Assumptions of the Bell theorem

[stevendaryl]

Your definition does not seem to be the same as that paper?
"A physical theory is EPR-‐local iff according to the theory procedures carried out in one region do not immediately disturb the physical state of systems in sufficiently distant regions in any significant way"

Well, my definition is more agnostic about what's going on. Alice's observations tell her something about a spacelike separated event, and it isn't apparently mediated by causal influences. If you assume that learning information is always mediated by causal influences, then you have to conclude that there are nonlocal influences going on.

This does not speak about information, it speaks about physical states. Which I think the author means to be be "elements of reality". ITs seems by changing definitions we can just decide if we want local or nonlocal :)

Physical states become involved if you're trying to understand how information can propagate. If you just leave it as a mystery, then you can just shrug your shoulders and say: I don't know what the heck is going on.

Anyway, this is was mote the question i considered worth asking. The answer to your question to me is, simply an information update, combined with the premise implied in pair creation. That Alices information has information about Bobs future is not a problem per see at all.

No, it's not simply an information update. If Alice is merely finding out information about Bob, then that information existed before she learned it. That's what Bell ruled out (except for the various loopholes such as FTL influences, back-in-time influences, Many-Worlds, superdeterminism, and ... I think that covers it).

 

[Fra]

If Alice is merely finding out information about Bob, then that information existed before she learned it. That's what Bell ruled out (except for the various loopholes such as FTL influences, back-in-time influences, Many-Worlds, superdeterminism, and ... I think that covers it).

I think you missed the distinction I tried to made then. I do not agree Bell ruled this out.

I tried to make the distinction between existence of

1) "hidden information" but that does not have causal influences, because its ISOLATED. Not just isolated from the experimenter (as in ignorance) but truly isolated from ALL environment (weter this makes sense in reality to accomplish over long distances is of course a practical question). This means this information really does NOT exist in the environemnt!

2) "ignorance" where the information exists, and in principle COULD be know to the experimenter, and the experimental apparatous, but isn't because the theorist making predictions didnt know about it. This is the case bell rules out. In this case the information exists in the environment, and possible known by the expeimental device, basically known but all exceopt Bob!

My point is that (1) remains a possibility, but this type of hidden information is NOT regular ignorance. It's a fundamental form of hidden information, just like you make consider how information is hidden in a black hole, or tha truth is "screened" from all inference.

But a real theory that realizes (1) is not yet know, The point is just that it remains not only possible, but at least in my mind extremely reasonable and almost like the only reasonble possibiity. To understad this, I think one needs to describe things not by means of a differential equation, but as agent based model. This has been iterating in my head for years and trying reconstruct things in a new framework is not easily done. Agent based models are quite alien to physicsts, but more common in economic interaction models etc. AS we know from history, some ways of describing things, like in terms of geometry, has certain intuitive advantages that helps understand and get insight. I see this just like that. Agent based models, nicely merget with various qbist kind of interpretations, especially if you add the oncept of evolution of law, that smoling talked about.

So the wet dream, informallyt is that say our standard model is a nash equiblirium, and the optimal strategies simple describe the equilibrium strategies of the elemetary particles.

/Fredrik

 

[stevendaryl]

1) "hidden information" but that does not have causal influences, because its ISOLATED. Not just isolated from the experimenter (as in ignorance) but truly isolated from ALL environment (weter this makes sense in reality to accomplish over long distances is of course a practical question). This means this information really does NOT exist in the environemnt!

I am not sure what that would mean. But it sounds nonlocal to me.

But there is another issue, which is that Bell’s proof shows that you can’t really separate the information about what result Bob will get from information about which measurement Bob will perform.

That is, there can’t be a predetermined “case” statement saying if Bob performs this measurement, he will get this result, and if he performs this other measurement he will this other result, etc. You can only meaningfully talk about his results (or the probability for different results) after you know the measurement that Bob will perform.

So I don’t see how you can have hidden information, nonlocal or not, about Bob’s result without knowledge of the measurement he will perform. Which in principle means some kind of superdeterminism.

 

[martinbn]

Sorry, I don't understand exactly what you're suggesting.

