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No-Go Theorems and the Foundations of Quantum Physics

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In the history of quantum physics several no-go theorems have been proved, and many of them have played a central role in the development of the theory, such as Bell’s or the Kochen–Specker theorem. A recent paper by F. Laudisa has raised reasonable doubts concerning the strategy followed in proving some of these results, since they rely on the standard framework of quantum mechanics, a theory that presents several ontological problems. The aim of this paper is twofold: on the one hand, I intend to reinforce Laudisa’s methodological point by critically discussing Malament’s theorem in the context of the philosophical foundation of quantum field theory; secondly, I rehabilitate Gisin’s theorem showing that Laudisa’s concerns do not apply to it.

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  1. It is interesting to note that physical theories supply salient information on the inherent limitations of knowledge we may have about the world: there are objective matters of fact about it that are not experimentally accessible to us according to specific theoretical frameworks, independently of the current technological resources available. These limitations are derivable from the structure of the given theory at hand, i.e. when axioms and laws of motion are established, and seem to be perfectly suitable examples of no-go results. There are several examples of such limitations in quantum physics, for instance, one may consider that according to QM it is not possible to measure the wave function of an individual system, or that it is not possible to measure the velocity of a particle in Bohmian mechanics (BM), or that it is impossible to make experiments able to distinguish between BM and QM, or between the mass density and the flash versions of the Ghirardi–Riminii–Weber theory (GRWm and GRWf respectively). Nevertheless, due to the lack of space, in this paper I will not focus on this kind of negative results connected to inherent limitations of knowledge in physical theories.

  2. For a general discussion of the conceptual issues in QM the reader may consider Bell (1987), Dürr et al. (2013) and Bricmont (2016).

  3. This result is nowadays under investigation: recently Dürr et al. (2013) and Dewdney and Horton (2002) have argued that there might be possible ways to implement relativistic covariance within the structure of BM.

  4. This argument assumes a preferred universal reference frame that determines uniquely the temporal order for events in space-time.

  5. In Halvorson and Clifton (2002) generalizations of Malament’s theorem are provided, but for the purposes of the paper is sufficient to consider the original result; in the present discussion I heavily rely on their exposition of Malament’s argument.

  6. It is interesting to note that Malament (1996, 2) carefully analyzes the costs implied by a QFT with a particle ontology, which is an unacceptable non-local act-outcome correlation:

    I want to use the theorem to argue that in attempting to do so (i.e. hold on to a particle theory), one commits oneself to the view that the act of performing a particle detection experiment here can statistically influence the outcome of such experiment there, where “here” and “there” are space like related. [...] I have always taken for granted that relativity theory rules out “act-outcome” correlations across space like intervals. For this reason, it seems to me that the result does bear its intended weight as a “no-go theorem”; it does show that there is no acceptable middle ground between ordinary, non-relativistic (particle) mechanics and relativistic quantum field theory.

    It is clear that QFT here is explicitly intended to be a combination of QM and SR: non-local correlations violate relativistic causality, then if a particle theory implies such non-locality it must be rejected.

  7. I have to thank C. Beck for his insightful and extensive comments on this topic.

  8. For lack of space I cannot recall here all the unwelcome implications of the identification of local observables with local beables; the reader should refer to Dürr et al. (2004) for a technical discussion.

  9. The following arguments apply even to the theorems contained in Halvorson and Clifton (2002).

  10. This idea is originally contained Beck et al. (2014). I owe this point to R. Tumulka, W. Myrvold and C. Beck.

  11. For the N-particle case Bohm introduced the Dirac sea hypothesis, for recent developments see Colin and Struyve (2007).

  12. Another argument against Malament’s claim and its generalization focused on the current scientific practice is contained in MacKinnon (2008).


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I would like to thank Federico Laudisa for his comments on the previous draft of this paper. I am grateful to the Swiss National Science Foundation for financial support (Grant No. 105212-175971).

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Correspondence to Andrea Oldofredi.

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Oldofredi, A. No-Go Theorems and the Foundations of Quantum Physics. J Gen Philos Sci 49, 355–370 (2018).

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