TL;DR

What demonstrates that spatially separated entangled particles are physically disconnected?

For example, Hensen et al. describe entangled electron spins at sites separated by 1.3 km, while photon Bell experiments such as Rauch et al. enforce spacelike-separated measurement conditions.

Nonetheless, an entangled state is still represented before measurement as a joint nonfactorizable state.

So, what experimentally demonstrates that distinguishability and spatial separation necessarily imply complete physical disconnection of entangled particles?

I wonder how the experiments and the theoretical and mathematical framework of quantum mechanics justify the premise that at preparation, by spatially separating and distinguishing the particles, there would also have been the full disconnection of the particles.

I mean: the factual results of the preparation are that they can become separate in space and can be distinguished and manipulated apart, but how experimentally is it known that the entangled particles have been fully physically disconnected one from the other?

I'm not sure why you use the term "physically disconnect". What is that based on?

This implicit assumption was later caught by Bell and used in his theorem proving that QM does not satisfy (Bell-type) local causality.

Bell inequality violations are a result whereby correlations of specific measurements of (an ensemble of) two entangled particles carried out at space like separation are stronger than can be explained by a local hidden variable theory. Or, as Bell would say, a locally causal theory.

However, these correlations can not be used to actually send signals.

Do you count that as "fully physically disconnected" or not?

In QFT, since particles are excitations of the same underlying field permeating all space, 'disconnected' particles, IMHO, aren't the right way to describe what's happening - entangled or not.

Thanks
Bill

The question, therefore, is: what physically establishes the transition at T from an interacting joint system to two non-interacting systems?

Perhaps my use of the word “disconnection” was misleading indeed.

You could imagine shielding the particles from each other or separating them apart by vast distances. In EPRs working model, it would then be absurd to think that the two particles could still interact, affect, or disturb each other in any way. To do so would be "spooky action at a distance" which was absurd to Einstein.

But EPR's argument was faulty. They wrote their paper in 1935, way before Bell proved his inequalities (in the mid 60s) and before violations of Bell inequalities were shown by experiment (in 80s, 90s, 00s, 10s).

This is the collapse of the wavefunction (or quantum field) that lies at the heart of QM. The cause is the interaction with whatever is doing the observing, etc.

You seem to be caught up in thinking of them as two interacting particles physically separated. They are not. When entangled, they can not be thought of as two particles, interacting, separated, or otherwise. As Peter pointed out, if the entangled state is 'asked' its particle number, you of course get 2, but that is all that can be inferred. This was, as @Matterwave pointed out, the error in EPR and the point Bell was making when talking about Bertlmann's socks.

Thanks
Bill

EPR simply didn't notice they were sneaking in a locality assumption into their argument.

Of course they were sneaking in a locality assumption by thinking in terms of individual separate particles, which is something not implied by QM.

They said: 'If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.' Measuring an entangled system disturbs the whole system. Again, I may be missing something.

Thanks
Bill

Wait a minute, if I remember correctly, EPR concerns that if you measure position or momentum, you can immediately predict the position or momentum of the other particle. This would seem to imply they are now separate particles and not entangled. What am I missing?

Thnks
Bill

The relevant quote (shortly after @aletheia provided quote):

“EPR made an implicit assumption in their argument that indeed you can stop the two particles from interacting with each other eventually. If the interaction never stops, their argument (that QM is incomplete) doesn't go through.”

Exactly — that’s the inference I was rejecting;

“You seem to be caught up in thinking of them as two interacting particles physically separated.”

Quite the contrary — that’s exactly the core of my question: why spatial separation and distinguishability should imply complete independence?

“the Hamiltonian no longer having any interaction terms between the two particle (maybe because they got separated really really far from each other)”

Maybe the error was to treat the disappearance of a direct interaction as implying complete physical independence, even though the entangled state itself remains joint.

I drew this image to better illustrate my question:

From my current understanding, the QM formalism does not seem to imply that preparation is followed by a complete physical separation of the entangled subsystems.

It establishes their distinguishability and allows their spatial separation, while the state itself remains joint and nonfactorizable.

My question is whether treating that spatial/dynamical separation as a complete physical independence could be precisely what creates the posterior “spooky” necessity to somehow reestablish a correlation that may never have been physically broken in the first place.

This sloppy wording in the EPR paper simply tries to say: The mutual influence of distant systems by physical interactions can be ignored if they are sufficiently remote.

For example, when EPR says "no longer any interaction", they don't mean measurements of the two particles will be statistically independent. Quite the contrary, their whole argument relies on perfect (anti) correlation.

EPR certainly understood that the entangled state persisted even after time ##T##. They need it for the rest of their argument.