The simple intuitive reasoning for why anti-correlated spin-1/2 EPR seems to show nonlocality is this:

Pick an inertial coordinate system in which Alice and Bob are at rest, and Alice's measurement takes place slightly before Bob's. Then let's talk about three different events:

1. $e_1$: Immediately before Alice makes her measurement.
2. $e_2$: Immediately after Alice makes her measurement.
3. $e_3$: When Bob makes his measurement.

Alice is trying, based on information available to her, to figure out what result Bob will get at event $e_3$. For simplicity, let's assume that Alice and Bob both agree ahead of time to measure spins along the z-axis.

At event $e_1$, Alice is completely uncertain about Bob's result at $e_3$. He might get spin-up. He might get spin-down. Her subjective probabilities for each possibility is 50%.

At event $e_2$, Alice is completely certain about Bob's result. If she got spin-up, she knows that Bob will get spin-down, and vice-versa.

So Alice's subjective knowledge about Bob's result changed drastically between event $e_1$ and event $e_2$. The issue, then, is what caused this change in her knowledge?

Classically, your knowledge about future events changes according to a two-step, back and forth process:

1. You learn something about past (or present) conditions.
2. Those facts allow you to recompute probabilities for those future events.

You can only learn something about conditions that are in your causal past (events that influence your present), and that can only give you information about the causal future of those conditions. The example I gave earlier in this thread is that Alice finds Bob's wallet, and she predicts that he will be unable to board a flight due to a lack of proper ID. Alice seeing the wallet in the present tells her something about the past: That Bob lost his wallet. That past tells you about Bob's future: that he will be unable to board the flight.

Without spending too much time on it, I think that it's pretty much true that every case of learning something about future events has this character: You go backwards in time, using deduction, from observation to facts about the past, and then you go forwards in time, again using deduction from past conditions to future events. Einstein's speed of light limitation on influences further restricts things: The causal past of your current observations can only tell you about conditions in your backwards light cone, and the causal future of those conditions can only tell you about events in the future light cone of those conditions.

In contrast, in EPR, Alice's observations now tell her something about Bob's future measurements in a way that is not (apparently) mediated by the back and forth causal influences within a light cone. That's a sense in which Alice's information is nonlocal information about Bob. That doesn't necessarily imply nonlocal influences.

I think that there is an important aspect that needs to be explicitly mentioned. Alice cannot make any predictions about event $e_3$ based only on the local measurements she makes. She also needs to know what the state of the two particle system is. That seems like nonlocal information to me. So Alice's input is the result of her measurement plus the state of the system, then the output of her prediction is the result of Bob's measurement.

 

[stevendaryl]

I think that there is an important aspect that needs to be explicitly mentioned. Alice cannot make any predictions about event $e_3$ based only on the local measurements she makes. She also needs to know what the state of the two particle system is. That seems like nonlocal information to me. So Alice's input is the result of her measurement plus the state of the system, then the output of her prediction is the result of Bob's measurement.

But the state of the system is presumably deductible from the fact that it was prepared in some particular way in Alice's past. There was, for example, a particle that decayed into an anti-correlated electron/positron pair.

 

[Fra]

I am not sure what that would mean. But it sounds nonlocal to me.

No, that is not the idea. It shold be local.

But there is another issue, which is that Bell’s proof shows that you can’t really separate the information about what result Bob will get from information about which measurement Bob will perform.

That is, there can’t be a predetermined “case” statement saying if Bob performs this measurement, he will get this result, and if he performs this other measurement he will this other result, etc. You can only meaningfully talk about his results (or the probability for different results) after you know the measurement that Bob will perform.

So I don’t see how you can have hidden information, nonlocal or not, about Bob’s result without knowledge of the measurement he will perform. Which in principle means some kind of superdeterminism.

If we for simplicitly introduce the "agent" notion also for the anti-correlated pair, it makes it easier to explain:

Consider the pair production produces two agents(particles) with correlated states (that's the premise). One heads towards Alice and one towards Bob. Then the idea is that the "hidden information" of each agent, IS the agents subjective expectation of its own environment. This is physically encoded in the microstate of the agent. The only way for any part of the environment(ie any other agent) to infer this hidden info, is to interact (ie make a measurement) (*)

This hidden info, can not predict outcomes of combinations with unknown future interactions that involves delayed choices from other agents in the environment. It just explains, the agents ACTION in response to perturbation. Ie. it explains ONE side of the interaction. The outcome of the interaction also depends on the ACTION of the other interacting part, ie Bobs measurement device; whose ACTION in turn depends on it's expectation of it's environment and incoming agent; and this expectation follows from device settings and information of the state preparation prior to pair production event.

