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Making the vague precise: What Bohmian mechanics really says

Adam Brownstein

Published Aug 12, 2026• 0 citations
OpenAlex

Abstract

The de Broglie-Bohm interpretation is known to make the vagueness of the Copenhagen interpretation precise. What this actually means is that it offers a purely materialist framework for understanding quantum mechanics, as opposed to a dualist or idealist framework. The Copenhagen interpretation introduces conscious observers into its ontology and therefore lacks the precision of a materialist scientific theory expressible in terms of mathematics. The corollary of this is that using the de Broglie-Bohm interpretation as a proof by contradiction, it can be shown that if consciousness is not epiphenomenal but instead has causal efficacy, then the Born rule probabilities must be incomplete, and both the de Broglie-Bohm and Copenhagen interpretations are incomplete.

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The de Broglie-Bohm interpretation is known to make the vagueness of the Copenhagen interpretation precise. What this actually means is that it offers a purely materialist framework for understanding quantum mechanics, as opposed to a dualist or idealist framework. The Copenhagen interpretation introduces conscious observers into its ontology and therefore lacks the precision of a materialist scientific theory expressible in terms of mathematics. The corollary of this is that using the de Broglie-Bohm interpretation as a proof by contradiction, it can be shown that if consciousness is not epiphenomenal but instead has causal efficacy, then the Born rule probabilities must be incomplete, and both the de Broglie-Bohm and Copenhagen interpretations are incomplete.
The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation contrasts with the Copenhagen orthodox interpretation, which conveys uncertainty through the commutator relationship between position and momentum operators. This is further exacerbated by the de Broglie-Bohm interpretation, which uses no operators corresponding to these observables. We reconcile these opposing viewpoints by introducing mathematical nonlinear transforms in Bohmian mechanics for the momentum observable. While these nonlinear operator-like transforms cannot be easily represented as matrices in the Hilbert space, we show that they can be utilized in the de Broglie-Bohm interpretations of quantum theory.
Bohmian mechanics also known as de Broglie-Bohm theory is the most popular alternative approach to quantum mechanics. Whereas the standard interpretation of quantum mechanics is based on the complementarity principle Bohmian mechanics assumes that both particle and wave are concrete physical objects. In 1993 Peter Holland has written an ardent account on the plausibility of the de Broglie-Bohm theory. He proved that it fully reproduces quantum mechanics if the initial particle distribution is consistent with a solution of the Schrödinger equation. Which may be the reasons that Bohmian mechanics has not yet found global acceptance? In this article it will be shown that predicted properties of atoms and molecules are in conflict with experimental findings. Moreover it will be demonstrated that repeatedly published ensembles of trajectories illustrating double slit diffraction processes do not agree with quantum mechanics. The credibility of a theory is undermined when recognizably wrong data presented frequently over years are finally not declared obsolete.
The de Broglie–Bohm interpretation (Bohmian mechanics, hidden-variables theory, causal interpretation or pilot-wave theory) is one of the interpretations of quantum mechanics which opposes to the claim of standard interpretation on the completeness of description of the state of quantummechanical system, that description in Bohmian mechanics is completed by defining positions of the particles of the system i.e. hidden variables and their dynamics. These facts are the basis of motivation for the introduction of a new theory that can describe dubious axiomatic requirements of standard interpretation. The presented theory is deterministic and explicitly nonlocal. Originators of Bohmian mechanics were L. de Broglie (1927.) and D. Bohm (1952.) who presented mathematically more general and conceptual elaborate formulation. Along with the historical overview, a note is given about the main properties of the theory, such as the issue of nonlocality and hidden variables. The aim of this paper is to present and explain the main ideas and properties of the theory as well as to give a systematic overview of present and historical mathematical construction of the theory and most of all to discuss implications of de Broglie–Bohm theory on the ontology of quantum-mechanical picture, showcasing examples of the equivalency of the description of a free particle as a propagation of the plane wave in space or as the ensemble of the trajectories and of the spreading of the Gaussian wave packet. The main example of the obvious conceptual clashing of the interpretations is presented: the double-slit experiment, with a detailed examination of the Bohmian mechanics’ predictions using presented formalism on the two double-slit experiment. The graphs of trajectories for given examples are obtained.
Bohmian mechanics, also known as pilot-wave theory or de Broglie–Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a “quantum theory without observers,” alongside with collapse theories and many-worlds theories and in contrast to orthodox quantum mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics for empirical predictions. Specifically, Bohmian mechanics asserts that electrons and other elementary particles have a definite position at every time and move according to an equation of motion that is one of the fundamental laws of the theory and involves a wavefunction that evolves according to the usual Schr\\"odinger equation. Bohmian mechanics is named after David Bohm (1917–1992), who was, although not the first to consider this theory, the first to realize (in 1952) that it actually makes correct predictions.
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a quantum theory without observers, alongside with collapse theories and many-worlds theories and in contrast to orthodox mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of mechanics for empirical predictions. Specifically, Bohmian mechanics asserts that electrons and other elementary particles have a definite position at every time and move according to an equation of motion that is one of the fundamental laws of the theory and involves a wave function that evolves according to the usual Schr\odinger equation. Bohmian mechanics is named after David Bohm (1917-1992), who was, although not the first to consider this theory, the first to realize (in 1952) that it actually makes correct predictions.
The de Broglie-Bohm interpretation of quantum mechanics (BM) has been favored as the preferred alternative to standard quantum mechanics on the ground that it allows a realist construal of the quantum world. We examine in the present work whether BM is consistent with scientific realism. Indeed, Bohmian mechanics makes strong ontological claims but accepts in principle the impossibility of generating epistemic warrants in support of its assumptions. We will argue that such a situation gives rise, at best, to an unsolvable underdetermination dilemma. This leads in turn to the following paradox: although Bohmian mechanics has frequently been invoked to reconcile quantum mechanics with realism, its status as a valid interpretation of quantum mechanics hinges nonetheless on nonevidential epistemological arguments traditionally associated with antirealism.