# Entanglement and Bell's theorem. Is the non-locality real?

1. Dec 12, 2012

### Sylvia Else

The results of measurements of phase entangled particles together with Bell's theorem provide pretty convincing evidence that the Universe contains non-local interactions.

Let's imagine the usual idealised experimental scenario, where there is an emitter of particles in a twin state and two measuring devices on opposite sides of the system performing measurements in a space-like separated way. The measurements on one side of the system are not interesting in themselves. They are just random. They only become interesting when they are compared with the measurements from the other side, with a correlation being observed. We know that when performed appropriately, this will show that the measurement results are correlated in a way that, by Bell's theorem, cannot be explained by any local interaction - the measurements appear to be non-locally linked.

Now step back. Consider that the above is performed in complete isolation, except that the results of the final step - comparison of the measurements, is transmitted to an outside observer. For the comparison to be made, the results have to be transferred from where they are made to a common place.

Since the experiment, except for the last step, is performed in isolation, the outside observer can regard the entire experimental situation as a superposition of quantum states with no decoherence except at the last step. The "measurements" are nothing but further entanglements between the twin state particles and the measuring apparatus. The last step involves an interaction between particles that represent the results of the earlier "measurements", with the states of particles for the two measurements for a given twin state pair of particles being already entangled. Those particles now further interact locally to produce the transmitted result of the comparison to the outside observer.

So the outside observer can (in principle, at least) calculate the evolution of the system, and the final transmitted results (in a probablistic sense), without needing to assume any non-local interactions. In particular, the outside observer cannot use Bell's theorem to prove that the system is non-local, because nothing in the system has a definite value that Bell's theorem requires.

From this perspective, it looks as if the appearance of non-locality in the system results from a false assumption by observers embedded in the system that they are somehow independent of it, and that their measurement results are definite values before they are compared.

A possible objection is that we can posit yet another observer outside the enlarged system that consists of the first system and the first outside observer, and do that again and again, making this look like some kind of infinite regression. However the first outside observer sits at the first place where a definite result can be obtained immediately without needing the enlarged system to evolve further.

Sylvia.

2. Dec 13, 2012

### nanosiborg

Depends on what you mean by nonlocal interactions. If you mean instantaneous action at a distance, then that is physically meaningless. If you mean faster than light propagations, then that has not been demonstrated. It is true that, so far, only nonlocal hidden variable models of quantum entanglement are unquestionably viable. But that doesn't mean that they're a true description of reality. There are local hidden variable models of quantum entanglement that are open to question and interpretation. Whether nature is local or nonlocal is still an open question. All that's known for sure is that Bell-type models of quantum entanglement are ruled out. Both mathemetically and experimentally. Whether or not there might be another class of models that might be considered local realistic remains an open question.

The bottom line is that it cannot be definitively said, from Bell tests, that nature is nonlocal. Not because of experimental loopholes, but because the Bell formulation of local hidden variable models might not be general.

We only know that these experimental results can't be explained by Bell's formulation of a local hidden variable supplement to QM. We don't know that this is general. We don't know that there might not be other ways of formulating viable local hidden variable supplements to QM. It might seem to you that Bell has covered all the bases. But has he? Those who say that Bell's formulation is general posit, from experimental violations of Bell inequalities, that nature is nonlocal. Yet, there's no physical evidence for this. The fact of the matter is that it's currently an interpretational, philosophical issue that experimental results can't definitively provide the answer to.

I've omitted the rest of your post because I think it's irrelevant. Even if all experimental loopholes in Bell tests are eventually closed, then what does that mean? It means that Bell-type formulations of quantum entanglement are not viable. And whether or not nature is nonlocal remains an open question.

Why Bell-type formulations of quantum entanglement preparations are nonviable has been the subject of numerous publications.

Here's another thing to consider. Suppose that it's found that absolutely no local model of quantum entanglement can be formulated. Does that mean that quantum entanglement is nonlocal? No, it doesn't. This is because the correspondence of theory to reality is, and will always be, essentially unknown.

Last edited: Dec 13, 2012
3. Dec 13, 2012

### Sylvia Else

It goes somewhat further than that. If the individual measurements have definite values at the time they are made, and the universe isn't cheating by exploiting some experimental loophole, then Bell's theorem shows that it is the measurements themselves that are non-locally linked, and it makes no difference at all what the physical underpinning is, whether it's QM or something else entirely. Whatever it is has to implement the non-locality inherent in the measurements, and the only way to avoid the non-locality is to show that Bell's theorem contains an assumption that is not actually met in reality, thus rendering the theorem inapplicable. One such assumption is that when you make a measurement, you get a definite result, then and there. If you drop that assumption, then Bell's theorem no longer forces you to accept non-locality. Instead the Universe needs some way of unravelling things later (preferably in a local manner) so that the results are consistent.

