I How can Bohmian mechanics explain entanglement?

[sahashmi]

TL;DR

How can any non local hidden variable theory explain entanglement?

Does this paper rule out all non local causal theories for entanglement?

This paper is titled “ Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling”: https://arxiv.org/abs/1110.3795

In the paper, they demonstrate that if there is any causal influence among entangled particles (under even a preferred reference frame like in non local hidden variable theories such as Bohmian mechanics), the no signalling theorem cannot hold.

In a particular 4 partite entanglement scenario they devise, they show that if there is a non local causal influence, it must trivially allow faster than light signalling. But QM, nor relativity, does not allow FTL signalling as far as I’m aware for any kind of entanglement scenario.

Is this paper correct or are the claims too bold? I’m genuinely confused and I’d appreciate any assistance.

 

[PeterDonis]

The paper's definition of "causal influence" is something propagated through space at a finite speed by something that carries the causal influence. As the paper points out (bottom of p. 2), models like Bohmian mechanics and the GRW collapse theory violate this definition, so they are not covered by the result the paper derives. Which means that the result doesn't really tell us very much.

 

[jambaugh]

When attending a quantum computing conference in Italy many years ago we referred to this "no FTL signalling" theorem as the "No Bell Telephones" theorem. In my opinion, with no observable supraluminal causation, we should dispense with assertions about hidden supraluminal causation (just like Einstein got rid of the luminiferous aether). [edit: reworded]

I think our use of the term entangled is somewhat unfortunate as it implies causal interactions that are not specifically asserted. Rather we should rename such systems as being quantum correlated IMNSHO. This still doesn't preclude our exploring the question about such interactions but does remove a certain implicit bias.

 

[sahashmi]

The paper's definition of "causal influence" is something propagated through space at a finite speed by something that carries the causal influence. As the paper points out (bottom of p. 2), models like Bohmian mechanics and the GRW collapse theory violate this definition, so they are not covered by the result the paper derives. Which means that the result doesn't really tell us very much.

Yes, but Bohmian mechanics does posit causal influences. And unless this influence is infinite speed (which Bohmian mechanics does not explicitly require as far as I’m aware), then this kind of influence would be ruled out IF no signalling holds for the kind of experiment that is proposed in the paper. No?

If you read the paper, all that’s required for the argument to go through it seems is having a privileged reference frame with a particular time order of events.

 

[DrChinese]

TL;DR Summary: This paper is titled “ Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling”.

Does this paper rule out all non local causal theories for entanglement?

This paper is titled “ Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling”: https://arxiv.org/abs/1110.3795

In the paper, they demonstrate that if there is any causal influence among entangled particles (under even a preferred reference frame like in non local hidden variable theories such as Bohmian mechanics), the no signalling theorem cannot hold.

Just echoing what PeterDonis said. There is no hint that QM requires either causality or a finite velocity for the interactions described in the paper. Experiments appear to show quite the opposite. And there is no hint that FTL signaling is possible.

 

[sahashmi]

Just echoing what PeterDonis said. There is no hint that QM requires either causality or a finite velocity for the interactions described in the paper. Experiments appear to show quite the opposite. And there is no hint that FTL signaling is possible.

Isn’t the hint that without having causality, you are left with non local correlations without an explanation? How else would they stay correlated? I understand that the traditional answer is to suggest that they act as one entity and all that but I feel as if that’s burying the problem a bit

 

[PeroK]

Isn’t the hint that without having causality, you are left with non local correlations without an explanation?

Causality is more appealing to the human mind, I guess. But, perhaps nature is just as happy with correlations.

How else would they stay correlated?

That's a law of physics, as it were.

I understand that the traditional answer is to suggest that they act as one entity and all that but I feel as if that’s burying the problem a bit

Correlation might be explained to a greater extent by some more fundamental theory. But, there is no guarantee that this more fundamental theory will be any more palatable.

 

[PeterDonis]

without having causality

The paper you referenced does not address "causality" in general. It only addresses one particular concept of "causality", the one I described in post #2. It says nothing whatever about other possible concepts of "causality".

