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arXiv:2409.01294

De Broglie-Bohm Quantum Mechanics

Antony Valentini

Published Sep 2, 2024• 0 citations
arXivHTMLPDF

Abstract

We provide an overview of the de Broglie-Bohm pilot-wave formulation of quantum mechanics, emphasising its applications to field theory, high-energy physics, gravitation, and cosmology.
DOI
10.48550/arxiv.2409.01294

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The Copenhagen interpretation has been the subject of much criticism, notably by De Broglie and Einstein, because it contradicts the principles of causality and realism. The aim of this essay is to study the wave mechanics as an alternative to traditional quantum mechanics, in the continuity of the ideas of Louis de Broglie: the pilot wave theory of De Broglie (where each particle is associated with a wave which guides it), De Broglie-Bohm theory, stochastic electrodynamics (where the stochastic character of particles is caused by the energy field of the fluctuating vacuum), and the analogies between quantum mechanics and hydrodynamics.
In this thesis we study the de Broglie-Bohm pilot-wave interpretation of quantum theory. We consider the domain of non-relativistic quantum theory, relativistic quantum theory and quantum field theory, and in each domain we consider the possibility of formulating a pilot-wave interpretation. For non-relativistic quantum theory a pilot-wave interpretation in terms of particle beables can readily be formulated. But this interpretation can in general not straightforwardly be generalized to relativistic wave equations. The problems which prevent us from devising a pilot-wave interpretation for relativistic wave equations also plague the standard quantum mechanical interpretation, where these problems led to the conception of quantum field theory. Therefore most of our attention is focussed on the construction of a pilot-wave interpretation for quantum field theory. We thereby favour the field beable approach, developed amongst others by Bohm, Hiley, Holland, Kaloyerou and Valentini. Although the field beable approach can be successfully applied to bosonic quantum field theory, it seems not straightforward to do so for fermionic quantum field theory.
As we discussed in Section 2.4, in his Solvay lecture of 1927 de Broglie presented the pilot-wave dynamics of a non-relativistic many-body system, and outlined some simple applications of his ‘new dynamics of quanta’ (to interference, diffraction and atomic transitions). Further, as we saw in Section 10.2, contrary to a widespread misunderstanding, in the general discussion de Broglie's reply to Pauli's objection contained the essential points needed to treat inelastic scattering (even if Fermi's misleading optical analogy confused matters): in particular, de Broglie correctly indicated how definite quantum outcomes in scattering processes arise from a separation of wave packets in configuration space. We also saw in Section 10.4 that de Broglie was unable to reply to a query from Kramers concerning the recoil of a single photon on a mirror: to do so, he would have had to introduce a joint wave function for the photon and the mirror. De Broglie's theory was revived by Bohm 25 years later (Bohm 1952a,b) (though with the dynamics written in terms of a law for acceleration instead of a law for velocity). Bohm's truly new and very important contribution was a pilot-wave account of the general quantum theory of measurement, with macroscopic equipment (pointers, etc.) treated as part of the quantum system. In effect, in 1952, Bohm provided a detailed derivation of quantum phenomenology from de Broglie's dynamics of 1927 (albeit with the dynamical equations written differently).
Quantum theory and the de Broglie – Bohm pilot-wave theory are empirically equivalent. In addition to other objections to the pilot-wave theory, many physicists (and some philosophers) take this to be enough to dismiss the pilot-wave theory, as they say it adds nothing to the standard theory. In this short paper I review some objections and replies to the pilot-wave theory. In particular I respond to the empirical equivalence challenge arguing that, given their mutual relationship, there is no reason to expect the two theories to make different predictions, even if they actually might.