2019 International Workshop: Beyond Bell’s theorem

A RE-EXAMINATION OF THE EPR ARGUMENT AND BELL'S THEOREM

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  • #5623
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    Federico Comparsi
    Participant

    In this paper I will re-examine the EPR argument and Bell’s theorem putting particular emphasis on the relevant points for the analysis of the problem of locality (milestone of general relativity and classical field theories). I will clearly state the logical and mathematical
    assumptions present in these cornerstones of foundations of quantum
    mechanics and from this analysis it will be clear that some recent
    claims by Rovelli et.al that relational quantum mechanics is local in the sense of Einstein (i.e. no superluminal or instantaneous influences/actions at
    a distance) are untenable.

    Link to download the latest version of the paper:

    https://www.researchgate.net/publication/335109600_A_RE-EXAMINATION_OF_THE_EPR_ARGUMENT_AND_BELL'S_THEOREM

    #5648
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    Federico Comparsi
    Participant
    #5658
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    Eric G. Cavalcanti
    Participant

    Hi Federico,

    Following up on our previous discussion, now that I’ve read your paper, can you provide a mathematical proof that assumptions 2 and 3 in your paper lead to predetermination of measurement outcomes? This should help clarifying that you actually need an extra assumption apart from Parameter Independence; i.e. you need an assumption amounting to Local Causality. That is, either by 3) you already mean Local Causality, or you will find that you cannot actually derive predetermination from 1-3.

    Note also that 1-3 are not the assumptions made by EPR at all, but that’s another matter. In my PhD thesis I’ve given a detailed analysis of the actual EPR argument, and how (what amounts to) the EPR locality assumption really is Local Causality. This is on page 45, Chapter 3:

    https://arxiv.org/abs/0810.4974

    This was 11 years ago, and I would have done it differently today, but the conclusion would be the same: you can’t run the EPR argument without Local Causality. By the way, on Chapter 2 you can also find detailed and careful definitions for Local Causality, Parameter Independence, Outcome Independence, etc.

    Cheers
    Eric

    #5666
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    Federico Comparsi
    Participant

    Hi Eric, thanks for the comment.

    #) “Note also that 1-3 are not the assumptions made by EPR at all”

    They are. Maybe the presentation of the argument written by Podolski in 1935 it’s not so clear, so I’m referring actually to the later presentation of the argument in Einstein 1948 (thanks for the implicit reminder, I need to add the reference in my paper), but the real assumptions are nevertheless present in the 1935 paper (if you don’t find them in the paper I can quote the relevant parts for you). They are:
    1) Psi is a complete description of the system (there exists only psi and it evolves according to the Schrödinger equation)
    2) Quantum mechanical predictions (collapse + Born’s rule) are exactly valid in every experimental situation (every possible physical context).
    3) “free will”: Alice and Bob can choose independently the kind of measurement and the instant to do it.
    4) “locality”: actions/physical influences cannot propagate in any frame at a speed faster than the speed of light.
    From these assumptions you can deduce with a simple counterfactual reasoning that there must exist the local information to calculate the outcomes of every possible measurement. At this point you can start with Bell’s theorem, as explained in my paper and I emphasise that I DON’T need the Outcome independence assumption.

    P.s. You can add as an implicit assumption the fact that S,a,b,A,B are real events occurring in space-time, as I noticed in the parallel discussion. This is true because otherwise you cannot even talk meaningfully about speed of real physical influences from Bob, Alice and the Source.

    #5668
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    Eric G. Cavalcanti
    Participant

    Hi Federico,

    One of the ways around the conclusion of predetermination, even while assuming Macroreality, is the “passion at a distance” resolution à la Shimony: the measurement outcomes happen to be correlated in the appropriate way, but it is not that one of the outcomes causes the other, or objectively collapses the state of the distant system. They just happen to occur spontaneously, undetermined, but correlated, even if at a distance. Since neither Alice nor Bob can choose what outcomes they obtain, they cannot use this correlation to send signals faster than light, nor are there any physical influences of any sort propagating faster than light.

    What you have to give up to accept a resolution of this sort is to give up the classical principle of causality encapsulated in Reichenbach’s principle of common cause. Bell’s and EPR’s notion of locality, or more precisely, of Local Causality, is essentially a consequence of Reichenbach’s principle. But one can relax that requirement, and get around Bell’s theorem that way. This is the direction taken, for example, by the quantum causal models program.

    See, e.g.
    https://arxiv.org/abs/1311.6852
    https://arxiv.org/abs/1503.06413

    #5670
    Avatar
    Federico Comparsi
    Participant

    # “the measurement outcomes happen to be correlated in the appropriate way, but it is not that one of the outcomes causes the other, or objectively collapses the state of the distant system. They just happen to occur spontaneously, undetermined, but correlated, even if at a distance”

    This is not a way out, this is purely nonsense, with all the due respect for Shimony. The assumptions of EPR are clear, so if you want to reject predetermination you need to reject or “locality” or “free will” or the correctness of quantum mechanics, since rejecting the reality of S,a,b,A,B preclude an operational definition of speed of influences in space (if you need a proof of this statement I can write something, but it seems obvious from my point of view).

