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Quantum Mechanics

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Typicality Reasoning in Probability, Physics, and Metaphysics

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Abstract

Our discussions have been based almost exclusively on deterministic laws. Some might object that this is not very naturalistic. Aren’t our best physical theories, viz. quantum theories, indeterministic? The short answer is that they most likely are not. While it is folklore that intrinsic randomness takes hold in quantum mechanics, the claim does not stand up well to scrutiny. Standard quantum mechanics involves only one precise dynamical equation—the Schrödinger equation describing the time evolution of the wave function—and this equation is perfectly deterministic.

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Notes

  1. 1.

    Witness, for instance, David Mermin’s defense of the so-called QBist interpretation:

    Albert Einstein famously asked whether a wavefunction could be collapsed by the observations of a mouse. Bell expanded on that, asking whether the wavefunction of the world awaited the appearance of a physicist with a PhD before collapsing. The QBist answers both questions with “no.” A mouse lacks the mental facility to use quantum mechanics to update its state assignments on the basis of its subsequent experience, but these days even an undergraduate can easily learn enough quantum mechanics to do just that. (Mermin, 2012)

  2. 2.

    See Allori et al. (2008), Allori et al. (2014), Allori (2013), Esfeld (2014a), Esfeld (2020); cf. Bell (2004, Chap. 4) on “local beables” and the notion of “primary ontology” in Maudlin (1997, 2019).

  3. 3.

    An option that is also available for Many-Worlds, see Allori et al. (2011).

  4. 4.

    If it even allows us to apply quantum mechanics to macroscopic systems like measurement devices.

  5. 5.

    See, in particular, Dürr et al. (2004) (reprinted as Chap. 3 in Dürr et al. (2013)) for a rigorous treatment.

  6. 6.

    For rigorous results about the existence and uniqueness of solutions, see Berndl et al. (1995), Teufel and Tumulka (2005).

  7. 7.

    I am using the “epistemic” argument for simplicity, but it is really a shorthand for the various reasons discussed throughout this book for why the empirical import of microscopic laws is always found in typical regularities.

  8. 8.

    That depends only locally on \(\Psi \) and its derivatives, see Goldstein and Struyve (2007).

  9. 9.

    Let \(B=\bigcup B_i\) be a pairwise disjoint with \(\mu (A|B_i)=a\) for all \(B_i\). Then we have \(\mu (B)a=\sum _i \mu (A|B_i)\mu (B_i)= \sum _i \mu (A\cap B_i)=\mu (A\cap B)\) and thus \(\mu (A|B)=\frac {\mu (A\cap B)}{\mu ( B)}=a\).

  10. 10.

    The analysis for “time-like ensembles,” i.e., consecutive measurements on the same system, is mathematically more involved and carried out in Dürr et al. (1992).

  11. 11.

    Absolute uncertainty is sometimes misunderstood as implying the impossibility of locating Bohmian particles with arbitrary precision. What it actually implies is the impossibility of locating Bohmian particles with arbitrary precision without affecting their quantum state.

  12. 12.

    E.g., the above-mentioned problem of arrival times Das & Dürr (2019), or “Wigner’s friend” gedankenexperiments, in which quantum measurements are performed on human observers Lazarovici & Hubert (2019).

  13. 13.

    Such as weak measurements of particle trajectories, see, e.g., Dürr and Lazarovici (2020, Chap. 8) for a discussion.

  14. 14.

    Archived by Physikalische Gesellschaft Zürich. http://www.pgz.ch/history/einstein/index.html.

  15. 15.

    Cf. Dürr et al. (2013, p. 65). See Chen (2021) for an interesting proposal to unite the two levels by conceiving the universal quantum state as represented by a density matrix.

  16. 16.

    As Wallace (2012) explains: “[T]here is no sense in which [decoherence] phenomena lead to a naturally discrete branching process: as we have seen in studying quantum chaos, while a branching structure can be discerned in such systems, it has no natural ‘grain’. To be sure, by choosing a certain discretization of (configuration-)space and time, a discrete branching structure will emerge, but a finer or coarser choice would also give branching. And there is no ‘finest’ choice of branching structure: as we fine-grain our decoherent history space, we will eventually reach a point where interference between branches ceases to be negligible, but there is no precise point where this occurs. As such, the question ‘How many branches are there?’ does not, ultimately, make sense.” (pp. 99–100).

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  1. University of Lausanne, Lausanne, Switzerland

    Dustin Lazarovici

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Lazarovici, D. (2023). Quantum Mechanics. In: Typicality Reasoning in Probability, Physics, and Metaphysics. New Directions in the Philosophy of Science. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-33448-1_13

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