This is a way to see how the physical interactions observed at Bobs lab, are really independent of wether Alice made a measurement or not. But in a way that also explains the correlation, without non-locality, and still allowing for a "hidden realism" that isn't ruled out by Bells theorem.

They key is in this view is the logic of causation. The hidden info, does not constitue a partition of the event space, so the the law of total probability does not hold, when summed over the "hidden variable indexes", and without this I think you can't prove Bells theorem. The possible hidden states, always overlap as they can randomly make transitions. To understand why this makes would force me into more speculation of a reconstruction of QM that what's warranted, but in short, that's the idea.

(*) ANY agent (=inteacting observer) holds hidden information. This "information" can be thoughto the index the observer just in the sense that as I think Zurek said, "What an observer knows is inseparable from what the observer is". One can also imagine construcing information based metrics from this, where the "distance" between two agents, does not refer to an embedding space, but related to their differing information.

It was in this sense I see this as an information update, but perhaps better put as an "DELAYED information update". I think all information updates in principled delayed, but if we envision the experiment where Alice and Bob are very far away, and that it would be possible to keep the pairs isolated from the environment for such a lone time, this becomes extremely delayed, which leads to the weirdness.

I supposed to explain this better one needs to construct and lookg at a model for this possibility.

/Fredrik

 

[Mary Conrads Sanburn]

NEWS RELEASE 24-SEP-2020

A question of reality​

SPRINGER
Research News

Physicist Reinhold Bertlmann of the University of Vienna, Austria has published a review of the work of his late long-term collaborator John Stewart Bell of CERN, Geneva in EPJ H. This review, 'Real or Not Real: that is the question', explores Bell's inequalities and his concepts of reality and explains their relevance to quantum information and its applications.

John Stewart Bell's eponymous theorem and inequalities set out, mathematically, the contrast between quantum mechanical theories and local realism. They are used in quantum information, which has evolving applications in security, cryptography and quantum computing.

The distinguished quantum physicist John Stewart Bell (1928-1990) is best known for the eponymous theorem that proved current understanding of quantum mechanics to be incompatible with local hidden variable theories. Thirty years after his death, his long-standing collaborator Reinhold Bertlmann of the University of Vienna, Austria, has reviewed his thinking in a paper for EPJ H, 'Real or Not Real: That is the question'. In this historical and personal account, Bertlmann aims to introduce his readers to Bell's concepts of reality and contrast them with some of his own ideas of virtuality.

Bell spent most of his working life at CERN in Geneva, Switzerland, and Bertlmann first met him when he took up a short-term fellowship there in 1978. Bell had first presented his theorem in a seminal paper published in 1964, but this was largely neglected until the 1980s and the introduction of quantum information.

Bertlmann discusses the concept of Bell inequalities, which arise through thought experiments in which a pair of spin-½ particles propagate in opposite directions and are measured by independent observers, Alice and Bob. The Bell inequality distinguishes between local realism - the 'common sense' view in which Alice's observations do not depend on Bob's, and vice versa - and quantum mechanics, or, specifically, quantum entanglement. Two quantum particles, such as those in the Alice-Bob situation, are entangled when the state measured by one observer instantaneously influences that of the other. This theory is the basis of quantum information.

And quantum information is no longer just an abstruse theory. It is finding applications in fields as diverse as security protocols, cryptography and quantum computing. "Bell's scientific legacy can be seen in these, as well as in his contributions to quantum field theory," concludes Bertlmann. "And he will also be remembered for his critical thought, honesty, modesty and support for the underprivileged."

###​

Reference:

R. Bertlmann (2020), Real or Not Real: that is the question, European Physical Journal H, DOI 10.1140/epjh/e2019-90071-6

https://www.eurekalert.org/pub_releases/2020-09/s-aqo092420.php

 

[martinbn]

But the state of the system is presumably deductible from the fact that it was prepared in some particular way in Alice's past. There was, for example, a particle that decayed into an anti-correlated electron/positron pair.

