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From the measurement problem to the primitive ontology programme

Michaël Esfeld

Published May 28, 2019• 10 citations
OpenAlex

Abstract

The paper retraces the development from the measurement problem to the primitive ontology programme. It assesses the contribution of the GRW theory to this programme and discusses the pros and cons of the GRWm matter density ontology and the GRWf flash ontology in comparison to the Bohmian particle ontology. It thereby pursues the evaluation of the proposals for a primitive ontology of quantum physics.

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Abstract We consider Wigner’s proposal for solving the quantum measurement problem. His solution involves a strong mind-body dualism, but it is also possible to provide a purely physical collapse solution to the quantum measurement problem. To this end, we consider the GRW formulation of quantum mechanics and three ways one might interpret it: GRWr, GRWm, and GRWf. These ways of interpreting the theory differ in the metaphysical commitments one makes and, hence, in how one explains one’s measurement records and hence one’s experience. This provides an introduction to the notions of an empirical ontology and a primitive ontology. We consider some of the comparative virtues and vices of the GRW formulation of quantum mechanics.

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A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focussing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory.11 Introduction2 The GRWm and GRWf Theories 2.1 The GRW process 2.2 GRWm 2.3 GRWf3 Predictions and Primitive Ontology 3.1 Calibration functions 3.2 Taking the PO seriously 3.3 Examples from the literature 3.4 The main theorem about operators in the GRW formalism 3.5 The GRW formalism4 A Set of Examples 4.1 Bohmian mechanics 4.2 Bohmian trajectories and GRW collapses 4.2.1 Bohm’s law and GRW’s law 4.2.2 Bohm’s law and a modified GRW law 4.2.3 Trajectories from the GRW wave function 4.2.4 Configuration jumps and GRW law 4.2.5 Another way of configuration jumps and GRW law 4.3 MBM: Bohm-like trajectories from the master equation 4.3.1 Empirical equivalence of MBM with GRWm and GRWf4.4 Master equation and matter density4.5 Master equation and flashes5 Conclusions

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This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.

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Spontaneous collapse theories provide a promising solution to the measurement problem. But they also introduce a number of problems of their own concerning dimensionality, vagueness, and locality. In response to these problems, advocates of collapse theories have proposed various accounts of the primitive ontology of collapse theories—postulated underlying entities governed by the collapse theory and underwriting our observations. The most prominent of these are a mass density distribution over three-dimensional space, and a set of discrete “flash” events at space-time points. My argument here is that these primitive ontologies are redundant, in the sense that the structures exhibited by the primitive ontologies that allow them to solve the problems facing spontaneous collapse theories are also present in the wave function. But redundancy is not nonexistence; indeed, the fact that the relevant structures are already there in the wave function shows that the mass density ontology and the flash ontology exist whether they are explicitly postulated or not. By the same token, there is no need to decide between a wave function ontology, a mass density ontology and a flash ontology.

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The paper retraces the development from the measurement problem to the primitive ontology programme. It assesses the contribution of the GRW theory to this programme and discusses the pros and cons of the GRWm matter density ontology and the GRWf flash ontology in comparison to the Bohmian particle ontology. It thereby pursues the evaluation of the proposals for a primitive ontology of quantum physics.
Abstract We consider Wigner’s proposal for solving the quantum measurement problem. His solution involves a strong mind-body dualism, but it is also possible to provide a purely physical collapse solution to the quantum measurement problem. To this end, we consider the GRW formulation of quantum mechanics and three ways one might interpret it: GRWr, GRWm, and GRWf. These ways of interpreting the theory differ in the metaphysical commitments one makes and, hence, in how one explains one’s measurement records and hence one’s experience. This provides an introduction to the notions of an empirical ontology and a primitive ontology. We consider some of the comparative virtues and vices of the GRW formulation of quantum mechanics.
A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focussing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory.11 Introduction2 The GRWm and GRWf Theories 2.1 The GRW process 2.2 GRWm 2.3 GRWf3 Predictions and Primitive Ontology 3.1 Calibration functions 3.2 Taking the PO seriously 3.3 Examples from the literature 3.4 The main theorem about operators in the GRW formalism 3.5 The GRW formalism4 A Set of Examples 4.1 Bohmian mechanics 4.2 Bohmian trajectories and GRW collapses 4.2.1 Bohm’s law and GRW’s law 4.2.2 Bohm’s law and a modified GRW law 4.2.3 Trajectories from the GRW wave function 4.2.4 Configuration jumps and GRW law 4.2.5 Another way of configuration jumps and GRW law 4.3 MBM: Bohm-like trajectories from the master equation 4.3.1 Empirical equivalence of MBM with GRWm and GRWf4.4 Master equation and matter density4.5 Master equation and flashes5 Conclusions
This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.
Spontaneous collapse theories provide a promising solution to the measurement problem. But they also introduce a number of problems of their own concerning dimensionality, vagueness, and locality. In response to these problems, advocates of collapse theories have proposed various accounts of the primitive ontology of collapse theories—postulated underlying entities governed by the collapse theory and underwriting our observations. The most prominent of these are a mass density distribution over three-dimensional space, and a set of discrete “flash” events at space-time points. My argument here is that these primitive ontologies are redundant, in the sense that the structures exhibited by the primitive ontologies that allow them to solve the problems facing spontaneous collapse theories are also present in the wave function. But redundancy is not nonexistence; indeed, the fact that the relevant structures are already there in the wave function shows that the mass density ontology and the flash ontology exist whether they are explicitly postulated or not. By the same token, there is no need to decide between a wave function ontology, a mass density ontology and a flash ontology.
Abstract This chapter introduces the ‘primitive ontology’ approaches to the measurement problem, including spontaneous collapse models and the de Brolige-Bohm approach. I consider some possible epistemic problems that could arise in a primitive ontology approach, but ultimately conclude that primitive ontology approaches do appear to solve the epistemic version of the measurement problem. However, I note that there are good reasons to think the existing primitive ontology approaches cannot be extended to quantum field theory, thus motivating a search for alternatives beyond the primitive ontology paradigm. I also discuss the role of autonomy of scales in physics.