    # “Bell’s and EPR’s notion of locality, or more precisely, of Local Causality”

    No, from my understanding EPR notion of locality only implies what you call “parameter independence”.

    # “to give up the classical principle of causality encapsulated in Reichenbach’s principle of common cause.”

    If you reject this principle (and I think that it would be even worse than the solipsism option) you would invalidate all the scientific knowledge we have. At this stage it would be useless to talk about locality or everything else. The hypothesis that causes are in the past and that correlations need an explanation in my opinion is necessary to do science.

    #5672
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    Eric G. Cavalcanti
    Participant

    Hi Federico,

    “If you reject this principle (and I think that it would be even worse than the solipsism option) you would invalidate all the scientific knowledge we have. At this stage it would be useless to talk about locality or everything else. The hypothesis that causes are in the past and that correlations need an explanation in my opinion is necessary to do science.”.

    I agree. And I have linked above to a paper where I proposed that Reichenbach’s principle can be broken down into two, independent principles: the Principle of Common Cause as such, which just says that if two events are correlated, then either one causes the other, or there exists a common cause that ‘explains’ the correlations, and the Principle of Factorisation of Probabilities, which says that a common cause ‘explains’ a correlation when, conditioned on that common cause, the correlations disappears. I’ve read your paper, so please read the papers I link or else I see no point in continuing this discussion. Here’s the published version:

    https://iopscience.iop.org/article/10.1088/1751-8113/47/42/424018

    I proposed in that paper that the first part of the PCC as such can be maintained, while the second can be dropped, to accommodate quantum correlations while maintaining a notion of causal explanation. I also proposed that the quantitative part could be replaced, within the framework of conditional quantum states of Leifer and Spekkens, by the factorisation of quantum channels, rather than of probabilities as in the original RPCC.

    A series of papers in the last several years have developed this framework of quantum causal models. A recent paper from Jon Barrett and others that explains these things in quite some detail is:

    https://arxiv.org/abs/1906.10726

    Now note that this framework maintains Macroreality, Parameter Independence and Freedom of Choice, reproduces quantum correlations, and generalises the classical framework of causality, reducing to it as a special case.

    So again, this is a constructive example of what you say is impossible. You can’t continue claiming that it is impossible, unless you show where this is wrong.

    Although I would perhaps say that depending on how you interpret assumption 1) (completeness of QM) it may already smuggle Local Causality (or what I call Causal Completeness, which is equivalent to RPCC). So you have to be careful when using that assumption. This framework is perhaps better understood from a point of view where quantum states are seen as representing information rather than ontic states. So completeness in that sense would mean that there’s no information to be obtained that is not already included in a (pure) quantum state an agent assigns to the system.

    #5674
    Avatar
    Federico Comparsi
    Participant

    Hi Eric, maybe we are not understanding each other, but if you read my paper you will clearly see that the EPR-Bell’s version that I have re-examined do not need neither “outcome independence” nor “factorization of probabilities”. They only (implicitly) need these two assumptions (implicit in the common scientific way of thinking):

    1) If there are correlations, then you need a causal explanation, that is to say or one caused the other (there is a physical influence of one on the other, so one is in the past light cone of the other) or they interacted appropriately in their common past, which I think you would call “Common Cause as such”.

    2) “intersubjective reality of S,a,b,A,B events in a definite space-time causal structure” which I think is what you would call “macrorealism”.

    At this point, if you assure to me that there exist some models that accept all these hypothesis and still explain EPR correlations without rejecting Einstein locality (which implies parameter independence) and S.I.+ “free will”, then I’m glad to find where the errors in their claims could be, otherwise I’m not interested in loosing my time, since 1) and 2) in my opinion are both necessary to do science.

    P.s. five years ago Rovelli told me that relational quantum mechanics reject Einstein locality and that it’s not a (multi) solipsistic interpretation (whatever this could mean), so let me think that he is confused more than at least one of us.

    #5676
    Avatar
    Eric G. Cavalcanti
    Participant

    Hi Federico,

    As I said, I have read your paper. But you do not provide a proof of that claim there. I’m saying that if you try to prove it you will find that you will fail, because there is a constructive example of a model that satisfies 1 and 2 above and reproduces quantum correlations (namely quantum causal models). In fact people even study GPT causal models satisfying 1 and 2 but going beyond quantum correlations. There’s a lot of work in this field in the last few years.

    Read the papers I’ve linked!

    Cheers
    Eric

    #5677
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    Federico Comparsi
    Participant

    Ok Eric, since the proof that the above listed assumptions lead to predeterminability of outcomes is straightforward, I will be glad to find which of the above assumptions the 2 theories you linked reject. But this will take me some time.

    Thanks for the discussion.

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