It doesn't matter. The point was tha it is not a local information, Alice has to have it to make the prediction.

 

[Fra]

It doesn't matter. The point was tha it is not a local information, Alice has to have it to make the prediction.

I presume the idea that the whole Alice+Bob experiment and preparation is a joint project in the sense that both Alice and Bob constructs the lab and the preparate procedure together, then goes to their remote detectors. The the expectations of Alice and Bob are based on information they "locally acquired" in the past, and keeps "locally stored". And their expectations has no reason to change unless the original preparation side is secrectly invaded by someone to sabotage the experiment: It would not change Alices expectation, but it would show disagreement between observation and expectation.

/Fredrik

 

[WernerQH]

the expectations of Alice and Bob are based on information they "locally acquired" in the past, and keeps "locally stored".

@Demystifier may have hoped to identify the one crucial assumption (habit of thought) that prevents us from really understanding quantum theory. But they all seem to be interrelated, and the ideas "measurement", "observer", or "agent" and "information" terribly tangled. Can information be strictly local?

 

[Fra]

@Demystifier may have hoped to identify the one crucial assumption (habit of thought) that prevents us from really understanding quantum theory. But they all seem to be interrelated, and the ideas "measurement", "observer", or "agent" and "information" terribly tangled. Can information be strictly local?

It's true that all terms and unclear definitions complicates the discussion, and one can question most things at different levels.

Observer and agents are sort of the same thing, except when I say agent I usually mean it as a thinking-tool or indicative of an ambition to realize a fully interacting observer, or an inside observer (in a qbist-like interpretation); as opposed to the external more passive observer, as part of hte classical context, that is the more conventional CI interpretations.

Can information be strictly local?

I think one can make this very complicated. Trying to avoid making it complicate, with local information I just meant local with respect to the agents. Ie. localized to an agent (internal structure of the agent). For example, information is "localized to Bob", then I mean the information is physically encoded an retained in Bobs microstructure.

One may ponder about what it means if one agent is extended in space, does this mean information is non-locally stored? An ambitious analysis probably needs to question and analyze the construction and emergence of spacetieme as well andt the relation between information divergence (a measure on the space of probability distributions) and metrics in spacetime. Perhaps one can argue that whenever there IS information divergence, space is defined. One also can't help thinking that storing information in a "point" will likely lead to problems, just as we have the problem of "point particles" with finite energy or mass. So thinking further about this, needs to rethink also continuum of both information and it's relations (spacetime). But for the OT I think this is not required at this point. I think one can discsusse the EPR an pretend spacetime and information are clear?

/Fredrik

 

[WernerQH]

So thinking further about this, needs to rethink also continuum of both information and it's relations (spacetime). But for the OT I think this is not required at this point. I think one can discsusse the EPR an pretend spacetime and information are clear?

My point of view is the exact opposite. I think that Bell's theorem shows that physics is fundamentally nonlocal. Spacetime seems reasonably clear to me :-), but information is too unspecific a term. None of the pixels on the computer screen carries information by itself - it is the pattern that's important.

 

[Fra]

My point of view is the exact opposite. I think that Bell's theorem shows that physics is fundamentally nonlocal. Spacetime seems reasonably clear to me :-), but information is too unspecific a term. None of the pixels on the computer screen carries information by itself - it is the pattern that's important.

One of my personal insights is that no matter what concepts you consider the best "starting points" for a reconstruction, there is no solid external reference. Everything tends to be referencing to other concepts like you note. But this is how a relational theory works. It's IMO neither a "problem" nor a "flaw". I try to embrace it and undestand how things ought to work in such a mode and how to get a handle to it. This is exactly why I think an evolutionary model remains the only rational viable framework. At least I have not been able to come up with something more clever. And its why the Agent based model abstraction seems "natural", and it's why Qbism seems the best way forwarf from some minimal interpretation if you leave the standard theory behind and seek a better theory..

