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One world, one beable

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Abstract

Is the quantum state part of the furniture of the world? Einstein found such a position indigestible, but here I present a different understanding of the wavefunction that is easy to stomach. First, I develop the idea that the wavefunction is nomological in nature, showing how the quantum It or Bit debate gets subsumed by the corresponding It or Bit debate about laws of nature. Second, I motivate the nomological view by casting quantum mechanics in a “classical” formalism (Hamilton–Jacobi theory) and classical mechanics in a “quantum” formalism (Koopman–von Neumann theory) and then comparing and contrasting classical and quantum wave functions. I argue that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits.

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Notes

  1. Strictly speaking, because the particle configuration doesn’t affect the wavefunction, we have only one half of Descartes’ problem. The question here is more like the “causation” problem afflicting the mind–body epiphenomenalist.

  2. Another much more radical notion is doing without the wavefunction at all; that is, writing the theory directly in terms of an equation for the beables and nothing more. Suggestive models exist that suggest this path both for GRW-type theories (e.g., Dowker and Henson 2004) and for Bohm-like theories (e.g., Poirier 2010); however, since the latter model is committed to an actual infinite ensemble of “world” trajectories, it seems more like an Everettian theory.

  3. As Goldstein and Zanghì (2013) point out, effective wavefunctions therefore have quasi-nomological status. They are a function over what is nomological, \(\Psi _{t}\), and the contingent environment, \(Y_{t}\).

  4. Both theories can be “squashed” together into many abstract formulations, so one has many choices. I’ll choose two that I find enlightening, but of course there are many others, e.g., phase space formulations of both theories. I’ll count classical statistical mechanics as classical physics. This move is justified in the present context, I believe, by the fact that “beable” interpretations of quantum mechanics often regard quantum mechanics as a kind of statistical mechanics of beables (Dürr et al. 1992).

  5. Note that matters don’t work out as simply when we add spin and move away from the Schrödinger equation; see Holland (1993).

  6. Here I stress ’alone’ because of course linearity is related to entanglement which is related to the difference I’ll mention momentarily. My point is not to de-emphasize the above differences but rather just to point out that more premises are needed to get from these to the reification of the wavefunction. An argument is needed, and one is supplied below. Others based on different formal differences may be possible, but I suspect that they will only reproduce the essence of the ’causal agent’ argument below.

  7. See Brown and Wallace (2005), Deutsch (1996), Wallace (2008) and Zeh (1999).

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  1. Department of Philosophy, UCSD, 9500 Gilman Drive, La Jolla, CA, 92093-0119, USA

    Craig Callender

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Callender, C. One world, one beable. Synthese 192, 3153–3177 (2015). https://doi.org/10.1007/s11229-014-0582-3

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