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Diagnosing the Trouble with Quantum Mechanics

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Abstract

We discuss an article by Weinberg (N Y Rev Books, 2017) expressing his discontent with the usual ways to understand quantum mechanics. We examine the two solutions that he considers and criticizes and propose another one, which he does not discuss, the pilot wave theory or Bohmian mechanics, for which his criticisms do not apply.

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Notes

  1. See however Sect. 6 for a serious qualification of that idea.

  2. There are also pedagogical videos made by students in Munich, available at: https://cast.itunes.uni-muenchen.de/vod/playlists/URqb5J7RBr.html.

  3. We use lower case letters for the generic arguments of the wave function and upper case ones for the actual positions of the particles.

  4. It is interesting to compare this numerical solution to results published in Science in June 2011 [31]: one finds that the profile of trajectories of photons obtained through a series of so-called “weak measurements” is qualitatively similar to that of Fig. 1.

  5. Equation (9) is useful primarily when it is applied to subsystems of a larger system, for example the universe, that has its own wave function. In that case, one can associate to the subsystem an effective wave function \(\Psi \) and the empirical distribution \(\rho \) of particle configurations in appropriate ensembles of subsystems, each having effective wave function \(\Psi ,\) is given by (9).

  6. This section is based on Chapter 7 of David Albert’s book “Quantum Mechanics and Experience” [1].

  7. Since the particles here have spin, the guiding equation is (6), not (5), but this does not affect our qualitative discussion.

  8. In fact, one can introduce a notion of wave function for a subsystem of a closed system (i.e., in principle of the Universe) that coincides with the wave function used in quantum mechanics and that does collapse when collapses occur according to the standard approach, see [25] for a detailed discussion. The wave function that never collapses is the one of the closed system.

  9. There exists also a no hidden variables theorem, due to Clifton [14], preventing us from assigning both a position and a velocity to two particles on a line, in such a way that the statistical distributions of these quantities and of certain functions of them coincide with the usual quantum predictions. See [12, p. 43] for a discussion of that theorem.

  10. For a further discussion of the need for local beables in theories that modify Schrödinger’s equation in order to produce spontaneous collapses, see [2]. For a similar discussion in the “many-worlds” theory of Everett, see [3].

References

  1. Albert, D.: Quantum Mechanics and Experience. Harvard University Press, Cambridge (1992)

    Google Scholar 

  2. Allori, V., Goldstein, S., Tumulka, R., Zanghì, N.: On the common structure of Bohmian mechanics and the Ghirardi–Rimini–Weber theory. Br. J. Philos. Sci. 59, 353–389 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Allori, V., Goldstein, S., Tumulka, R., Zanghì, N.: Many-worlds and Schrödinger’s first quantum theory. Br. J. Philos. Sci. 62, 1–27 (2011)

    Article  MATH  Google Scholar 

  4. Bassi, A., Ghirardi, G.C.: Dynamical reduction models. Phys. Rep. 379, 257–427 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966) (reprinted as Chap. 1 in [7])

  6. Bell, J.S.: Against measurement. Phys. World 3, 33–40 (1990) (reprinted as Chap. 23 in [7])

  7. Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Collected Papers on Quantum Philosophy, 2nd edn, with an introduction by Alain Aspect, Cambridge University Press, Cambridge (2004); 1st edn (1993)

  8. Blanchard, P., Fröhlich, J., Schubnel, B.: A “Garden of Forking Paths”–the quantum mechanics of histories of events. Nucl. Phys. B 912, 463–484 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden variables,” Parts 1 and 2. Phys. Rev. 89, 166–193 (1952)

    Article  ADS  MATH  Google Scholar 

  10. Bohm, D., Hiley, B.J.: The Undivided Universe. Routledge, London (1993)

    MATH  Google Scholar 

  11. Bohr, N.: Discussion with Einstein on epistemological problems in atomic physics. In: Schilpp, P.A. (ed.) Albert Einstein. Philosopher-Scientist, pp. 201–241. The Library of Living Philosophers, Evanston (1949)

    Google Scholar 

  12. Bricmont, J.: Making Sense of Quantum Mechanics. Springer, Cham (2016)

    Book  MATH  Google Scholar 

  13. Bricmont, J.: Quantum Sense and Nonsense. Springer, Cham (2017)

    Book  MATH  Google Scholar 

  14. Clifton, R.: Complementarity between position and momentum as a consequence of Kochen–Specker arguments. Phys. Lett. A 271, 1–7 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. DeWitt, B.B., Graham, R.N. (eds.): The Many-Worlds Interpretation of Quantum Mechanics. University Press, Princeton (1973)

    Google Scholar 

  16. Dürr, D., Goldstein, S., Zanghì, N.: Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67, 843–907 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Dürr, D., Teufel, S.: Bohmian Mechanics. The Physics and Mathematics of Quantum Theory. Springer, Berlin (2009)

    MATH  Google Scholar 

  18. Dürr, D., Goldstein, S., Zanghì, N.: Quantum Physics Without Quantum Philosophy. Springer, Berlin (2012)

    MATH  Google Scholar 

  19. Everett, H.: ‘Relative state’ formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957) (reprinted in [15, pp. 141–149])

  20. Fröhlich, J.: The quest for laws and structure. In: König, W. (ed.) Mathematics in Society, pp. 101–130. EMS Publishing House (2016).