And the relational nature of this, suggests to me that parts of nature hold information about other parts of nature, this defined by assymmetric mutual expectaions, which creates tensions and explains interactions. Evolutionary learning models are more robust with respect to initinal conditions than the conventional paradigms that typically ends up in a finetuning trap. So the information Agent A has About B is to me synonous with "expected predictive power" in an evolutionary context, which is related to subjective probabilites. And this is exactly what is evolving as the agent "expects" about each other. Emphasis on expected because the preducttion can prove wrong, but still be correctly constructed. The action is assumed to follow from the correctly constructed expectation, not from the hidden truth.

/Fredrik

 

[eloheim]

Necessary assumptions:
- macroscopic realism (macroscopic measurement outcomes are objective, i.e. not merely a subjective experience of an agent)

So does macroscopic realism cover any many world or multi-timeline trickery? Like i recall a demonstration of "saving locality" by having each of the two separated bell measurements create a bubble where both possible results (like spin up and down) exist simultaneously. Then when the two bubbles meet the appropriate pairs of results connect into two seemingly-non-local (parallel) universes, or one pair of results survives to become permanent and the other disappears. Obviously anywhere measurement result information spread to would become part of these "bubbles," including agents, so in that sense I'm guessing these parallel experimenter-experiences would be considered subjective?

 

[Demystifier]

So does macroscopic realism cover any many world or multi-timeline trickery?

That's a good question. The answer is - yes. But Bell theorem assumes that there is only one outcome, so it should be added to the list. That being said, I have to stress that I don't think that many worlds is a way to save locality, see my https://arxiv.org/abs/1703.08341.

 

[martinbn]

Is there an assumption that on doesn't use a statistical interpretation? Or if this is not off topic how does Bell's theorem go in a statistical intepretation? Bell's inequalities are fine. It's the theorem I am asking about? In fact how does EPR gor for a statistical interpretation?!

 

[Demystifier]

Is there an assumption that on doesn't use a statistical interpretation? Or if this is not off topic how does Bell's theorem go in a statistical intepretation? Bell's inequalities are fine. It's the theorem I am asking about? In fact how does EPR gor for a statistical interpretation?!

Ballentine in his book says explicitly that Bell theorem implies nonlocality. But the Ballentine's version of statistical interpretation is not the only version of statistical interpretation. The problem with the statistical interpretation is that it's very close to "shut up and calculate", in the sense that on many conceptual questions it's agnostic or refuses to give an explicit answer. For that reason, it's hard to tell precisely what the statistical interpretation says related to the Bell theorem.

 

[stevendaryl]

That's a good question. The answer is - yes. But Bell theorem assumes that there is only one outcome, so it should be added to the list. That being said, I have to stress that I don't think that many worlds is a way to save locality, see my https://arxiv.org/abs/1703.08341.

If I understand @eloheim's suggestion, it sounds local, in a weird way. Imagine that associated with each tiny region in spacetime, there are many (maybe infinitely many) versions of what conditions are like in that region. When two neighboring regions interact, the different versions become correlated.

So for example, in the EPR experiment, Alice measures the spin of her particle along the z-axis. Her region of spacetime (not the entire universe) splits into two versions, one where she gets spin-up, one where she gets spin-down. The same thing when Bob measures the spin of his particle along the z-axis. He splits his region into two versions. Nothing nonlocal happening. Then when Alice communicates with Bob to find out what result he got, the two versions line up. The version with Alice getting spin-up lines up with the version with Bob getting spin-down.

I don't know how this could work out, mathematically, but it seems as if it could be local.

 

[martinbn]

Ballentine in his book says explicitly that Bell theorem implies nonlocality. But the Ballentine's version of statistical interpretation is not the only version of statistical interpretation. The problem with the statistical interpretation is that it's very close to "shut up and calculate", in the sense that on many conceptual questions it's agnostic or refuses to give an explicit answer. For that reason, it's hard to tell precisely what the statistical interpretation says related to the Bell theorem.

My question is how does the logical argument run in the statistical interpretation? In the vague language, you insist on using, the argument goes as follows: from the scholarpedia article

The proof of Bell's theorem is obtained by combining the EPR argument (from locality and certain quantum predictions to pre-existing values) and Bell's inequality theorem (from pre-existing values to an inequality incompatible with other quantum predictions).

How do the details of this go in the statistical interpretation language? Or is it that the theorem doesn't apply to the statistical interpretation?

 

[Demystifier]

Imagine that associated with each tiny region in spacetime, there are many (maybe infinitely many) versions of what conditions are like in that region.