 

[jambaugh]

Isn’t the hint that without having causality, you are left with non local correlations without an explanation? How else would they stay correlated? I understand that the traditional answer is to suggest that they act as one entity and all that but I feel as if that’s burying the problem a bit

It might be better phrased as "non localized correlations". Remember that even a single particle in a momentum eigen-"state" is a non-localized quantum system. A positive detection at a given point is correlated with the null detection at all other points in space. That's not shocking. The same happens classically in spades but we feel comfortable with it because we can fit classical phenomena within our models of objective reality.

As to "how they stay correlated" they do so through the absence of further intermediate interactions and that need not happen. Indeed it's rather tricky to maintain such when desired which is why quantum computing devices typically need extra refrigeration.

I say, don't get hung up in the locality in Bell's theorem. The critical implication is that there is no fundamental objective reality based description of quantum phenomena. What we think of as reality is only our conceptual model of the actuality of natural phenomena. Replace conceptualization in terms of "what is" with conceptualization of "what happens".

 

[sahashmi]

It might be better phrased as "non localized correlations". Remember that even a single particle in a momentum eigen-"state" is a non-localized quantum system. A positive detection at a given point is correlated with the null detection at all other points in space. That's not shocking. The same happens classically in spades but we feel comfortable with it because we can fit classical phenomena within our models of objective reality.

As to "how they stay correlated" they do so through the absence of further intermediate interactions and that need not happen. Indeed it's rather tricky to maintain such when desired which is why quantum computing devices typically need extra refrigeration.

I say, don't get hung up in the locality in Bell's theorem. The critical implication is that there is no fundamental objective reality based description of quantum phenomena. What we think of as reality is only our conceptual model of the actuality of natural phenomena. Replace conceptualization in terms of "what is" with conceptualization of "what happens".

Locality has been ruled out by Bell. There’s no way around this. No local but “non realistic” theories can reproduce the correlations we see in QM

 

[martinbn]

Locality has been ruled out by Bell. There’s no way around this. No local but “non realistic” theories can reproduce the correlations we see in QM

This is not the usual understanding of Bell.

 

[PeterDonis]

No local but “non realistic” theories can reproduce the correlations we see in QM

That's not correct. Violations of the Bell inequalities rule out theories that meet all of the assumptions of Bell's Theorem; those assumptions include both locality and realism. All a theory needs to do is violate one assumption to not be ruled out by Bell's Theorem; so theory that is local but violates realism would not be ruled out.

 

[jambaugh]

Locality has been ruled out by Bell. There’s no way around this. No local but “non realistic” theories can reproduce the correlations we see in QM

No, Bell utilizes an RAA hypothesis of local causality and that probability acts as a measure over a state manifold and thus is additive. The local causality is just one of many ways to invoke the hypothesis that a system can be factored and interactions between components can be prevented. The commutativity of two observables with non-trivial spectra is all that is needed.

Bell's inequality is equivalent to the triangle inequality for the metric: d(A,B)=P(A xor B). (It takes a wee bit of math to convert between Bell's correlations and these probabilities but it is straightforward.)

Note that you lose objective reality anyway if you allow that all events in the universe are causally connected to all others. What does it mean for a system to be in an "objective state" today if some future action can change this past state. The only real choice is non-reality with local causation or non-reality without local causation.

(Clarification: Reality = objective ontological model = the universe of object with objective states. Actuality is a better word, as in "what goes on out there".)

 

[DrChinese]

Locality has been ruled out by Bell. There’s no way around this. No local but “non realistic” theories can reproduce the correlations we see in QM

As @PeterDonis says, Bell rules out either locality or realism, or both. This is generally accepted physics.

On the other hand, Bell is not the only theorem or experiment on the block that tackles this subject. 2 important developments (actually many) might be worth looking at. Both of these are “new” (meaning only about 30 years old).

GHZ Theorem
Entanglement Swapping with Remote/Delayed Choice

Both of these papers, when added with Bell, cast substantial doubt on any remaining ideas about locality and realism. However, there are still interpretations (such as MWI and Bohmian Mechanics) of QM that seek to preserve one or the other. So it is up to you as to what you conclude.