4. Dec 13, 2012

### nanosiborg

No. It doesn't show that. What Bell's theorem shows is that a certain way of modelling quantum entanglement experiments isn't viable.

Nobody knows, or can ever know, what the "physical underpinning" is. It's a matter of metaphysical speculation.

There's no nonlocality inherent in the measurements. The measurements simply indicate correlations between instrumental parameters and rate of coincidental detection. The correlations might be entirely due to local interactions or they might be due to nonlocal interactions. Nobody knows, and experimental violations of Bell inequalities don't inform regarding this.

The correlations are such that empirical laws from classical optics are applicable to the QM treatment of entanglement. This simple fact would seem to indicate that whatever is going on in quantum entanglement has nothing to do with nonlocality.

Bell's theorem (experimental violations of Bell inequalities) can't show that nature is nonlocal. For those who want to believe that nature is nonlocal, then that's a metaphysical assumption for which there's absolutely no evidence.

Last edited: Dec 13, 2012
5. Dec 14, 2012

### DrChinese

The usual escape from non-locality is denial of realism. That is, there is no definite value for a measurement outcome which is not performed. I believe this is "somewhat" akin to what you are saying. This is a normal part of Bell's Theorem, not a flaw in the theorem.

Your alternative is to postulate macroscopic entanglement, which you would need to keep the entanglement alive. Because usually the results are encoded to computers and then compared. In your view: when the results are brought together, the entanglement ends.

6. Dec 14, 2012

### Sylvia Else

Something like that. I was looking at the decoherence model, in which nothing fundamental changes in a measurement, just that the thing being measured gets entangled with the measuring device, and then ultimately with more and more of its environment. The idea that the entanglement with the measuring device delivers a definite result that can be fed into Bell's theorem looks a bit suspect when the entire experiment is viewed from the outside.

I'm pondering whether one can come up with a version of the EPR experiment where the entanglements are sufficiently clearly specified that the system appears non-local from the inside (an admitedly vague term in this context), but is manifestly local from the outside (ditto). I confess that I haven't made much progress there.

Sylvia.

7. Dec 19, 2012

### JesseM

I think this is the essence of the argument made by advocates of the many-worlds interpretation in explaining why there doesn't need to be any violation of locality in their interpretation--basically if each measurement just puts each experimenter into a superposition of different measurement results, then there is no need for nature to decide which measurement result "here" is paired with which measurement result "there" until there's been time for a signal from each experimenter to reach someone at the midpoint. See for example Vindication of Quantum Locality by David Deutsch and The EPR paradox, Bell's inequality, and the question of locality by Guy Blaylock.

8. Dec 20, 2012

### bohm2

An interesting paper on this topic that came out today:
Simplest proof of Bell’s inequality
http://lanl.arxiv.org/pdf/1212.5214.pdf

Last edited: Dec 20, 2012
9. Dec 20, 2012

### Sylvia Else

People clearly have differing notions of what constitutes simple ;)

The background to my interest in this issue is the experiments that continue to explore the lower bound on the speed of some hypothetical influences that implement the apparent non-locality. I think the experimenters themselves do understand that the results they're getting only have meaning if the influences are real, but this caveat tends to get lost when the results are reported in the popular science media. I was wondering whether these experiments are even worthwhile in the absence of any concrete evidence of the existence of the influences, and while other models of reality remain viable. Of course, one can say that doing experiments that test the limits of theory is necessarily part of what science is about. And that's true, but there are not infinite resources available for doing experiments, so it's inevitable that they get prioritised.

Just yesterday I came across this recent paper

http://arxiv.org/pdf/1210.7308.pdf

in which the authors claim to have proved that if phase entanglement involves influences that travel at a superluminal but finite speed, then it's inevitable that actual FTL communication be possible. That is, it's not possible for such influences to be forever hidden.

Note that their proof does not purport to apply to influences that are instantaneous (necessarily in some privileged reference frame), so some versions of the pilot wave theory would remain possible without allowing FTL communication.

Sylvia

10. Dec 20, 2012

### San K

Interesting paper/hypothesis.

Question: If phase/quantum entanglement is considered random (a basic premise in QM)

then

even if "influences" are assumed to travel FTL, I cannot see how, the author can show that, FLT communication/information would, even theoretically, be possible

Last edited: Dec 20, 2012
11. Dec 21, 2012

### Sylvia Else

If influences are travelling at some FTL but finite speed then it will necessarily by possible to arrange that some measurements on entangled particles are made so close together that the influence cannot arrive in time. The results would then have to respect Bell's inequality.

So if entanglement is actually mediated by FTL finite speed influences, then QM is capable of being falsified, with the required experiment simply not having been done yet.

