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De Broglie-Bohm Theory, Quo Vadis?

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Abstract

The purpose of this contribution is to examine the current state of the de Broglie-Bohm theory (dBB) in light of Bohm’s vision as he explicitly set it out in his book Quantum theory [In Bohm, D., Quantum theory, Courier corporation, (1961b)]. In particular, two programmes that differ in many crucial respects are currently being pursued. On the one hand, the Bohmian mechanics school, founded by Dürr Goldstein and Zanghì, considers the theory to be Galilean invariant, regards particles’ motion as determined by a nomological entity, the universal wave function, upholds the quantum equilibrium hypothesis and explains probabilities in terms of typicality. On the other hand, the Pilot-wave school advocated by Valentini considers the theory to be based on Aristotelian dynamics, regards the wave function as a physical field displaying a contingent nature, and explains quantum equilibrium as the result of a process of relaxation from quantum non-equilibrium. Looking at Bohm’s work [In Bohm, D., Quantum theory, Courier corporation, (1961b)], it is clear that his intention was to construct a theory that was empirically different from standard quantum mechanics, so that it would be testable and falsifiable. Only this way could he defend dBB from the criticism that accused the theory of being 'metaphysical'. These methodological concerns about the falsifiability of the theory constitute, in my opinion, a strong reason for regarding Valentini's programme as methodologically valuable, even if it might turn out to be wrong. Indeed, the programme of the Pilot-wave school aims to be falsifiable with respect to standard quantum mechanics and can in principle defend the empirical status of particle trajectories.

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Notes

  1. Within the Bohmian mechanics school, this can be easily explained because any measurement procedure transforms (effectively collapse) the effective wave function, a well-decoupled function that obeys the Schrödinger equation and that provides a description of the subsystem (see [2]).

  2. However, notice that one may object that the Schrödinger equation is not empirically supported.

  3. For a detailed discussion on the relation between ad hocness, falsifiability and scientific advancement, see [30].

  4. Regarding standard quantum mechanics, his concern was that its main assumption that the complete description of the system is given by the wavefunction alone is not testable. This what he writes in the abstract of his 1952 paper (p. 166): ‘The usual interpretation of the quantum theory is self-consistent, but it involves an assumption that cannot be tested experimentally, viz. that the most complete possible specification of an individual system is in terms of a wave function’.

  5. Everett many world is not testable or falsifiable with respect to standard quantum mechanics. But this is not problematic, as it does not introduce different postulates with respect to standard quantum mechanics. As Wallace stresses ([36] = , many worlds is just a literal reading of standard quantum mechanics. Moreover, even though there won’t be any empirical test to decide between the two, everettians still hope that physicists will endorse an interpretation of quantum probabilities that will favour EMW with respect to standard quantum mechanics. In this sense, there is still some hope that there is some reason to prefer the former with respect to the latter. A differentiation based on interpretation of their empirical support (which is statistical in nature) is considered to be an advantage rather than a disadvantage.

  6. Indeed, according to the Bohmian mechanics (2) describes a Galilean invariant dynamics, according to the Pilot-wave school (2) describes an Aristotelian dynamics.

  7. For a discussion on measurements of the initial conditions of particle configuration and wavefunction in Bohmian mechanics, and the case of highly localized wavefunction, see [24].

  8. See for instance the following quotation in [2]: “That the quantum equilibrium hypothesis conveys the most detailed knowledge possible concerning the present configuration of a subsystem” (p. 64). “From our conclusion that when a system has wave function ψ we cannot know more about its configuration X than what is expressed by \({|\uppsi|}^{2}\), it follows trivially that knowledge that its wave function is ψ similarly constrains our knowledge of the configuration” (p. 69). For a clarification on this point, see Lazarovici [3].

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  1. Institute of Philosophy, The University of Bern, Bern, Switzerland

    Vera Matarese

  2. Center for Space and Habitability, The University of Bern, Bern, Switzerland

    Vera Matarese

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Matarese, V. De Broglie-Bohm Theory, Quo Vadis?. Found Phys 53, 18 (2023). https://doi.org/10.1007/s10701-022-00647-w

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