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No-Go Theorems and the Foundations of Quantum Physics

Abstract

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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Notes

  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).

References

  • Baker, D. J. (2009). Against field interpretations of quantum field theory. British Journal for the Philosophy of Science, 60, 585–609.

    Article  Google Scholar 

  • Barrett, J. A. (2002). The nature of measurement records in relativistic quantum field theory. In M. Kuhlmann, H. Lyre, & A. Wayne (Eds.), Ontological aspects of quantum field theory (pp. 165–180). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Barrett, J. A. (2014). Entanglement and disentanglement in relativistic quantum mechanics. Studies in History and Philosophy of Modern Physics, 48, 168–174.

    Article  Google Scholar 

  • Beck, C., Myrvold, W., Tumulka, R., & Oldofredi, A. (2014). Physical meaning of Malament’s theorem on the position operators in relativistic quantum theory. Unpublished manuscript, pp. 1–11.

  • Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics, 1(3), 195–200.

    Article  Google Scholar 

  • Bell, J. S. (1975). The theory of local beables. TH 2053-CERN, pp. 1–14.

  • Bell, J. S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bohm, D. (1953). Comments on an article of Takabayasi concerning the formulation of quantum mechanics with classical pictures. Progress of Theoretical Physics, 9(3), 273–287.

    Article  Google Scholar 

  • Bricmont, J. (2016). Making sense of quantum mechanics. Berlin: Springer.

    Book  Google Scholar 

  • Colin, S., & Struyve, W. (2007). A Dirac sea pilot-wave model for quantum field theory. Journal of Physics A, 40(26), 7309–7341.

    Article  Google Scholar 

  • Cowan, C., & Tumulka, R. (2016). Epistemology of wave function collapse in quantum physics. The British Journal for the Philosophy of Science, 67(2), 405–434.

    Article  Google Scholar 

  • Daumer, M., Dürr, D., Goldstein, S., & Zanghì, N. (1996). Naive realism about operators. Erkenntnis, 45, 379–397.

    Google Scholar 

  • Dewdney, C., & Horton, G. (2002). Relativistically invariant extension of the de Broglie–Bohm theory of quantum mechanics. Journal of Physics A: Mathematical and General, 35, 10117–10127.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., Norsen, T., Struyve, W., & Zanghì, N. (2013). Can Bohmian mechanics be made relativistic? Proceedings of the Royal Society A, 470(2162), 20130,699.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., Tumulka, R., & Zanghì, N. (2004). Bohmian mechanics and quantum field theory. Physical Review Letters, 93, 090,402.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., Tumulka, R., & Zanghì, N. (2005). Bell-type quantum field theories. Journal of Physics A: Mathematical and General, 38(4), R1–R43. https://doi.org/10.1088/0305-4470/38/4/R01.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., & Zanghì, N. (2004). Quantum equilibrium and the role of operators as observables in quantum theory. Journal of Statistical Physics, 116, 959–1055.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., & Zanghì, N. (2013). Quantum physics without quantum philosophy. Berlin: Springer.

    Book  Google Scholar 

  • Dürr, D., & Teufel, S. (2009). Bohmian mechanics: The physics and mathematics of quantum theory. Berlin: Springer.

    Google Scholar 

  • Fraser, D. (2006). Haag’s theorem and its implications for the foundations of quantum field theory. Erkenntnis, 64, 305–344.

    Article  Google Scholar 

  • Fraser, D., & Earman, J. (2008). The fate of ‘particles’ in quantum field theories with interactions. Studies in History and Philosophy of Modern Physics, 38, 841–859.

    Article  Google Scholar 

  • Gisin, N. (2011). Impossibility of covariant deterministic nonlocal hidden variable extensions of quantum theory. Physical Review A, 83(2), 020,102(R).

    Article  Google Scholar 

  • Halvorson, H., & Clifton, R. K. (2002). No place for particles in relativistic quantum theories? Philosophy of Science, 69, 1–28.

    Article  Google Scholar 

  • Hiley, B., & Callaghan, R. E. (2010). The Clifford algebra approach to quantum mechanics B: The Dirac particle and its relation to the Bohm approach. arxiv.org/abs/1011.4033.

  • Horton, G., & Dewdney, C. (2001). A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories. Journal of Physics A: Mathematical and General, 34(46), 9871–9878.

    Article  Google Scholar 

  • Kochen, S., & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17(1), 59–87.

    Google Scholar 

  • Laudisa, F. (2014). Against the ‘no-go’ philosophy of quantum mechanics. European Journal for Philosophy of Science, 4, 1–17.

    Article  Google Scholar 

  • MacKinnon, E. (2008). The standard model as a philosophical challenge. Philosophy of Science, 75, 447–457.

    Article  Google Scholar 

  • Malament, D. (1996). In defense of dogma: Why there cannot be a relativistic quantum mechanics of (localizable) particles. In R. Clifton (Ed.), Perspectives on Quantum Reality (pp. 1–11). Dordrecht: Kluwer.

    Google Scholar 

  • Struyve, W. (2010). Pilot-wave approaches to quantum field theory. Journal of Physics: Conference Series, 306, 012,047.

    Google Scholar 

  • von Neumann, J. (1955). Mathematical foundations of quantum mechanics. Princeton: Princeton University Press.

    Google Scholar 

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Acknowledgements

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). https://doi.org/10.1007/s10838-018-9404-5

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Keywords

  • No-go theorems
  • Quantum mechanics
  • Quantum field theory
  • Gisin’s theorem
  • Malament’s theorem