What do violations of Bell's inequalities tell us about nature?

[bohm2]

Relational BlockWorld is local. I consider it non-realistic.

How about this model? One of the papers just came out today. The author argues that it is local and makes all the predictions of QM:

But, by combining Richard Feynman’s formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the “space of all paths,”- SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set λ of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set λ is nonmeasurable, and therefore the above equation is meaningless in SP. Moreover, using another simple mathematical expression (based on the exponentiated-action over a path) as an alternative to the above equation, we show in a straightforward argument that SP is a local system.

Failure Of The Bell Locality Condition Over A Space Of Ideal Particles And Their Paths
http://lanl.arxiv.org/ftp/arxiv/papers/1302/1302.5418.pdf

Bell inequalities and hidden variables over all possible paths in a quantum system
http://lanl.arxiv.org/ftp/arxiv/papers/1207/1207.6352.pdf

The Space of all paths for a quantum system: Revisiting EPR and BEll's Theorem
http://lanl.arxiv.org/ftp/arxiv/papers/1109/1109.6049.pdf

What is interesting is the author's argument is similar to rubi's, I think (?), but he arrives at it using a different model:

The interesting thing, though, is that all proofs of Bell’s theorem (his original arguments and those by others in the same vein) for two entangled particles involve a probability distribution. This means that there is indeed a hidden premise, a tacitly assumed “X”—namely, that the underlying space for a quantum system is measurable. In other words, if we choose “X” to be “measurable” then in Maudlin’s formula we have the proposition, “No local, measurable theory can make The Predictions for the results of experiments carried out very far apart.” We consider Bell’s simple proof of this specific proposition (that is, when “measurable” is substituted for X) to be obviously valid.

 

[stevendaryl]

How about this model? One of the papers just came out today. The author argues that it is local and makes all the predictions of QM:

Failure Of The Bell Locality Condition Over A Space Of Ideal Particles And Their Paths
http://lanl.arxiv.org/ftp/arxiv/papers/1302/1302.5418.pdf

Bell inequalities and hidden variables over all possible paths in a quantum system
http://lanl.arxiv.org/ftp/arxiv/papers/1207/1207.6352.pdf

The Space of all paths for a quantum system: Revisiting EPR and BEll's Theorem
http://lanl.arxiv.org/ftp/arxiv/papers/1109/1109.6049.pdf

What is interesting is the author's argument is similar to rubi's, I think (?), but he arrives at it using a different model:

Thanks for these references. They are fascinating, and very exciting. However, in
"Bell Inequalities And Hidden Variables Over All Possible Paths In A Quantum System" (http://lanl.arxiv.org/ftp/arxiv/papers/1207/1207.6352.pdf), the author says something false, which already came up in this thread:

It seems surprising that no one until now has noticed the hidden premise of measurability in Bell’s definition of locality

As I pointed out, Pitowky and others came up with counterexamples to Bell's Theorem that exploited nomeasurability of the space of hidden variables. Pitowsky's model was very ad hoc, and Leffler's model seems much more natural and physically meaningful, but it's false to say that nobody had looked at nonmeasurability before.

 

[rubi]

What is interesting is the author's argument is similar to rubi's, I think (?), but he arrives at it using a different model:

The problems with measurability that i mentioned earlier don't apply to the argumentation of ttn, because Bell locality doesn't require something like a translation-invariant measure on the space of wave-functions. It's only needed if you want to rule out all theories with huge hidden-variable spaces using Bell's theorem. That's why the counterexamples stevendaryl mentioned can work.

My latter argument doesn't require any fancy math. I just argue that standard QM doesn't account for individual outcomes of measurements an thus they can't be beables of the theory. Ttn's proof (post #204) of non-locality however requires individual outcomes to be beables and thus it can't be applied to standard QM in this way. The beables are the probability distributions instead and if you apply Bell's condition to them, it reduces to the statement of the no communication theorem, so the theory is Bell local whenever the no communication theorem holds.

