The physics and metaphysics of Tychistic Bohmian Mechanics (original) (raw)

Notes on the ontology of Bohmian mechanics

It is argued that in Bohmian mechanics the effective wave function of a subsystem of the universe does not merely encode the influences of other particles on the subsystem. This suggests that the ontology of Bohmian mechanics does not consist only in Bohmian particles and their positions. It is nonetheless pointed out that since the wave function in configuration space may represent the state of ergodic motion of non-Bohmian particles in three-dimensional space, the ontology of Bohmian mechanics may still consist only in particles.

The Ontology of Bohmian Mechanics

The British Journal for the Philosophy of Science, 2013

The paper points out that the modern formulation of Bohm's quantum theory known as Bohmian mechanics is committed only to particles' positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm's theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general.

The emergence and interpretation of probability in Bohmian mechanics

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2007

The Bohm interpretation of quantum mechanics is capable of illustrating, by itself, virtually every philosophical and foundational conundrum associated with physical probability. One reason this is true is that the Bohm interpretation comes in many forms, both stochastic and deterministic. The other reason is that quantum mechanics is to Bohmian mechanics roughly as statistical mechanics is to classical mechanics; hence the notorious problems in the foundations of statistical mechanics are reprised within the foundations of Bohmian mechanics. The present paper is an opinionated survey of this literature. In it I focus on the meaning of Born's rule in a Bohmian universe. After considering various rationales for this rule, I settle on one based on the law of large numbers as the best bet. This option leaves open how the probabilities in this result ought to be interpreted, or so I shall argue. When delivering an interpretation of these probabilities, the history of probability warns us of a number of pitfalls. I show how these pitfalls manifest themselves in the Bohmian case and then show that at least one class of interpretations seems to successfully navigate these problems.

Individuality and the account of non-locality: the case for the particle ontology in quantum physics

The paper explains why an ontology of permanent point particles that are individuated by their relative positions and that move on continuous trajec-tories as given by a deterministic law of motion constitutes the best solution to the measurement problem in both quantum mechanics and quantum field theory. This case is made by comparing the Bohmian theory to collapse theories such as the GRW matter density and the GRW flash theory. It is argued that the Bohmian theory makes the minimal changes, concerning only the dynamics and neither the ontology nor the account of probabilities, that are necessary to get from classical mechanics to quantum physics. There is no cogent reason to go beyond these minimal changes.

Quantum mechanics as a deterministic theory of a continuum of worlds

Quantum Studies: Mathematics and Foundations, 2015

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both "time" and "world" are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett's many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.

Can the ontology of Bohmian mechanics consists only in particles? The PBR theorem says no

The meaning of the wave function is an important unresolved issue in Bohmian mechanics. On the one hand, according to the nomological view, the wave function of the universe or the universal wave function is not ontic but nomological, like a law of nature. On the other hand, the PBR theorem proves that the wave function in quantum mechanics or the effective wave function in Bohmian mechanics is ontic, representing the ontic state of a physical system in the universe. It is usually thought that the nomological view of the universal wave function is compatible with the ontic view of the effective wave function, and thus the PBR theorem has no implications for the nomological view. In this paper, I argue that this is not the case, and these two views are in fact incompatible. This means that if the effective wave function is ontic as the PBR theorem proves, then the universal wave function cannot be nomological, and the ontology of Bohmian mechanics cannot consist only in particles. This incompatibility result holds true not only for Humeanism and dispositionalism but also for primitivism about laws of nature, which attributes a fundamental ontic role to the universal wave function. Moreover, I argue that although the nomological view can be held by rejecting one key assumption of the PBR theorem, the rejection will lead to serious problems, such as that the results of measurements and their probabilities cannot be explained in ontology in Bohmian mechanics. Finally, I briefly discuss three psi\psipsi-ontologies, namely a physical field in a fundamental high-dimensional space, a multi-field in three-dimensional space, and RDM (Random Discontinuous Motion) of particles in three-dimensional space, and argue that the RDM of particles ontology can answer the objections to the psi\psipsi-ontology raised by the proponents of the nomological view.

Why the quantum equilibrium hypothesis? From Bohmian mechanics to a many-worlds theory

The status and justification of the quantum equilibrium hypothesis (QEH) in Bohmian mechanics is "a rather delicate matter". In this paper, I present a new analysis of this hypothesis. It is argued that the QEH should be regarded not as a mere initial condition but more appropriately as one part of the law of motion. Moreover, it is more reasonable and simpler to assume that the QEH holds true consistently at all time. The resulting theory is a many-worlds theory of random discontinuous motion of particles in three-dimensional space. This new theory agrees with experiments, and it is arguably the simplest realist version of quantum mechanics.

Formalism, Ontology, and Methodology in Bohmian Mechanics

Foundations of Science, 2003

The relationship between mathematical formalism, physical interpretation and epistemological appraisal in the practice of physical theorizing is considered in the context of Bohmian mechanics. After laying out the formal mathematical postulates of the theory and recovering the historical roots of the present debate over the meaning of Bohmian mechanics from the early debate over the meaning of Schrödinger's wave mechanics, several contemporary interpretations of Bohmian mechanics in the literature are discussed and critiqued with respect to the aim of causal explanation and an alternative interpretation is proposed. Throughout, the over-arching aim is to exhibit the connections between mathematical, ontological and methodological questions in physical theory and to reflect on the rationality of physical theorizing in light of the present case.