 

[sahashmi]

I’m having trouble how this theory can explain entanglement. In entanglement, local hidden variables have been ruled out. Note that this means entangled particles in some sense must be interacting with each other if one believes in a non local hidden variable theory.

Note that this interaction must happen at measurement. Before each particle is measured, it does not have a predefinite spin. If it did, one can just imagine a local hidden variable for each particle, but those have been ruled out by Bell’s theorem.

In other words, once and **after** particle A is measured, this outcome must somehow, in some cases, determine particle B’s outcome. This does not mean particle B cannot have a local hidden variable. It can, especially in the case where particle A is not measured. But in some cases, when particle A is measured, it must influence B’s result

Here’s the problem. We’ve done measurements on entangled particles that are practically at or near the same time. We’ve even created a bound on this where the time between these measurements is so short, any influence of particle A on particle B at measurement must be atleast 10,000 times faster than the speed of light: https://www.livescience.com/27920-q...hat the slowest,least relative to light beams.

But wouldn’t such an influence be detectable? How can an influence this fast be occurring everywhere and yet not be detected?

 

[sahashmi]

That's not correct. Violations of the Bell inequalities rule out theories that meet all of the assumptions of Bell's Theorem; those assumptions include both locality and realism. All a theory needs to do is violate one assumption to not be ruled out by Bell's Theorem; so theory that is local but violates realism would not be ruled out.

There is no realism assumption in Bell’s theorem: only locality and statistical independence. So this is incorrect.

 

[martinbn]

There is no realism assumption in Bell’s theorem: only locality and statistical independence. So this is incorrect.

What is the full statement of Bell's theorem?

 

[sahashmi]

As @PeterDonis says, Bell rules out either locality or realism, or both. This is generally accepted physics.

On the other hand, Bell is not the only theorem or experiment on the block that tackles this subject. 2 important developments (actually many) might be worth looking at. Both of these are “new” (meaning only about 30 years old).

GHZ Theorem
Entanglement Swapping with Remote/Delayed Choice

Both of these papers, when added with Bell, cast substantial doubt on any remaining ideas about locality and realism. However, there are still interpretations (such as MWI and Bohmian Mechanics) of QM that seek to preserve one or the other. So it is up to you as to what you conclude.

Bell’s theorem does not have realism as an assumption. It only has locality and statistical independence as an assumption. Local but non realistic theories cannot generate the correlations. The same way two independent coins cannot be correlated to each other since the probability of it would be very low

 

[pines-demon]

The answer is very clear, spin (which in Bohmian is not even a particle property but that does not matter much) can be influenced faster-than-light in Bohmian mechanics. That's it.

Note that Bohmian mechanics was developed before Bell's inequalities and yet Bohm had already noticed that his theory was non-local. From interpretations of quantum mechanics, this is one did not need to be revised or reinterpreted in any way after violations of Bell's inequalities were confirmed.

Note that this interaction must happen at measurement. Before each particle is measured, it does not have a predefinite spin. If it did, one can just imagine a local hidden variable for each particle, but those have been ruled out by Bell’s theorem.

In Bohmian mechanics particles have predefinite values. This hidden value would be some global parameter of the universe that could be modified from anywhere else independent of distance.

 

[sahashmi]

The answer is very clear, spin (which in Bohmian is not even a particle property) can be influenced faster-than-light in Bohmian mechanics. That's it.

Note that Bohmian mechanics was developed before Bell's inequalities and yet Bohm had already noticed that his theory was non-local. From interpretations of quantum mechanics, this is one did not need to be revised or reinterpreted in any way after violations of Bell's inequalities were confirmed.

Sure, but this means that the spin of one measurement must somehow cause the spin of another measurement in some cases in bohmian mechanics. The problem is that this is still a physical influence and it must be atleast 10,000x as fast as light. Is this not an issue?

 

[DrChinese]

There is no realism assumption in Bell’s theorem: only locality and statistical independence. So this is incorrect.

Sure there is.

Look around Bell’s (14) where he says: “It follows that c is another unit vector…” - that is in addition to an and b. So the usage of all 3 - a, b and c - is a concrete expression of Realism. To fully follow this point, you must go back to the EPR paper it references. There, at the end, they talk about the simultaneous elements of reality they explicitly assume. Bell attacks that by incorporating their assumption into his formula. He then proves there are no simultaneous values for a, b and c that can reproduce the quantum expectation.