 

[stevendaryl]

The problems with measurability that i mentioned earlier don't apply to the argumentation of ttn, because Bell locality doesn't require something like a translation-invariant measure on the space of wave-functions. It's only needed if you want to rule out all theories with huge hidden-variable spaces using Bell's theorem. That's why the counterexamples stevendaryl mentioned can work.

I have to say, though, that there is something philosophically screwy about nonmeasurable sets when you try to apply them to the real world.

Here's a very weird example: Suppose we have a game in which two people, Alice and Bob, generate random real numbers in the set \lbrace x\ \vert\ 0 \leq x \leq 1 \rbrace. (Imagine spinning a dial, and taking the resulting angle, divided by 2 \pi.) Beforehand, we pick a total ordering on the reals x \succ y (not the usual ordering). If Alice's number is a and Bob's number is b, then Alice wins if a \succ b. Otherwise, Bob wins.

Suppose that our two players are Alice and Bob. Alice generates her real, a, and looks at it, but doesn't tell Bob what it is. Based on the value of her real, she is allowed to place a wager on the game. She notices the following fact:

There are only countably many values b that would beat her number a.
​

She reasons that the probability of Bob generating a real number that lies in any countable set is rigorously zero. So almost certainly (with probability 100%), Alice will win the game. So she's justified in betting her life savings on the outcome.

However, Bob takes a look at his real, b and sees that there are only countably many values for a that would beat it. So, similarly, Bob is justified in betting his life savings on the outcome of the game.

Obviously, someone is not only wrong, but in a sense is infinitely wrong. The outcome that seemed almost certain didn't happen for one of them. Well, that's the breaks, sometimes things of measure zero happen. But they certainly shouldn't happen very often.

Well, it is mathematically possible to construct a total ordering \succ on reals so that absolutely every round of the game, either Alice or Bob will experience something of probability zero happening. That is, we can arrange it so that for every real x, there are only countably many values of y that would beat it.

Pitowsky's model uses exactly the same type of construction as the one that would produce the total ordering \succ. So there is something a little unsettling about it. For probabilities to behave the way we think they should, we need for things of probability zero to never happen (or practically never). But in Pitowsky's construction, there are events of probability zero that happen every single time.

 

[DrChinese]

While many of these have been mentioned on various threads/posts I thought I'd post a list of the major papers I've come across arguing that violations of Bell's inequality implies non-locality, irrespective of any other issues (e.g. realism, determinism, hidden variables, pre-existent properties, etc.):

Bertlmann’s socks and the nature of reality
http://cds.cern.ch/record/142461/files/198009299.pdf

...

As rubi and morrobay point out, there are papers that come out the other way on the subject. I.e. that violations of Bell Inequalities indicate it is local non-realism that should be selected. Here is once example:

http://arxiv.org/abs/0909.0015

Abstract:

"It is briefly demonstrated that Gisin's so-called 'locality' assumption [arXiv:0901.4255] is in fact equivalent to the existence of a local deterministic model. Thus, despite Gisin's suggestions to the contrary, 'local realism' in the sense of Bell is built into his argument from the very beginning. His 'locality' assumption may more appropriately be labelled 'separability'. It is further noted that the increasingly popular term 'quantum nonlocality' is not only misleading, but tends to obscure the important distinction between no-signalling and separability. In particular, 'local non-realism' remains firmly in place as a hard option for interpreting Bell inequality violations. Other options are briefly speculated on. "

 

[stevendaryl]

As rubi and morrobay point out, there are papers that come out the other way on the subject. I.e. that violations of Bell Inequalities indicate it is local non-realism that should be selected. Here is once example:

http://arxiv.org/abs/0909.0015

Abstract:

"It is briefly demonstrated that Gisin's so-called 'locality' assumption [arXiv:0901.4255] is in fact equivalent to the existence of a local deterministic model. Thus, despite Gisin's suggestions to the contrary, 'local realism' in the sense of Bell is built into his argument from the very beginning. His 'locality' assumption may more appropriately be labelled 'separability'. It is further noted that the increasingly popular term 'quantum nonlocality' is not only misleading, but tends to obscure the important distinction between no-signalling and separability. In particular, 'local non-realism' remains firmly in place as a hard option for interpreting Bell inequality violations. Other options are briefly speculated on. "

The lack of separability in quantum mechanics is reflected in the fact that the wave function for more than one particle is not a function in 3 dimensional physical space, but a function in 3N dimensional configuration space. It's hard to know what "local" means for such a theory.