But the second question is whether it would actually then be possible to exploit the influences. In the paper they show a simple case where an exploit is possible if entanglement is only mediated by such influences, but then show that the exploit is trivially avoided by adding a shared hidden variable. That leaves the question of whether an exploit could still be achieved despite any mechanism based on both FTL finite speed influences and hidden variables. They appear to be showing (I haven't checked the math - I'd have to learn some more of it first) that based on QM, it is possible to construct an exploit. Though as I write this, it occurs to me that their proof appears to be based on a theory, QM, that is, ex hypothesi, in any case wrong. The ramifications of that are currently beyond me.

Sylvia.

12. Dec 22, 2012

### mbd

I posted yesterday a short paper in which I show a deterministic model of quantum spin interactions that achieves the same correlations as QT with only luminal signaling in EPR/CHSH experiments. The paper includes the source code for the simulation. Although not indicated in the paper, in the talk I gave I also showed an experiment than can confirm or rule out the hypothetical mechanism that is the basis for the model. I am working on getting endorsed for arxiv, but in the meantime here it is:

Last edited: Dec 22, 2012
13. Dec 22, 2012

### Sylvia Else

It appears to me from the code that the probability of alice and bob both detecting a given particle is a function of the difference between their respective measurement angles, being higher when the difference between the angles is smaller. This would skew the results.

Second thoughts, scrub that, a model is permitted to do that, provided it achieves it locally.

Last edited: Dec 22, 2012
14. Dec 22, 2012

### lugita15

I think "quantumtantra.com/bell2.html" [Broken] deserves the honor of simplest known proof of Bell's theorem.

Last edited by a moderator: May 6, 2017
15. Dec 23, 2012

### mbd

Thanks for looking at it, Sylvia! That code is there to identify the alpha2 and beta2 angle set upon coincident detections for which correlation and anti-correlation are swapped in the tally. An experiment by Rowe et al has a really clear articulation of CHSH in the paper. I'm at a bar right now or I'd find a proper reference.

16. Dec 23, 2012

### Sylvia Else

Ok, I am bothered by the fact that a lower difference in the angles of Bob and Alice leads to a greater probability of simultaneous detection together with the code that inverts the meaning of correlation for angle differences less than PI/4. This latter seems exactly equivalent to inverting one result, say Alice's, immediately after detection, but only when the angles differ by less than PI/4. That would be manifestly non-local.

17. Dec 23, 2012

### mbd

It is an exploit of a class of coincidence loopholes. It is based on the relative size of the phenomenon to the size of the coincidence window. The counting is correct. If you add a linked list for the sequence of past states you can expand the window. You will also have to reduce the step of the walk of Emmitt. This is the process of finding the constants in a new theory. It's hard...help needed!

Last edited: Dec 23, 2012
18. Dec 23, 2012

### mbd

Note also the other event may never happen. We're not necessarily talking particles travelling and not being counted. Rather, the events actually happen at separate times or perhaps the other never happens.

Last edited: Dec 23, 2012
19. Dec 23, 2012

### sanman

I always feel troubled by Bell's Inequality, and it leads me to ask what would the implications be if Bell's Inequality didn't exist? (ie. what could be inferred if the behavior noted through Bell's Inequality didn't actually happen?) Suppose there was no statistical correlation to be found at all between what Alice, Bob, Joe, Gina or whoever observed?

Of course we know that it happens, and so it's troubling, because it means that something is going on that cannot be dismissed or overlooked. We just don't have the means to further probe it in more detail. Do we?

Metaphorically, it feels as if we are trapped inside a Cage known as SpaceTime, and that Bell's Inequality is revealing to us something that is dangling outside the cage beyond our reach. We cannot grab or grasp this thing, because we are constrained by the bars of SpaceTime.
We are unable to discern what is actually going on behind Bell's Inequality, because it is obscured by SpaceTime itself.

Last edited: Dec 23, 2012
20. Dec 23, 2012

### mbd

Suppose two points in space have a relationship through which the state of each can be seen by the other via a speed-of-light mechanism, i.e. they see each other in the past, and that they react to that state? Then it is certainly possible for the other event to not happen, or happen at time outside the coincidence window.

Really, it is speed-of-light teleportation with a segment of time going from E to A and E to B, which I have shown can achieve the same results as instantaneous teleportation between A and B.

This makes it Einstein-local.

The model can, with a smart agent at E, achieve CHSH results as high as 4.0. That was the substance of my gedanken experiment. It very much involves the other event not happing at all unless both will correlate. The "smart" agent remembers the set of state information (angles) it gets, uses this to optimize strategy of what angle to send down next, and these can be different for A and B. In this way, the agent can make any combination of events happen. There are even some potentially natural rules that can be devised to make it seem more plausible.

Last edited: Dec 23, 2012