement

[Ben vdP]

The most entangled might (in general) be the problem description.

Maybe in first order:

Step 1, suppose there is a process in which two quantum particles are created that move away in opposite directions with opposite spins due to conservation laws.
Here we are talking about two specific instances of quantum particles that are correlated.

In the second step there is time evolution with schrodinger equation or other method, wave function, interaction with other quantum particles or fields and all put together as a "state". This leads to probabilities that can be calculated.
And probabilities lead to statistics and ensembles, although there can be an interpretation dependency.
But at this step it is no longer the same system being described as in step 1, it is now a broader system than "two specific instances of quantum particles that are correlated".

Only at the third step there are measurements made with macro world outcomes and how this affects the quantum system or it is yet another qsystem. Now there is interaction between the quantum particles under investigation with measuring devices. That leads to additional disturbances of the "states". At this step the opinions might be diverging the most on for example what that "state" actually is that you are measuring or what the wave function stands for.



Maybe a minor note, but if a measurement is made and that results into a "state" outcome then there is still limited knowledge of the "state" just before the measurement.

 

[Peter Morgan]

The correlations associated with "thermal nonlocality" can't violate the Bell inequalities, so no, I would not say they're "similar enough", since Bell inequality violations are the key issue that undermines intuitive "classical" explanations of the correlations.

Classical measurement theory in the presence of thermal noise can and should include contextuality as noncommutativity, because it's a useful tool for describing multiple complex experiments. Without noncommutativity, Classical measurement theory is straw-manned relative to quantum measurement theory; using the Poisson bracket to include noncommutativity steel-mans classical measurement theory, so that in my AnnPhys 2020 (arXiv, DOI there) I call the expanded classical measurement theory 'CM+'.
With noncommutativity, Bell-type inequalities can be violated. There is an article by Arthur Fine in PhysRevLett 1982, "Hidden Variables, Joint Probability, and the Bell Inequalities", but the mathematics is much more succinctly stated on just the first page of an article by Lawrence J. Landau in PhysLettA 1987,

I rehearse that same mathematics in Section 7.2 of my AnnPhys 2020. In QFT, microcausality requires an exact relationship between locality and noncommutativity, which must play out in a detailed discussion of how the introduction of noncommutativity into classical measurement theory can model a violation of Bell-type inequalities.

[Unacceptable reference and discussion deleted by the Mentors]

 

[Fra]

How do a pair of particles via entanglement “know” what the other particle is doing? Any help is appreciated.

"I think I can safely say that nobody understands quantum mechanics."
"in mathematics you don't understand things. You just get used to them.”
-- Richard Feynman

Mathematically, they are one entity.
...
That is not one causing the other, and it is not a case of a "hidden variable". Simply, knowing one tells you what the other is.

The OP apparently seeks at plausible conceptual understanding of how nature can possibly logically pull this off, rather than just understanding or learning how to use the mathematics of quantum theory.

As someone subscribing to an agentic qbist like interpretation I can interpret OP question quite cleanly and "conceptually" I would personally answer it like this:

1. The particles/part definitely does NOT "know" what the other particle/part "is doing". And there is no need for it.

2. However, following from how the became entangled(there are different ways), their behaviour to certain environmental perturbations are complementing each other in an exact way provided that theiy are both not further manipulated after beeing entangled. But the environment can not infer their behavioural states without destrying it. Neither can a bell type HV over the states explain it, as that isnt how the interaction works.

This is what can explain the correlations. The hard mathematics that "they have as one unity" is conditional on that they are isolated from interactions which would destroy the entanglement. But in terms of reality, this condition stands and falls with wether the experimental conditions can maintain the isolation and entanglement, which is a nontrivial task experimentally. This is also why no other system in the environment can "find out" or "know" or even parameterize any conventional hidden variables that determines their states, becuase that same inference is exactly what would break entanglement as well. Also one particle really does not "know" if the entanglement to the other particle is instantly broken either. That would requirement some other system to collect information from interactions of them both, directly or indirectly. And this is why bell inequality is always violated.

/Fredrik

 

[Demiurge]

The OP apparently seeks at plausible conceptual understanding of how nature can possibly logically pull this off, rather than just understanding or learning how to use the mathematics of quantum theory.

As someone subscribing to an agentic qbist like interpretation I can interpret OP question quite cleanly and "conceptually" I would personally answer it like this:

1. The particles/part definitely does NOT "know" what the other particle/part "is doing". And there is no need for it.

2. However, following from how the became entangled(there are different ways), their behaviour to certain environmental perturbations are complementing each other in an exact way provided that theiy are both not further manipulated after beeing entangled. But the environment can not infer their behavioural states without destrying it. Neither can a bell type HV over the states explain it, as that isnt how the interaction works.

This is what can explain the correlations. The hard mathematics that "they have as one unity" is conditional on that they are isolated from interactions which would destroy the entanglement. But in terms of reality, this condition stands and falls with wether the experimental conditions can maintain the isolation and entanglement, which is a nontrivial task experimentally. This is also why no other system in the environment can "find out" or "know" or even parameterize any conventional hidden variables that determines their states, becuase that same inference is exactly what would break entanglement as well. Also one particle really does not "know" if the entanglement to the other particle is instantly broken either. That would requirement some other system to collect information from interactions of them both, directly or indirectly. And this is why bell inequality is always violated.

/Fredrik

This is not an explanation but a description.

 

[Fra]

This is not an explanation but a description.

Fair point! I should have written that it is a conceptual framework that "allows" for an explanation - witout one particle in som omnipotent way "knows" what the other remote part is doing. The implicit possibility was that the particle just acts out of its expectations; and these are aligned from the entanglement created.

But yes a detailed explanation is not known by anyone so far, so its not what i talk about. I tried to provie a conceptual answer as detailed as possible without going down in some inappropriate whole.

/Fredrik

 

[FactChecker]

This is also why no other system in the environment can "find out" or "know" or even parameterize any conventional hidden variables that determines their states,

I thought that Bell's theorem/test ruled out the existence of local hidden variables.

 

[Fra]

I thought that Bell's theorem/test ruled out the existence of local hidden variables.

Correc,t there is nothing wrong with Bells theorem. There is no local hidden variables in the way of Bell definitions.

/Fredrik