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Philosophers Look at Quantum Mechanics pp 63–86Cite as

The Reality of the Wavefunction: Old Arguments and New

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Part of the book series: Synthese Library ((SYLI,volume 406))

Abstract

The recent philosophy of Quantum Bayesianism, or QBism, represents an attempt to solve the traditional puzzles in the foundations of quantum theory by denying the objective reality of the quantum state. Einstein had hoped to remove the spectre of nonlocality in the theory by also assigning an epistemic status to the quantum state, but his version of this doctrine was recently proved to be inconsistent with the predictions of quantum mechanics. In this essay, I present plausibility arguments, old and new, for the reality of the quantum state, and expose what I think are weaknesses in QBism as a philosophy of science.

We show that not only individual atoms but matter in bulk would [in the absence of the Pauli exclusion principle] collapse into a condensed high-density phase. The assembly of any two macroscopic objects would release energy comparable to that of an atomic bomb (Freeman Dyson 1967). Thus our daily experience that 2 l of gasoline contain only twice as much energy as 1 l is a pathological property of small clumps of matter containing fermions. …For fermi-matter only objects somewhat heavier than our sun are doomed to gravitational collapse but if mountains were made of bose-matter they would crush under their own weight (Walter Thirring 1986, p. 345).

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Notes

  1. 1.

    See, e.g., Wallace and Timpson (2010) and Myrvold (2015).

  2. 2.

    I will bypass here the debate between realists about the quantum state regarding whether the state should be defined on configuration space (see e.g. Ney 2015) or (nonseparably) on space (see Wallace and Timpson op.cit.).

  3. 3.

    See Wallace and Timpson op.cit. and Brown and Wallace (2005). The strongest arguments for the nomic reading of the wavefunction in my opinion are found in Callender (2017), which build on the case made by Dürr et al. (1997), and address the criticism in Brown and Wallace ibid. In this connection see also Maudlin (2010).

  4. 4.

    Fuchs (2002a).

  5. 5.

    See Fuchs et al. (2014) and Leifer (2014), p. 68.

  6. 6.

    See Fuchs et al. (2014) and Timpson (2008).

  7. 7.

    See Harrigan and Spekkens (2010).

  8. 8.

    This is particularly clear in Einstein (1970), pp. 670 and 683.

  9. 9.

    A detailed review of these recent results is found in Leifer (2014).

  10. 10.

    For details see Squires et al. (1994), p. 429.

  11. 11.

    The de Broglie-Bohm theory suffers from no such incompatibility, but it is not a ψ-epistemic theory of the Einstein version.

  12. 12.

    For a recent comprehensive collection of essays on this matter, see Bell and Gao (2016).

  13. 13.

    Bell (1990).

  14. 14.

    Fuchs et al. (2014).

  15. 15.

    See Fuchs et al. (2014) and Timpson (2008).

  16. 16.

    See Pusey et al. (2012) and Leifer (2014), section 14.4. For details of advocates of such ψ-epistemic views other than the authors of QBism, see ibid p. 72, and Healey (2016), which also contains a useful review of QBism and its history. Healey’s own “pragmatist” approach of the wavefunction (for details see ibid) has much in common with QBism but important differences as well.

  17. 17.

    The following section of this paper is an attempt to make the case for the realist interpretation of the wavefunction; a more elaborate discussion is found in Gao (2017).

  18. 18.

    David Bohm’s 1952 hidden variable theory had already shown that von Neumann’s 1932 no-go result was inconclusive.

  19. 19.

    For a striking experimental version of the latter involving atomic interferometry, see Szriftgiser et al. (1996). For an experimental proposal involving neutrons, with references to earlier optical variants, see Brown et al. (1992).

  20. 20.

    Leifer op. cit., p. 79.

  21. 21.

    See Bush (2015) and further references therein.

  22. 22.

    That (first order) redshift is consistent with flat Minkowski spacetime has long been known, but it is not always acknowledged; for details see Brown and Read (2016).

  23. 23.

    Attempts to describe all known gravitational effects in a theory based on flat spacetime generally turn out to be awkward reformulations of general relativity, and I suspect that any future “toy” model that accounted for more than a fragment of quantum theory would likewise be an awkward reformulation of that theory.

  24. 24.

    For further details on all these cases, see Kaloyerou and Brown (1992).

  25. 25.

    See Brown et al. (1995).

  26. 26.

    Merzbacher (1962).

  27. 27.

    Leinaas and Myrheim (1977).

  28. 28.

    See, e.g., Prange and Girvin (1990). It is notable that space reflections and time reversal are not symmetries of such electron gases. See Frohlich (2009), p. 56.

  29. 29.

    See Leifer (2014), p. 139.

  30. 30.

    Timpson (2008).

  31. 31.

    I will restrict myself to non-relativistic quantum mechanics; the relativistic version of the story of stability can be found in Lieb and Seiringer (2010).

  32. 32.

    See Lieb (1990), p. 7.

  33. 33.

    Lieb (1990).

  34. 34.

    Sobolev (1938). We are concerned here with the three-dimensional version of the original inequality. For further details see Seiringer (1990) section 1.3.