The catch is that, at the fundamental level, the many world interpretation does not associate things with regions of spacetime. That's because the wave function, which is the only fundamental thing according to MWI, does not live in spacetime (except for a 1-particle wave function).

 

[Demystifier]

How do the details of this go in the statistical interpretation language?

I cannot tell, because the statistical interpretation is too vague (even for me) to answer such questions.

 

[martinbn]

I cannot tell, because the statistical interpretation is too vague (even for me) to answer such questions.

Ok, how do the details go in any other interpretation? For example the part that EPR implies preexisting values. How does that follow?

 

[Demystifier]

Ok, how do the details go in any other interpretation? For example the part that EPR implies preexisting values. How does that follow?

The idea of the Bell theorem is that it does not depend on details of any specific interpretation. Therefore, the first question does not make sense. Concerning the second question, see e.g. http://www.scholarpedia.org/article...nFWw#The_EPR_argument_for_pre-existing_values

 

[martinbn]

The idea of the Bell theorem is that it does not depend on details of any specific interpretation. Therefore, the first question does not make sense. Concerning the second question, see e.g. http://www.scholarpedia.org/article/Bell's_theorem?fbclid=IwAR2EAAT--l463yaZabl-MDCBnyParUKlQwvpUCAJq-HreA6CP43LflHnFWw#The_EPR_argument_for_pre-existing_values

But that is phrased in therms of particles and their spin.

But without any such interaction, the only way to ensure the perfect anti-correlation between the results on the two sides is to have each particle carry a pre-existing determinate value (appropriately anti-correlated with the value carried by the other particle) for spin along the z-axis.

But in the statistical interpretation the state and the observables are not of a single particle but of the ensemble. My question is how do you phrase it in the statistical interpretation language? I am not asking about any particular statements of the interpretation that you find vague.

 

[Demystifier]

But in the statistical interpretation the state and the observables are not of a single particle but of the ensemble. My question is how do you phrase it in the statistical interpretation language?

Ah, that should be easy. In the first step, instead of saying "each particle carry a pre-existing determinate value", you make it a bit more precise by saying "each particle in the pair carry a pre-existing determinate value". In the second step, you generalize the pair to an ensemble of pairs and say "in every member of the ensemble of pairs, each particle in the pair carry a pre-existing determinate value".

 

[stevendaryl]

But in the statistical interpretation the state and the observables are not of a single particle but of the ensemble. My question is how do you phrase it in the statistical interpretation language? I am not asking about any particular statements of the interpretation that you find vague.

I don't understand this business of the "ensemble" having properties, independent of the systems making up the ensemble.

In the particular case of EPR, Alice and Bob repeatedly do the same thing:

1. A third party prepares an anti-correlated electron/positron pair.
2. Alice chooses an axis $\vec{\alpha}$.
3. Bob chooses an axis $\vec{\beta}$.
4. They each measure the spin of one of the particles relative to their chosen axis.

Then after doing this many many rounds, for many different combinations of axes, they compute statistics for their measurements.

So what does it mean to say that quantum mechanics applies to the ensemble, and not to the individual rounds of this experiment?

 

[Demystifier]

So what does it mean to say that quantum mechanics applies to the ensemble, and not to the individual rounds of this experiment?

I think it is just the frequentist probabilistic interpretation of the wave function. It says that the wave function is just a tool to compute the probability, where probability, in the frequentist interpretation, cannot be associated with an individual round of an experiment.

 

[stevendaryl]

I think it is just the frequentist probabilistic interpretation of the wave function. It says that the wave function is just a tool to compute the probability, where probability, in the frequentist interpretation, cannot be associated with an individual round of an experiment.

But that's not an interpretation. That seems to me to be just leaving it without an interpretation.

 

[Demystifier]

But that's not an interpretation. That seems to me to be just leaving it without an interpretation.

Well, many interpretations claim that the wave function is something more than just a tool to compute the probability. So claiming the opposite, that the wave function is not something more, is an interpretation too. More precisely, it's a denial of a large class of interpretations, but denial of an interpretation is an interpretation, isn't it? In fact, I argued elsewhere that the statistical interpretation is the maximal denial interpretation https://www.physicsforums.com/threa...al-nor-statistical.998661/page-4#post-6450421

 

[martinbn]

I'll try to explain what I mean. Of course, it is possible that it is just terminology, but it bothers me.

