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The ontology of Bohmian mechanics
Michael Esfeld, Dustin Lazarovici, Mario Hubert, Detlef Dürr
TL;DR
The paper asks how Bohmian mechanics can account for particle motion without treating the wave-function as an additional physical entity, and how its law of motion should be grounded. It develops nomological, Humean, dispositionalist, and primitivist options, concluding that primitive-ontology approaches can accommodate both Humeanism and dispositionalism, though each faces philosophical limitations.
Problem
The paper addresses the ontological status of the wave-function and the grounding of Bohmian mechanics’ law of motion, including whether Humeanism can explain physical development.
Method
The paper analyzes Bohmian mechanics through the nomological interpretation of the wave-function and compares Humean, dispositionalist, and primitivist accounts of laws.
Results
Bohmian mechanics can be formulated with particles and their positions as the ontology, while the wave-function functions in the law of motion; both Humeanism and dispositionalism can be applied to this framework.
Takeaways & Limitations
The wave-function need not be added to physical reality, and primitive-ontology approaches can remain compatible with different philosophical accounts of laws.
Takeaways & Limitations
Dispositionalism does not explain why the fundamental disposition of motion is holistic rather than belonging to individual particles.
Abstract
from arXiv · showhide
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.
1 Introduction
Modern Bohmian mechanics posits particles and their positions as its primitive ontology, together with a law of motion describing their temporal development. Its formulation uses a universal wave-function and Schrödinger equation, but excludes Newtonian forces and acceleration from the theory.
- The Bohmian law of motion combines a guiding equation for particle configurations with the Schrödinger equation governing the wave-function.The wave-function enters the guiding equation and its Schrödinger evolution.
- Bohmian mechanics is a first-order theory: given the wave-function and particle positions at one time, future and past motion can be calculated.
- Bohmian mechanics is committed only to particles, their positions, and a law describing how those positions develop in time.Particles are the local beables or primitive ontology; Newtonian acceleration and forces are not part of the formulation.
2 What is the ontological status of the wave-function?
The paper argues that the wave-function need not be an additional physical entity: it can function as a mathematical object in the law governing particles, while subsystem wave-functions are derived from the universal state and environment. It then contrasts Humean, dispositionalist, and primitivist ways of understanding that law.
- 2 What is the ontological status of the wave-function?: The universal wave-function is fundamental only for the universe as a whole; subsystem descriptions use effective laws of the same form without having the same fundamental status.
- 2 What is the ontological status of the wave-function?: Effective wave-functions describe subsystems but are derived from the universal wave-function and the actual configuration of particles outside the subsystem.In suitable situations, inserting the environment configuration into the universal wave-function yields an autonomous effective wave-function for the subsystem.
- 2 What is the ontological status of the wave-function?: Treating the wave-function as a physical field is problematic because it would require a field on high-dimensional configuration space rather than ordinary three-dimensional space.
- 2 What is the ontological status of the wave-function?: Bohmian mechanics describes particles with determinate trajectories, while a non-local law accounts for motion through the positions of all particles without requiring a guiding field as physical reality.
- 2 What is the ontological status of the wave-function?: The wave-function can be treated as a mathematical object in the law of motion rather than a physical object existing in addition to particles.On this nomological interpretation, mathematical objects in a law need not correspond to physical objects.
- 2 What is the ontological status of the wave-function?: The paper presents dispositionalism as grounding the law in law-making properties, while primitivism treats the law itself as fundamental.
3 Humeanism about laws
The paper argues that Humeanism can ground Bohmian mechanics in particle positions throughout spacetime, treating the universal wave-function and law of motion as supervenient descriptions. This avoids taking entanglement or the wave-function as additional physical structure, while leaving explanatory objections to Humean laws.
- Humeanism treats laws as descriptive summaries of the distribution of particulars rather than real connections that explain temporal evolution.This view follows from the possibility of varying other property tokens while holding any one token fixed.
- Humeanism can apply to Bohmian mechanics by treating particle positions throughout the universe’s history as fundamental.The universal wave-function and law of motion then supervene on the complete spacetime distribution of those positions.
- The universal wave-function is nomological, whereas effective subsystem wave-functions have no nomological status.Effective wave-functions arise through quantum equilibrium as descriptions of subsystems under conditions of ignorance about exact particle positions.