I don't know how significant this is, but in the Heisenberg picture, where the wave function is static and the operators evolve, all evolution is described by perfectly normal evolution equations involving ordinary 3D space plus time. So that is a sense in which the dynamics of quantum mechanics is perfectly local. Any nonlocality happens when you sandwich an operator between in- and out- states, which isn't something that takes place in time.

 

[billschnieder]

What do violations of Bell's inequalities tell us about nature?

Nothing.

http://neuron2.net/papers/bell.pdf

 

[stevendaryl]

What do violations of Bell's inequalities tell us about nature?

Nothing.

http://neuron2.net/papers/bell.pdf

My feeling is that that paper is either wrong, or tautological. In neither case does it tell us anything about Bell's inequalities.

 

[DrChinese]

My feeling is that that paper is either wrong, or tautological. In neither case does it tell us anything about Bell's inequalities.

For what it's worth, billschnieder is a local realist. His reference does not meet the standards for PF. But as long as everyone knows it, considering this thread is essentially an opinion thread anyway, I guess it can't hurt.

 

[billschnieder]

My feeling is that that paper is either wrong, or tautological...

And you are never wrong or misguided.

 

[nitsuj]

I don't see how 'action at a distance' applies to entanglement in quantum world, even by analogy, where/(if) there is no 'action' or 'distance'. Of course ultramicroscopic particles are subject to other properties dependent on space and time. They are 4-space dependent, but quantum-wise non-local. Or to put it less prejudicially (since 'non-local' has the connotation of being somehow defective, deviant, odd), quantum-entanglement has only one locale.

Of course, there are spins that are not entangled, but I could speculate further that all spin-baggage, correlated or not, is permanently stuck in some cosmic LaGuardia airport.

I've always been in the shallow end with respect to an "understanding" of QM because of this "entanglement" thing. It simply doesn't make sense to me strictly because of [STRIKE]causality[/STRIKE]/localism. So no matter how much I would read, it just wouldn't stick.

This perspective you presented makes so much more sense. Essentially the same as Maui post23.

I feel a little slow, not realizing this horse&carriage arrangement on my own .

I guess to say it different, QM isn't so stupid anymore Thanks!

 

[bohm2]

As rubi and morrobay point out, there are papers that come out the other way on the subject. I.e. that violations of Bell Inequalities indicate it is local non-realism that should be selected. Here is once example:

http://arxiv.org/abs/0909.0015

Leaving aside the issue of whether a local non-separability makes sense consider this quote in the paper you linked:

One sentiment of Gisin’s that I do strongly agree with is expressed in the first paragraph of [1]: “why should one use the word local realism rather than local determinism?” The second term is, after all, far less loaded with metaphysical luggage. The popularity of the first term, despite the vagueness of ‘realism’, is due of course to its introduction by Bell in his famous paper [2] [(no doubt as a homage to the discussion of ‘elements of reality’ in the similarly famous paper of Einstein, Podolsky and Rosen.

Given what has been mentioned previously by ttn, do you still feel like this makes any sense to you? And here's the 1964 Bell paper in your link [reference 2 above]:

On the EPR paradox
http://www.drchinese.com/David/Bell_Compact.pdf

Can you hi-lite a relevant part of Bell's 1964 (reference 2) paper where Bell discusses "local realism" or "realism"?

 

[DrChinese]

Leaving aside the issue of whether a local non-separable theorem makes sense consider this quote in the paper you linked:

Given what has been mentioned previously by ttn, do you still feel like this makes any sense to you? And here's the 1964 Bell paper in your link [reference 2 above]:

On the EPR paradox
http://www.drchinese.com/David/Bell_Compact.pdf

Can you hi-lite a relevant part of Bell's 1964 (reference 2) paper where Bell discusses "local realism" or "realism"?

