Bohm's Ontological Interpretation and its Relations to Three Formulations of Quantum Mechanics

Emilia Margoni

Abstract Michael Esfeld’s minimalist ontology is committed to two axioms relating to (1) distance relations that identify simple objects (permanent matter points) while (2) the distances between them change. This article scrutinizes such a conceptual strategy to determine whether it can successfully be applied to all levels of physical reality, as Esfeld contends. To do so, it explores one of his paradigmatic sources, that is, Bohmian mechanics. Two arguments are proposed. First, while Bohm’s original formulation of Bohmian mechanics and the interpretation advocated by Dürr, Goldstein & Zanghì are typically taken as mathematically equivalent, this article argues that Esfeld’s minimalist ontology does not cover the former’s ontological richness. To secure its achievement, the minimalist ontology framework needs to (i) break the equivalence between the two versions via a commitment to the nomological interpretation of the wavefunction (ii) yet attribute some kind of physical efficacy to the wavefunction as a guiding parameter for the evolution of particles living in three-dimensional space. Both requirements will be critically addressed. Second, the article shows that Esfeld’s metaphysical program is not only forced to rely on a theoretically suspicious formulation of quantum mechanics, but that more fundamental, under-development approaches in theoretical physics are way less reconcilable with its axioms, thus questioning its alleged universality.

Michael Epperson

Jorge Manero

Abstract It has been argued that in the context of Bohm’s approach to quantum mechanics, the postulation of a three-dimensional ontology (as opposed to a high-dimensional one) is presumed to be the only interpretation that may reliably support object-oriented realism by virtue of the fact that this ontology is approximately preserved through scientific change, at least in the classical–quantum transition. Based on an interpretative analysis of the Bohmian formulation, I shall critically evaluate the tenability of this argument. In so doing, I shall argue that this formulation admits the postulation of an alternative ontology that is properly defined in a high-dimensional space, and is approximately preserved among this transition. As a result, both the three-dimensional and the high-dimensional worldviews shall form the basis of an equally reliable endorsement of object-oriented realism in the context of the Bohmian framework. I shall conclude that this argument becomes a problem of metaphysical underdetermination between a three and a high-dimensional Bohmian interpretation.

Shan Gao

Born’s interpretation of the squared modulus of a wave function (|ψ|2) as the probability density of finding a particle within a specified region of space is a key ingredient of the standard framework of quantum mechanics, thereby implying that the standard interpretation of quantum mechanics is inherently epistemological. On the other hand, the possibility of an alternative interpretation of quantum mechanics by interpreting |ψ|2 as the probability density of a particle being actually present within a specified region was first suggested by de Broglie [1]. Later, Bohm [2-4] developed the details of such an ontological model of quantum mechanics by using the notion of an observer-independent spacetime trajectory of an individual particle T&F Cat # K11224, Chapter 8, Page 114, 15-9-2010 that is determined by its wave function through an equation of motion which is formulated in a way consistent with the Schrödinger time evolution. Bohm’s model, thus, explicitly refuted the counterarguments (such as those put forward by Pauli [5] and von Neumann [6]) that claimed to have ruled out the formulation of such a model. Subsequently, much work has been done on various aspects of the Bohmian model [7-10]. That such a model is not unique has been elaborately discussed [11,12] while different versions of the ontological model of quantum mechanics have been proposed [13-21].