But what they had in mind was to resolve the problem via some local hidden variables. Indeed, their entire argument was that the QM description of physical reality is incomplete (hence their title).

Local hidden variable theories were proven impossible later, as I noted in post #11.

I recommend reading the paper @bhobba referenced in post #12: "Bertleman's Socks and the Nature of Reality" by John Bell. It might prove illuminating.

Summarizing the analogy: the case is not that one sock was pink and the other was not pink, but rather that both were pink and at the measurement one is discovered as red leaving the other as white.

First:
View attachment 373884
brings the assumption that at the preparation both particles are physically separated — meaning that they would have lost their previously joint state —, each of them as a complete whole on their own, which it seems (to me at least) an inference that both the experiments and the QM formalism don’t entitle.

It is only the later experimental proof that those inequalities are violated by nature that local hidden variable theories were disproved (barring any loopholes).

The rest of your argument sounds like (an analogized and rather muddled version of) some of the arguments given by physicists that Bell directly addresses.

The figure is just a figure. It doesn't make any assumptions. It just shows you what the experiment is and what happens.

I'm unclear on what the highlighting of the pants means. The analogy is about socks.

Strictly speaking, Bell's inequalities didn't disprove local hidden variable (LHV) theories. They just put a bound on particular combinations of correlations of specific measurements of pairs of particles that any LHV theory must obey under a mild assumption of statistical independence of measurements.

It is only the later experimental proof that those inequalities are violated by nature that local hidden variable theories were disproved (barring any loopholes).

We usually call a theory such as this a LHV theory. It is what Einstein had in mind to avoid spooky action at a distance.

Did you try reading further into the paper?

The rest of your argument sounds like (an analogized and rather muddled version of) some of the arguments given by physicists that Bell directly addresses.

As far as I can understand, in quantum entanglement, it seems to be assumed that the preparation of the entangled particles would physically disconnect them at the origin, therefore, creating the necessity for an additional explanation for their remaining correlation, which Einstein termed as “spooky action at distance”.

I wonder how the experiments and the theoretical and mathematical framework of quantum mechanics justify the premise that at preparation, by spatially separating and distinguishing the particles, there would also have been the full disconnection of the particles.

I mean: the factual results of the preparation are that they can become separate in space and can be distinguished and manipulated apart, but how experimentally is it known that the entangled particles have been fully physically disconnected one from the other?

I don’t think it would imply it.

@PeterDonis @Matterwave
They state that the systems interact until T,
“[...] let us suppose that we have two systems, I and II, which we permit to interact from the time t =0 to t=T, after which time we suppose that there is no longer any interaction between the two parts.. [...]”,
without deriving it from the observations; then they use
“[...] since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system.[...]”
as a physical premise of the argument, thereby apparently not following their own earlier statement that
“[...] The elements of the physical reality [...] must be found by an appeal to results of experiments and measurements. [...]”,
since the assumed transition from interaction to non-interaction is not itself established there by experiment, nor derived from the quantum-mechanical formalism.

The question, therefore, is: what physically establishes the transition at T from an interacting joint system to two non-interacting systems?

Perhaps my use of the word “disconnection” was misleading indeed.

1. Spatial separation — A and B occupy distinct spatial regions.
2. Operational distinguishability — A and B can be separately labelled, routed, manipulated or detected.
3. Direct dynamical interaction — there is a direct A–B coupling affecting their joint dynamics.
4. Dynamical decoupling / non-interaction — such a direct coupling is absent or negligible, e.g., Hint ≃ 0
5. Jointness / nonfactorizability — the complete quantum state is not reducible to a product of subsystem states.
6. Physical disconnection — some previously existing joint physical structure has actually ceased to obtain.
7. Local real-state attribution — each spatially separated subsystem possesses or admits a real physical state of its own.
8. Locality / real-state autonomy — what is done at A does not physically alter the real state at spacelike-separated B.
9. Exhaustive ontological decomposition / supervenience — the states/properties of A and B plus their spacetime relations exhaust the physical state of the whole.
10. Bell-local factorization — given a sufficiently complete λ, the joint probabilities factorize into local response probabilities.

There is also an important correction to how I formulated the issue earlier in this thread: Murgueitio Ramírez, in Separating Einstein’s Separability (2020), argues that Einsteinian separability should not be identified with supervenience.

So, today I’d put the question like this: which physical operation establishes the transition from an initially joint nonfactorizable structure to physical disconnection or to exhaustively independent local wholes?

Saying that the particles are spatially separated, separately addressable, and no longer directly interacting establishes 1, 2 and perhaps 4. The entangled state establishes 5. But I still do not see the inference that establishes 6 or 9.

That is, I think, a more precise version of the question I was trying — rather clumsily — to ask here early on.