I realize that a lot of people make a distinction between EPR "realism (or simultaneous elements of reality) and Bell "hidden variables (determinism)". Personally, I use them interchangeably when discussing EPR and Bell. The reason I do that is because Bell's paper is a follow up to EPR (see its title) and therefore one must assume Bell begins where EPR left off.

For all practical purposes: if you have hidden variables that determine the outcome of individual measurements, you also have realism. If there are simultaneous elements of reality, there must be determinism as well. So they seem to act together. Despite all the semantics, I rarely see much difference in application between these.

Bell never spells out what he means by "realism" other than mathematically (see his 14 where he is adopting the EPR definition by inference). I say they are the same (Bell determinism = EPR realism).

As I have discussed with ttn previously, and I think he agrees, EPR effectively says that the existence of elements of reality (considering you have the perfect correlations) implies hidden variables and/or determinism. Of course they also assume (and they say explicitly) there must also be observer independence, as well as locality (no action at a distance). So you end up with a bunch of terms that are closely associated, and it is difficult to embrace one over the other without referring back to EPR or Bell.

Elements of Reality / Realism / Hidden Variables / Causality / Determinism

Observer Independence / Separability

Locality / No Action at a Distance

I have placed terms on lines not trying to be exact, but just to show that you could pick a couple of these terms and end up with a phrase that has probably just by an author at some point or another to describe Bell's result.

 

[1977ub]

Is superdeterminism ever taken seriously in these discussions?
http://en.wikipedia.org/wiki/Superdeterminism

I had a similar thought when I heard about Alain Aspect experiments - I mean however far apart the measurements are being made, you can fit the entire situation in a light cone.

If one is truly serious about determinism, then you can't take too seriously a suggestion that someone is "freely" or "randomly" making a particular measurement!

As "unlikely" as superdeterminism might seem... as time drags on, aren't abandonment of locality or causality even harder to swallow?

 

[DennisN]

Is superdeterminism ever taken seriously in these discussions?
http://en.wikipedia.org/wiki/Superdeterminism

I can only speak for myself; I don't take it seriously. How do you show/falsify superdeterminism? If it can't be evaluated, does superdeterminism have any scientific value? The question of quantum locality/nonlocality has at least a fair chance of being evaluated IMO, but I guess it will take a while.

 

[1977ub]

I can only speak for myself; I don't take it seriously. How do you show/falsify superdeterminism? If it can't be evaluated, does superdeterminism have any scientific value? The question of quantum locality/nonlocality has at least a fair chance of being evaluated IMO, but I guess it will take a while.

Can one show/falsify "free" / "random" measurements? Aren't those the pieces which don't fit in the scientific puzzle?

 

[DennisN]

Can one show/falsify "free" / "random" measurements?

No, and that was actually my point (if this is said in terms of superdeterminism). Therefore I don't see the question [nonsuperdeterminism vs superdeterminism] as scientifically interesting. But I see the question [locality vs nonlocality] as scientifically interesting. But that's only my opinion of course.

 

[1977ub]

No, and that was actually my point (if this is said in terms of superdeterminism). Therefore I don't see the question [nonsuperdeterminism vs superdeterminism] as scientifically interesting. But I see the question [locality vs nonlocality] as scientifically interesting. But that's only my opinion of course.

If one doesn't take too seriously the idea of free or random measurements, is there anything in Bell's inequality to call into question our usual confidence in locality?

 

[stevendaryl]

For what it's worth, billschnieder is a local realist. His reference does not meet the standards for PF. But as long as everyone knows it, considering this thread is essentially an opinion thread anyway, I guess it can't hurt.

I think that it's a matter of opinion what is the best explanation for EPR-type correlations, but it seems to me that the claim made in that paper, that Bell's local realism claim is either false or tautologous, isn't just a matter of opinion. You can show that it's not tautologous by showing how his inequalities are easily violated if we allow for instantaneous action-at-a-distance. Showing that they are not wrong is harder, but Bell's theorem, or related theorems have been investigated by many people over many years.