- Under this ontology, quantum entanglement belongs only to the wave-function and does not require a non-supervenient relation in physical spacetime.The wave-function of the universe supervenes on particle positions across four-dimensional spacetime.
- Bell’s instrumental reading of the wave-function makes its unusual behavior acceptable when the wave-function is not granted beable status.It can function as a mathematical device for formulating correlations between experimental procedures and results.
- A central objection is that Humean laws lack explanatory force because they do not explain why events occur given initial conditions.The paper contrasts this concern with the view that science seeks laws revealing real connections in nature, motivating discussion of dispositionalism.
4 Laws grounded in dispositions
The paper applies dispositionalism to Bohmian mechanics by treating the universal wave-function as a representation of a holistic disposition of motion rather than an additional physical entity. It argues that this approach answers major objections while acknowledging that dispositions need not determine a unique wave-function.
- Dispositionalism and laws: Dispositionalism grounds Bohmian laws in properties understood as dispositions whose manifestations are the particles’ motions.The disposition is a holistic property of all particles in the universe, and the law expresses what they can do in virtue of possessing it.
- The Bohmian disposition: The universal wave-function represents the disposition of motion, with configurations as inputs and particle velocities as outputs of the Bohmian law.Only the universal wave-function has nomological status; effective subsystem wave-functions are derived and do not express fundamental dispositions.
- Physical content: Dispositional histories retain the relevant physical content because Bohmian mechanics treats particle configurations and their common disposition of motion as fundamental.Energy is not primitive in Bohmian mechanics, and different wave-functions associated with different energy eigenvalues need not describe different physical facts for a universe containing only one particle.
- Non-uniqueness: A disposition history need not determine a unique universal wave-function because the wave-function can function as an unambiguous-enough formal representation rather than an additional physical object.Primitive ontology makes it possible to distinguish physical reality and laws from potentially non-unique mathematical representations.
- Time dependence: Dispositionalism need not make particles sensitive to absolute time: identical universal spatial configurations can be assigned the same disposition of motion.This commits the theory to a time-independent universal wave-function, while stationary universal states can still yield evolving effective wave-functions for subsystems.
5 Advantages of dispositionalism
Dispositionalism relocates the explanatory role of Bohmian dynamics into particles and their relations in physical space, avoiding a separate field on configuration space. It thereby supplies causal connections and explanations of temporal evolution, while treating quantum non-locality as a possible fundamental feature rather than something requiring further explanation.
- Ontological advantages: Dispositionalism avoids the configuration-space ontology problem by locating particles and their motion-related disposition in three-dimensional physical space.The universal wave-function represents that disposition over actual and counterfactual configurations rather than functioning as an additional physical field.
- Causal explanation: The disposition of motion gives the Bohmian law a causal interpretation by making the particles themselves the efficient cause of their motion.Its manifestation is a certain particle velocity, rather than motion produced by a force or pilot-wave external to the particles.
- Property ontology: A disposition and its manifested velocity do not create a problematic property dualism, because the manifestation is analytically tied to the disposition.The relevant ontology remains located in physical space and concerns properties of particles rather than particles plus a configuration-space field.
- Connections in nature: Dispositionalism treats the universal disposition as establishing real connections among particles and between configurations at successive times.Given an initial configuration, this disposition can explain the temporal development of the universe’s particle configuration.
- Non-locality: The view accepts that it does not explain why the fundamental disposition is holistic, but argues that quantum non-locality can itself be fundamental.The demand for a further explanation presupposes locality as the natural state of affairs, which Bohmian mechanics need not assume.
6 Conclusion
The paper extends its nomological analysis of Bohmian mechanics to primitive-ontology approaches, defending dispositionalism as a way to ground the law of motion without treating the wave-function as physical reality.
- Bohmian mechanics exemplifies primitive ontology through particles in three-dimensional space and a guiding equation into which the wave-function enters.The broader framework also includes GRW mass density and flash ontologies.
- Dispositionalism grounds the law of motion by including in the ontology something that accounts for the temporal development of primitive-ontology entities.The authors favor this option because it provides real connections in nature.
- In Bohmian mechanics, a disposition can be understood as a holistic property of particles that constitute the primitive ontology.This contrasts with GRW, where localization of mass-density or flashes manifests the disposition.
- The dispositionalist account avoids accepting the configuration-space wave-function as an additional element of physical reality.