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International Journal of Applied Science and Engineering Review

RANDOM AND ARBITRARY CONTINGENCIES IN HISTORY OF SCIENCE AND TECHNOLOGY [8] – THE MARGINAL STATUS OF BOHMIAN QUANTUM MECHANICS

Yeuncheol Jeong

Published Jan 1, 2026• 0 citations
Publisher

Abstract

David Bohm transformed Schrödinger equation into a form of Newton’s second law of motion, revoking causality, determinism and realism in quantum mechanics. However, the newly created term of quantum potential in Bohm’s transformation is taken to be non-physical to many physicists. Besides, Bohm’s quantum mechanics came one generation later after Copenhagen counterpart. At the same time, Bohm could not advocate his quantum mechanics with other physicists, due to his involuntary exile from the US, leading to the marginality of his theory in the general physics community today.

DOI
10.52267/ijaser.2026.7317

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David Bohm transformed Schrödinger equation into a form of Newton’s second law of motion, revoking causality, determinism and realism in quantum mechanics. However, the newly created term of quantum potential in Bohm’s transformation is taken to be non-physical to many physicists. Besides, Bohm’s quantum mechanics came one generation later after Copenhagen counterpart. At the same time, Bohm could not advocate his quantum mechanics with other physicists, due to his involuntary exile from the US, leading to the marginality of his theory in the general physics community today.
Copenhagen interpretation of quantum mechanics has become a groundbreaking fundamental approach toward the sub-atomic world, even though Einstein himself never fully acknowledge its frameworks. The interpretation assumes that all the quantum processes and phenomena are random and arbitrary. All we can do is the probabilistic understanding of random occurrences. This empiricist’ ideas of anti-realism, non-causality, and indeterminism have been a text standard presentation of quantum mechanics today. Physics textbooks today follow the interpretation, describing all the sub-atomic phenomena as random, arbitrary and non-causal, solely dependent on probabilistic pure chance.
Schrodinger’s equation is a basic mathematical expression for a single particle in quantum mechanics. However, its physical meaning has never been assigned in any standard quantum mechanics text book. Here, a detailed complete re-derivation of hidden variable equation in David Bohm’s 1952 papers is given to assign some physical meanings to Schrodinger’s equation. This work shows some required detailed transformation of Schrodinger’s Equation into a form of Newtonian second law of motion with definite trajectory with some initial conditions given. All the quantum effects come from the single localized term called the quantum potential.
Abstract The paper investigates David Bohm’s philosophy of science as a form of fallibilist realism that underpins his causal interpretation of quantum mechanics Bohm (Bohm 1952a, 1952b, 1984, 1985, 1988, 1989, 1990; Bohm and Hiley 1975, 1984, 1993). Bohm’s central aim is to establish the superiority of his interpretation over the standard Copenhagen framework, particularly in contrast to that of Niels Bohr. Whereas Bohr asserts that knowledge of quantum phenomena is restricted to the statistical outcomes of measurement, Bohm’s approach is distinctly realist in orientation. Responding to the challenges posed by Einstein and other physicists, Bohm relies on extra-empirical criteria such as determinism, objectivity and intelligibility. The paper develops what will be termed the methodology of intuitive intelligibility (II), consisting of four stages: (1) reformulation of the standard quantum equations, (2) physical interpretation of the mathematical symbols, (3) drawing analogies with classical laws, and (4) drawing analogies with common experience. It is argued that Bohm applies the (II) methodology consistently, with the notable exception of the ontological status of the wave function and quantum potential. In attempting to explain causal relations from a 3N-dimensional configuration space (where N is the number of particles) to familiar three-dimensional space through an appeal to ‘information’, Bohm arguably commits a category mistake. A proposed resolution—drawing on Bohm’s own holistic analogies—is supported by the recent multi-field interpretation (Romano Multi-field and Bohm’s theory. Synthese, 198(30), 10587–10609, 2021). The term fallibilist realism aptly characterizes Bohm’s stance in the philosophy of science: he repeatedly emphasizes that the causal interpretation is not intended as a final theory. Nevertheless, holism constitutes a substantive ontological commitment that he is unwilling to abandon.
In this article, we investigate Bohm's view of quantum theory, especially Bohm's quantum potential, from a new perspective. We develop a quasi-Newtonian approach to Bohmian mechanics. We show that to arrive at Bohmian formulation of quantum mechanics, there is no necessity to start from the Schrödinger equation. We also obtain an equation that restricts the possible forms of quantum potential and determines the functional form of it without appealing to the wave function and the Schrödinger equation. Finally, we discuss about the significance of quantum potential in the conceptual structure of quantum theory.
Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a "probability amplitude." A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or "Quantal Newtonian" Laws obeyed by each electron. These Laws, derived from the temporal and stationary-state Schrödinger equation, are interpreted in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. According to the Second Law, each electron experiences an external field-the quantal Coulomb-Lorentz law. It also experiences an internal field representative of properties of the system: correlations due to Coulomb repulsion and Pauli principle; the density; kinetic effects; and an internal magnetic field component. There is a response field. The First Law states that the sum of the external and internal fields experienced by each electron vanishes. These fields are akin to those of classical physics: They pervade all space; their structure is descriptive of the quantum system; the energy of the system is stored in these fields. It is in the classical behavior of these fields, which arise from quantal sources that one may then speak of determinism in quantum mechanics.
Short introduction to Bohmian mechanics Sheldon Goldstein in a Foundations of Physics paper [1] indicates (p. 341): “Since macroscopic objects are normally regarded as built out of microscopic constituents …there can be no problem of macroscopic reality per se in Bohmian mechanics.” Goldstein in the same paper remarks (p. 342) that this | ψ | 2 has “a status very much the same as that of a thermodynamic equilibrium.” Basil Hiley the closest collaborator of David Bohm, says the following (Hiley [2] (p. 2)): “What Bohm (1952a; 1952b) did was to show how to retain a description of all the usual properties of a classical world and yet remain completely within the quantum formalism.” The Bohm (1952) [3] [4] references in that quote refer to the original work of Bohm in which he sets out the basics of the Bohmian mechanics. As we will see later in the next section of this chapter, the appearance of an “additional term” in the Hamilton-Jacobi equation, is the hallmark of Bohmian mechanics and it is very often termed the “quantum potential.” Hiley [2] (p. 2) remarks that since the Bohmian momentum is a well-defined function of position and time, an ensemble of trajectories can be found when the quantum potential is non-zero. A unique, classical path is found when the quantum potential is zero. From the outset, we hope the reader can savor the beauty of this simple but very powerful result. Bohmian mechanics indeed shows this very gentle transition from quantum mechanics to classical mechanics via the value of the quantum potential.