 

[DennisN]

If one doesn't take too seriously the idea of free or random measurements, is there anything in Bell's inequality to call into question our usual confidence in locality?

(note: I may misunderstand you, and if I do, please be more specific)
Most of this thread we're in is an example that the (Bell inequality) question of [locality/nonlocality] is disputed. I voted "anti-realism" (for these reasons), and I definitely lean towards locality, but I can't yet personally completely rule out nonlocality. I put my faith in future science/experiments to shine more light on the matter.

 

[1977ub]

(note: I may misunderstand you, and if I do, please be more specific)

If you look at the whole experiment as a deterministic process unfolding inside a light cone, and therefore without any particular free/random measurement taking place or even making sense (the very terminology seems to be temporarily setting aside a deterministic view) and then there are the correlated measurements at different locations which are preceded by the only superficially "at the last minute" or "freely" or "randomly" chosen settings on the measuring devices - seen from this perspective, is there anything in the Bell/Alain result which might even lead one to question local causality?

Is (odd? supernatural?) belief in non-deterministic free-will essential to finding Bell's inequality a perplexing challenge to local determinism?

 

[DennisN]

[...] seen from this perspective, is there anything in the Bell/Alain result which might even lead one to question local causality?

I suppose you are referring to some kind of superdeterminism, am I correct? If so, I won't argue for or against your particular questions, maybe someone else here will. As I said I don't consider superdeterminism as scientifically interesting, since I can't imagine any way to test it; IMO it's like a chicken'n'egg thing in this respect. Therefore I see it as a too easy and nontestable way out of the (Bell inequality) question of [locality/nonlocality], which is a question which I on the other hand can imagine we might be able to solve in the future.

 

[Nugatory]

If you look at the whole experiment as a deterministic process unfolding inside a light cone, ... is there anything in the Bell/Alain result which might even lead one to question local causality?

No.

Is (odd? supernatural?) belief in non-deterministic free-will essential to finding Bell's inequality a perplexing challenge to local determinism?

Yes.

However, superdeterminism is subject to two major challenges (as well as the general untestability problem, which is common to all interpretations). The first is the philosophical question of free will versus mechanistic determination; I cannot refute the possibility that my free will is an illusion, but it sure doesn't feel that way to me. This was problem for philosophers and theologians long before there were physicists, and I don't see (Penrose notwithstanding) QM helping any with that argument or vice versa.

Second, even if you're willing to come down hard on the no-free-will side, superdeterminism still has a problem: even when A is in the past light cone of B and C, it's not always plausible that A explains correlations between B and C. Put the source of the entangled pair on alpha centauri, four light years away. Give me a Stern-Gerlach machine, put a second one eight light years away with alpha centauri in the middle. The setting of the distant SG machine will be determined by a random radioactive decay; and the setting of my machine will be made based on where I eat lunch two years before the measurement of the entangled pair.

Am I supposed to believe that something that happened on alpha centauri six years before the measurement (to get into the past light cone of my lunch) and two years before the entangled pair is produced, can influence the settings of the two SG machines? Enough to produce Bell-violating correlations?

There's this tiny dark cave where I can placidly shut up and calculate. I retreated to this cave rather than choose between locality and realism, and superdeterminism isn't going to tempt me out of it.

 

[1977ub]

Am I supposed to believe that something that happened on alpha centauri six years before the measurement (to get into the past light cone of my lunch) and two years before the entangled pair is produced, can influence the settings of the two SG machines? Enough to produce Bell-violating correlations?

Sounds absurd, but it's up against greater absurdity... I think you can't study physics for long without looking at everything more and more in terms of intricate determinism you might not have considered before... I almost can't enjoy any time-travel fiction anymore... characters are trying to work out specific identifiable things that if they go back to such-and-such a time would end up changing the future. I'm always thinking "are you kidding?!" what about breathing? what about just standing there?

I don't feel that firm belief in superdeterminism is superior to shut-up-and-calculate, but I guess before we go off too far believing in violations of cause/locality it seems to me that it would need to be kept in mind as in some ways more plausible. If we are determinists, then we can't be too enamoured in free will! quantum or no quantum.