I receive one particle at a time and measure the spin along the z-axis. Half of the time I get "up", half of the time I get "down". In a statistical interpretation the spin-z observable doesn't have a specific value, because there isn't a single value that I get on this equivalence class of measurements. In a non statistical interpretation it is still possible to have the case, at least apriori, that each particle was in a state |up> or |down> and that the spin-z observable has a value for each of them. But in the statistical interpretation it makes no sense to even make the statement.

Going back to EPRB, the quantum mechanic system is the equivalence class of equally prepared pairs of particles and the Bohm state is the sate of that ensemble. The possible outcomes of a measurement are (up, down) or (down, up). And half of the time one happens, the other half the other one. So I don't understand what it means (let alone how it follows from EPR) that the spin had a preexisting value! What is the value of the spin?

 

[Demystifier]

I'll try to explain what I mean. Of course, it is possible that it is just terminology, but it bothers me.

I receive one particle at a time and measure the spin along the z-axis. Half of the time I get "up", half of the time I get "down". In a statistical interpretation the spin-z observable doesn't have a specific value, because there isn't a single value that I get on this equivalence class of measurements. In a non statistical interpretation it is still possible to have the case, at least apriori, that each particle was in a state |up> or |down> and that the spin-z observable has a value for each of them. But in the statistical interpretation it makes no sense to even make the statement.

Going back to EPRB, the quantum mechanic system is the equivalence class of equally prepared pairs of particles and the Bohm state is the sate of that ensemble. The possible outcomes of a measurement are (up, down) or (down, up). And half of the time one happens, the other half the other one. So I don't understand what it means (let alone how it follows from EPR) that the spin had a preexisting value! What is the value of the spin?

The spin, of course, does not have the value in the whole ensemble. But it does have a value (at least a postexisting value, if not a preexisting one) in each individual member of the ensemble. The statistical interpretation does not deny the existence of individual members. It only denies that the wave function describes an individual member. But then what describes an individual member? The statistical interpretation remains agnostic (at best), inconsistent (at worst) or vague (at somewhere in between best and worst) on that.

 

[eloheim]

If I understand @eloheim's suggestion, it sounds local, in a weird way. Imagine that associated with each tiny region in spacetime, there are many (maybe infinitely many) versions of what conditions are like in that region. When two neighboring regions interact, the different versions become correlated.

Yes this is the idea (and I think Demystifier did understand correctly too). The point being that the super-classical correlations only become apparent when the two results have been brought back into contact and compared, so until that happens the possibilities can sort of ride along in their bubbles without fear of violating causality. Like I said I saw it presented as a demonstration of a type of theory that could side-step bell's theorem but it wasn't anything more than that.

 

[martinbn]

The spin, of course, does not have the value in the whole ensemble. But it does have a value (at least a postexisting value, if not a preexisting one) in each individual member of the ensemble. The statistical interpretation does not deny the existence of individual members. It only denies that the wave function describes an individual member. But then what describes an individual member? The statistical interpretation remains agnostic (at best), inconsistent (at worst) or vague (at somewhere in between best and worst) on that.

It also says that the observables are for the whole ensemble not the individual representatives. And the theory is concerned with the values of the observables. Now my question is probably clearer. Bell's theorem, vaguely stated, says that under some assumptions any theory that has the prediction of QM is nonlocal. My question is: is one of the assumption that the theory needs to apply to the individual objects, not the ensembles?

 

[Demystifier]

My question is: is one of the assumption that the theory needs to apply to the individual objects, not the ensembles?

Yes, I would say so. After all we measure individual events and the theory is supposed to explain the measurements. But (to avoid a frequent misunderstanding), it does not mean that the theory needs to be deterministic, a theory of individual events may also be stochastic.

 

[martinbn]

Yes, I would say so. After all we measure individual events and the theory is supposed to explain the measurements. But (to avoid a frequent misunderstanding), it does not mean that the theory needs to be deterministic, a theory of individual events may also be stochastic.

So, the theorem does not prove that QM is nonlocal, given that there is at least one interpretation that the theorem does not apply to.