  35. 35.

    See Lieb (1976), section 1, Lieb (1990) Part III, and Seiringer (1990), section 1.4. It should not be concluded however that a proof of this kind of the stability of the hydrogen atom was only possible in 1938, with the appearance of the Sobolev inequality. A weaker, but less useful inequality due to Hardy (1920) suffices; see, e.g., Seiringer (1990) and particularly Frank (2011).

  36. 36.

    For further details see Lieb (1976), p. 555, or Seiringer (1990), p. 9.

  37. 37.

    Lieb (1990). Note that none of the considerations here require that the wavefunction be complex.

  38. 38.

    Fuchs et al. (2014).

  39. 39.

    See Loss (2005) p. 53.

  40. 40.

    Lieb (1990), p. 23.

  41. 41.

    Dyson and Lenard (1967, 1968).

  42. 42.

    Dyson (1967). For further details see Loss (2005), p. 7.

  43. 43.

    Lieb (1990), p. 15.

  44. 44.

    One such feature is the important result originally due Teller that atoms do not bind: the energy of a system of electrons and nuclei is minimised if the atoms are infinitely far apart and neutral.

  45. 45.

    Lieb and Thirring (1975).

  46. 46.

    See Lieb and Seiringer (2010).

  47. 47.

    Lieb and Thirring (1976).

  48. 48.

    Lieb and Lebowitz (1972).

  49. 49.

    See Lieb (1976), section V.

  50. 50.

    Quoted in Dyson (1967); see also Lieb (1990), p. 25.

  51. 51.

    Fuchs et al. (2014).

  52. 52.

    Mermin (2016).

  53. 53.

    Fuchs et al. (2014).

  54. 54.

    Fuchs et al. (2014).

  55. 55.

    My own views on probability are partly spelt out in Brown (2011). But for a critique of the subjectivist interpretation of probability in the context of QBism, see Timpson (2008).

  56. 56.

    For a clear account of why Jaynes thought equilibrium statistical mechanics works, which has little to do with the choice of probability assignments, see Jaynes (1957). Fuchs (2016) himself states that “there is more to quantum mechanics than just three isolated terms (states, evolution, and measurement)”, but he has something quite different in mind; see (vi) below.

  57. 57.

    Mermin (2016).

  58. 58.

    Consider the claim made recently by Leifer (op. cit., p. 71) that in the epistemic view of the state in quantum mechanics “the appropriate analogies are between quantum states and probability distributions, and between the Schrödinger equation and Liouville’s equation.” This holds for the Einstein version of the epistemic state, but not for QBism. Timpson (2008), section 2.2, is also concerned with the issue of objective evolution of the state in QBism, but to different ends.

  59. 59.

    Mermin (2016).

  60. 60.

    Lieb (1990), p. 1. See also the two first epigraphs at the start of the present paper.

  61. 61.

    Mermin (2016).

  62. 62.

    Fuchs (2016), footnote 5.

  63. 63.

    Chandrasekhar (1931).

  64. 64.

    Fuchs et al. (2014).

  65. 65.

    Mermin (2016).

  66. 66.

    Fuchs (2016), p. 1.

  67. 67.

    Fuchs and Schack (2004).

  68. 68.

    Mermin (2016).

  69. 69.

    Fuchs (2002b), also quoted in Fuchs (2016).

  70. 70.

    Berkeley (1710).

  71. 71.

    For an introduction to the problem of qualia, see Tye (2016).

  72. 72.

    Fuchs et al. (2014).

  73. 73.

    Fuchs et al. (2014).

  74. 74.

    Taken from the introduction to a 2004 lecture by Christopher Fuchs, and reproduced in Fuchs (2016).

  75. 75.

    Fuchs (2016).

  76. 76.

    Fuchs et al. (2014).

  77. 77.

    Fuchs (2016).

  78. 78.

    Einstein (1970), p. 674. This is part of a longer Einstein quotation found in Fuchs (2016).

  79. 79.

    See Einstein (1970), p. 680, where Einstein attributes this position to the influence of Immanuel Kant. For further references to Einstein’s realist philosophy, and to that of commentators, see Brown and Lehmkuhl (2016), footnote 4.

  80. 80.

    Einstein (1970), pp. 673–4; again this is part of the longer quotation given in Fuchs (2016).

  81. 81.

    Fuchs (2016).

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Acknowledgements

I thank the organisers of the XII International Ontology Congress for the kind invitation to contribute to these proceedings. I am also grateful to David Wallace for useful remarks, and to Rhys Borchert, James Read and particularly Christopher Fuchs and Christopher Timpson for invaluable critical comments on the first draft of this paper. None should be taken to endorse the arguments presented here.

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    Harvey R. Brown

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    Alberto Cordero

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Brown, H.R. (2019). The Reality of the Wavefunction: Old Arguments and New. In: Cordero, A. (eds) Philosophers Look at Quantum Mechanics. Synthese Library, vol 406. Springer, Cham. https://doi.org/10.1007/978-3-030-15659-6_5

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