Spatial separation of entangled particles implies physical separability?

[aletheia]

TL;DR

What demonstrates that spatially separated entangled particles are physically disconnected?

In experiments with entangled systems, the two subsystems can clearly become spatially separated and operationally distinguishable: they propagate to different locations, can be addressed by different apparatuses, and eventually produce separate local detection records.

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?

 

[PeterDonis]

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

What do you mean by "complete physical disconnection", and why do you think "distinguishability and spatial separation" would necessarily imply it?

 

[aletheia]

What do you mean by "complete physical disconnection", and why do you think "distinguishability and spatial separation"

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?

would necessarily imply it?

I don’t think it would imply it.

 

[PeterDonis]

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

If you mean they usually move away from the source in different directions, yes, that's a common feature of such experiments.

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

creating the necessity for an additional explanation for their remaining correlation

The explanation in QM is the wave function. Yes, Einstein did not like that explanation. But it's the only one we have.

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.

Again, why do you think that is even a premise of QM at all? What is that based on?

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?

Once more: why do you think they have? Where is that coming from?

I don’t think it would imply it.

Then why are you even asking the question at all? What prompted it? All this that you are saying about "fully physically disconnected" must have come from somewhere. Where?

 

[Matterwave]

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”.

Are you reading the EPR paper? It was an implicit assumption of EPR that sufficient spatial separation implies non-interaction. They basically argue that since the entangled particles are far apart from each other, they can not affect each other. This is manifest in special relativity as space like separated events are causally disconnected.

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

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.

It depends on what you mean by "full disconnection of the particles". I don't know what this means and I have not heard this terminology before.

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?

 

[bhobba]

It's better to think in terms of Quantum Field Theory (QFT) for this one. Entangled particles are a single excitation of the field, so thinking in terms of two separate particles makes no sense. If you think of the quantum field, when one particle is detected, the entanglement is broken, and you have two separate excitations. I like to think of it like a stretched piece of elastic. Cut it, and you immediately get two pieces that are no longer stretched. Is it non-local in that picture? I think so, but others may like to debate it.

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

 

[Matterwave]

Entangled particles are a single excitation of the field, so thinking in terms of two separate particles makes no sense.

Hmmm, what are you counting as a "single excitation" here? If you hit the state with the number operator, you don't get 2?

 

[PeterDonis]

what are you counting as a "single excitation" here? If you hit the state with the number operator, you don't get 2?

You do get 2, but you can't split the state up into a product of two states each with a value 1 for the number operator. That's what it means for the state to be entangled.

 

[bhobba]

Hmmm, what are you counting as a "single excitation" here? If you hit the state with the number operator, you don't get 2?

Peter beat me to the punch - he often does

Thanks
Bill

 

[aletheia]

@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.

 

[Matterwave]

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.

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).

 

[bhobba]

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

The general principle is that in QM the outcome is the eigenvector of the observable. Here it is a product state of 2 separate single particles.

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

 

[Matterwave]

Here it is a product state of 2 separate single particles.

Not for the EPR state. It is still an entangled state and not a product state. When EPR says (something like) "after T, the two particles no longer interact" they mean something more akin to the Hamiltonian no longer having any interaction terms between the two particles (maybe because they got separated really really far from each other) and not that the state has collapsed into a product state.

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

 

[bhobba]

Not for the EPR state.

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?

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

 

[Matterwave]

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

Just the time order of things as the paper presents it. T is not the time of the measurement, it's the final time after which the entanglement is "locked in" so to speak. It is only after some more time, at a time $t'>T$ that the measurement happens.

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

We can then calculate with the help of Schroedinger's equation the state of the combined system I+II at any subsequent time; in particular, for any $t>T$.

 

[bhobba]

Just the time order of things as the paper presents it.

Got it.

Thanks
Bill.

 

[Matterwave]

The EPR paper is always worth a (re)read . It is a delightful paper, though it has its faults.