 

[stevendaryl]

Am I supposed to believe that something that happened on alpha centauri six years before the measurement (to get into the past light cone of my lunch) and two years before the entangled pair is produced, can influence the settings of the two SG machines? Enough to produce Bell-violating correlations?

Yes, that sounds absurd. However, there's something a little strange about the time symmetry of fundamental laws which might be relevant here. A rock smashes a glass bottle, sending shards of glass in all directions. Nothing surprising about this. But if you reverse the direction of time, then it looks like: Bits of glass from many locations are thrown toward a rock in just such a way as to cause the glass to fuse into a bottle and expel the rock. The time reversal sounds like a ridiculous conspiracy theory. But both the forward and backward descriptions are equally valid, according to the laws of physics.

I don't have a well-formed thought to express here, but it seems possible to me that a super-determinism theory, which looks like a conspiracy from the usual point of view, might seem more natural in a time-symmetric description.

 

[Nugatory]

I don't have a well-formed thought to express here, but it seems possible to me that a super-determinism theory, which looks like a conspiracy from the usual point of view, might seem more natural in a time-symmetric description.

That's an interesting thought, and I'm inclined to agree with you... Although I'm also inclined to think that the bolded text should read something like "marginally less unnatural"... It's not going to lure me out of my cave any time soon.

 

[bohm2]

This is an interesting paper relevant to the thread that just came out today. The abstract:

This paper addresses arguments that “separability” is an assumption of Bell’s theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as “holism”) will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately. In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (b) the definition of Bell’s locality condition does not rely on separability in any way; (c) the proof of Bell’s theorem does not use separability as an assumption. If, inspired by considerations of nonseparability, the assumptions of Bell’s theorem are weakened, what remains no longer embodies the locality principle. Teller’s argument for “relational holism” and Howard’s arguments concerning separability are criticised in the light of these results. Howard’s claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem.

Non-separability does not relieve the problem of Bell’s theorem
http://lanl.arxiv.org/pdf/1302.7188.pdf

 

[morrobay]

Another relevant article with a geometric model/explanation for interpreting spin correlations
www.ejtp.com/articles/ejtpv9i27p111.pdf and
www.arxiv.org/pdf/quant-ph/0005103.pdf

 

[rkastner]

There are different interpretations, but generally violations of Bell's inequalities imply what's already known - that classical mechanics(strict materialism) is just one aspect of reality and so no longer an adequate explanation of observations. As Heisenberg once put it/quoted by Nick Herbert in Quantum Reality/:

"The ontology of materialism rested upon the illusion that the kind of existence, the direct 'actuality' of the world around us, can be extrapolated into the atomic range. This extrapolation, however, is impossible... atoms are not things."

The way to keep the strict materialism intact is by accepting a small conspiracy - superdeterminsim or hidden variables(or to deny interest into the inner workings of reality).

I propose an exploration of Heisenberg's ideas about quantum objects as 'potentia' or 'possibilities' in my new book:

The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility
www.cambridge.org/9780521764155

Introductory and preview material (and a publisher's discount) is on my website,
rekastner.wordpress.com. I welcome questions and comments on this material.

 

[bohm2]

I propose an exploration of Heisenberg's ideas about quantum objects as 'potentia' or 'possibilities' in my new book: The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility www.cambridge.org/9780521764155

Ruth,
From reading some of your papers you seem to argue that locality cannot be saved. (e.g. 'Quantum Nonlocality: Not Eliminated by the Heisenberg Picture). With respect to 'possibilities' or 'potentia', would the views you favour be anything like Gisin's views summarized here:

For me realism means, very briefly, that physical systems possesses properties preexisting and independent of whether we measure the system or not; however these preexisting properties do not determine measurement outcomes, but only their propensities. Accordingly, there are realistic random events that reflect preexisting properties, as required by realism, simply the reflection is not deterministic.

Non-realism: Deep Thought or a Soft Option?
http://www.gap-optique.unige.ch/wiki/_media/publications:bib:nonrealismfinal.pdf