  21. Gell-Mann, M., Hartle, J.B.: Quantum mechanics in the light of quantum cosmology. In: Zurek, W. (ed.) Complexity, Entropy, and the Physics of Information, p. 425. Addison-Wesley, Reading (1990)

    Google Scholar 

  22. Gell-Mann, M., Hartle, J.B.: Alternative decohering histories in quantum mechanics. In: Phua, K.K., Yamaguchi, Y. (eds.) Proceedings of the 25th International Conference on High Energy Physics, Singapore, 1990. World Scientific, Singapore (1991)

  23. Gell-Mann, M., Hartle, J.B.: Classical equations for quantum systems. Phys. Rev. D 47, 3345–3382 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  24. Ghirardi, G.C., Rimini, A., Weber, T.: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470–491 (1986)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Goldstein, S.: Bohmian mechanics and quantum information. Found. Phys. 40, 335–355 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Goldstein, S.: Bohmian mechanics. In: Zalta, E.N. (ed.), The Stanford Encyclopedia of Philosophy, Spring 2013 Edition. https://plato.stanford.edu/archives/spr2013/entries/qm-bohm/

  27. Griffiths, R.B.: Consistent Quantum Theory. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  28. Friedberg, R., Hohenberg, P.C.: Compatible quantum theory. Rep. Prog. Phys. 77, 092001–092035 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  29. Friedberg, R., Hohenberg, P.C.: What is quantum mechanics? A minimal formulation. Found. Phys. 48, 295–332 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Kochen, S., Specker, E.P.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)

    MathSciNet  MATH  Google Scholar 

  31. Kocsis, S., Braverman, B., Ravets, S., Stevens, M.J., Mirin, R.P., Shalm, L.K., Steinberg, A.M.: Observing the average trajectories of single photons in a two-slit interferometer. Science 332, 1170–1173 (2011)

    Article  ADS  MATH  Google Scholar 

  32. Mermin, D.: Hidden variables and the two theorems of John Bell. Rev. Mod. Phys. 65, 803–815 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  33. Norsen, T.: Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory. Springer, Cham (2017)

    Book  MATH  Google Scholar 

  34. Omnès, R.: Logical reformulation of quantum mechanics. I. Foundations. J. Stat. Phys. 53, 893–932 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Omnès, R.: Logical reformulation of quantum mechanics. II. Interference and the Einstein–Podolsky–Rosen experiment. J. Stat. Phys. 53, 933–955 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  36. Omnès, R.: Logical reformulation of quantum mechanics. III. Classical limit and irreversibility. J. Stat. Phys. 53, 957–975 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  37. Omnès, R.: Logical reformulation of quantum mechanics. IV. Projectors in semiclassical physics. J. Stat. Phys. 57, 357–382 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  38. Peres, A.: Incompatible results of quantum measurements. Phys. Lett. A 151, 107–108 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  39. Peres, A.: Two simple proofs of the Kochen–Specker theorem. J. Phys. A 24, L175–L178 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Philippidis, C., Dewdney, C., Hiley, B.J.: Quantum interference and the quantum potential. Il Nuovo Cim. B 52, 15–28 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  41. ’t Hooft, G.: The Cellular Automaton Interpretation of Quantum Mechanics. Springer, Cham (2016)

  42. Tumulka, R.: Understanding Bohmian mechanics—a dialogue. Am. J. Phys. 72, 1220–1226 (2004)

    Article  ADS  Google Scholar 

  43. Weinberg, S.: The trouble with quantum mechanics. N. Y. Rev. Books (19 January 2017)

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Acknowledgements

We thank Tim Maudlin for very interesting discussions on the subject of this paper.

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Authors and Affiliations

  1. IRMP, Université catholique de Louvain, chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Jean Bricmont

  2. Department of Mathematics, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Sheldon Goldstein

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  1. Jean Bricmont
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Correspondence to Jean Bricmont.

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Dedicated to the memory of Pierre Hohenberg.

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Bricmont, J., Goldstein, S. Diagnosing the Trouble with Quantum Mechanics. J Stat Phys 175, 690–703 (2019). https://doi.org/10.1007/s10955-018-2113-y

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