On the EPR Paradox (1964)

Admittedly most folks don’t point to this specifically. But there it is.

Quantum mechanics is contextual, so such realism can - in principle - be rejected. That could lead one to “save” locality. But that then depends on a suitable interpretation.

 

[pines-demon]

The problem is that this is still a physical influence and it must be atleast 10,000x as fast as light. Is this not an issue?

It is an issue and many people do not like Bohmian mechanics because of that. Is it a physical issue? Yes, but as long as you can show that it does not allow OTHER faster than light influences we are all ok. If it somehow allows faster-than-light signaling then it is no longer an interpretation and has to be tested experimentally, some people look for evidence of this.

 

[sahashmi]

Sure there is.

Look around Bell’s (14) where he says: “Let c be a unit vector…” - that is in addition to a and b. So the usage of all 3 - a, b and c - is a concrete expression of Realism. To fully follow this point, you must go back to the EPR paper it references. There, at the end, they talk about the simultaneous elements of reality they explicitly assume. Bell attacks that by incorporating their assumption into his formula. He then proves there are no simultaneous values for a, b and c that can reproduce the quantum expectation.

Admittedly most folks don’t point to this specifically.

This does not mean that a non realistic local theory can reproduce the results. If certain measurables are not pre determined, then they are determined at measurement. But if there are no influences between particles, then there is no reason why the measurements should stay correlated unless you incorporate some form of non locality. The point is that the two particles function as one, non local object. Any measurement of one constrains the other, even if they are space like separated.

 

[sahashmi]

It is an issue and many people do not like Bohmian mechanics because of that. Is it a physical issue? Yes, but as long as you can show that it does not allow OTHER faster than light influences we are all ok. If it somehow allows faster-than-light signaling then it is no longer an interpretation and has to be tested experimentally, some people look for evidence of this.

They have shown that for particular multi partite entanglement scenarios, there should be superluminal signalling allowed if this influence is propagated at a finite speed faster than light. This may not include Bohmian mechanics but this is a testable scenario.

The experiments are outlined in this paper:
https://www.nature.com/articles/nphys2460

 

[pines-demon]

They have shown that for particular multi partite entanglement scenarios, there should be superluminal signalling allowed if this influence is propagated at a finite speed faster than light. This may not include Bohmian mechanics but this is a testable scenario.

The experiments are outlined in this paper:
https://www.nature.com/articles/nphys2460

Does that rule out the case of instantaneous speed?

Edit: also please do not use this thread to bypass the discussion on the other thread.

 

[DrChinese]

Local but non realistic theories cannot generate the correlations.

If you believe this, you should read the 2 references I provided you. Those support your position - they go beyond Bell.

 

[DrChinese]

This does not mean that a non realistic local theory can reproduce the results. If certain measurables are not pre determined, then they are determined at measurement. But if there are no influences between particles, then there is no reason why the measurements should stay correlated unless you incorporate some form of non locality. The point is that the two particles function as one, non local object. Any measurement of one constrains the other, even if they are space like separated.

All this may be correct, but you are missing a key point. Bell doesn’t prove what you say above. It only rules out local realism. That was your original question. Bell alone doesn’t prove there is nonlocality. But other evidence easily could.

If you dive into the Interpretations subforum, you can probably discuss this in a bit more depth. You will find folks giving spirited defenses of locality. But those involve interpretation issues that are not universally accepted.

 

[martinbn]

Local but non realistic theories cannot generate the correlations.

Well, quantum mechanics can generate the correlations!

 

[berkeman]

Edit: also please do not use this thread to bypass the discussion on the other thread.

Thread closed temporarily for review by the Mentors.

 

[sahashmi]

Can someone please explain whether the experimental scenarios in the paper have actually been performed? They outline a specific scenario and a specific inequality. Is the experiment is performed and the inequality is broken, then we can safely rule out all finite speed causal influence models even if they’re faster than light.

To anyone who has read the paper, have these experiments been done? If not, is it still feasible for the results to be explained by finite speed causal influence models?