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In search of local beables

Peter J. Lewis

Published Sep 14, 2015• 1 citation
OpenAlex

Abstract

The call to supplement the quantum wave function with local beables is almost as old as quantum mechanics. But what exactly is the problem with the wave function as the representation of a quantum system? I canvass three potential problems with the wave function: the well-known problems of incompleteness and dimensionality, and the lesser known problem of non-locality introduced recently by Myrvold. Building on Myrvold's insight, I show that the standard ways of introducing local beables into quantum mechanics are unsuccessful. I consider whether we really need local beables, and assess the prospects for a new theory of local beables.

Related papers

Local Beables and the Foundations of Physics

Tim Maudlin

Introduction: The Theory of Local Beables John Bell's most celebrated contribution to the foundations of physics is his famous theorem. The theorem demonstrates that any physical theory capable of generating the predictions of the standard quantum-mechanical algorithm, in particular the prediction of violations of Bell's inequality for experiments done at spacelike separation, cannot be local. The sense of “locality” used here is the same sense that Einstein had in mind when he pointed out that the standard interpretation of the quantum algorithm was committed to “spooky action at a distance” To this day, the import of Bell's theorem is not universally appreciated. I have written about this elsewhere [1], and others in this volume will take up that task. It is properly the main focus during this 50th anniversary of that great achievement. But it is also important to recall and celebrate Bell's other achievements. In many of his later writings, including “The Theory of Local Beables,” “Quantum Mechanics for Cosmologists,” “On the Impossible Pilot Wave,” “Beables for Quantum Field Theory,” “Six Possible Worlds of Quantum Mechanics,” “Are There Quantum Jumps?” and “Against ‘Measurement,”’ 1 Bell turned his attention to the more general problem of physically construing the mathematical formalism used to derive these predictions. This activity is often denominated “interpreting quantum theory” as if there were some precise physical theory that might somehow be supplemented with an “interpretation” Once the issue is framed this way it is easy to ask: But if I already have a theory in hand, what can be gained by supplementing it with an “interpretation”? Many physicists, at this juncture, are happy to conclude that “interpretations” are not a matter of physics at all – maybe they are only of interest to philosophers – and that therefore the whole enterprise of “interpreting quantum theory” is not within the purview of physics per se. What then is in the purviewof physics proper?One answer to this question goes under the banner “instrumentalism”: all physics as such, is concerned about is predicting the outcomes of experiments .

Cambridge University Press eBooks•Aug 31, 2016•11 citations

Further on Pilot-Wave Theories

Elemér Elad Rosinger

In [2], a detailed argument is presented on a version of pilot-waves, given by at Theory of Exclusively Local Beables. What the author of [2] considers to be his crucial proposal is described in the title of section 3 as 'complicated, ugly, and highly contrived'. The reason for such a proposal is claimed to be the widespread perception among quantum physicists, according to which 'those sympathetic to the pilot-wave ontology no doubt expected that, for a system of N particles moving in three spatial dimensions, the theoretical description would be of N wave-particle pairs - each pair consisting of a point particle guided in some way by an associated wave propagating in 3-space. But Schroedinger's wave function for such an N-particle system was emphatically not a set of N (interacting) waves, each propagating in 3-space. It was, rather, a single wave propagating in the 3N-dimensional configuration space for the system', [2, p. 5]. In the present paper it is argued that the mentioned widespread expectation need not be seen as being betrayed by what actually happens. In particular, the construction in section 3 of [2] may be avoidable.

arXiv:0910.0344•Oct 2, 2009•0 citations

Must an Ontology for Quantum Theories Contain Local Beables?

Alyssa Ney

Abstract This chapter considers and responds to the objection that a wave function in a high-dimensional space cannot ultimately constitute the low-dimensional macroscopic objects of experience. It discusses two forms this objection takes: one based on the putative fact that our evidence for quantum theories consists of low-dimensional objects, and another based on the putative fact that quantum theories are about low-dimensional objects, that they have primitive ontologies of local beables. Even admitting that there may be something straightforward and comprehensible about the fundamental ontologies for quantum theories proposed by the wave function realist, the philosophers who raise these objections see a problem with these ontologies in that they cannot serve as the constitutive foundation for the world as we experience it. And this undermines the promise of wave function realism to serve as a framework for the interpretation of quantum theories.

•May 19, 2021•1 citation

Non-local beables

Lee Smolin

I discuss the idea that the beables underlying quantum physics are non-local and relational, and give an example of a dynamical theory of such beables based on a matrix model, which is the bosonic sector of the BFSS model. Given that the same model has been proposed as a description of M theory, this shows that quantum mechanics may be emergent from a theory of gravity from which space is also emergent.

arXiv:1507.08576•Jul 30, 2015•3 citations

The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics

Shan Gao

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).

arXiv:1611.02738•Nov 7, 2016•31 citations

A local-realistic model for quantum theory

Paul Raymond-Robichaud

We provide a rigorous definition of local realism. We show that the universal wave function cannot be a complete description of a local reality. Finally, we construct a local-realistic model for quantum theory.

arXiv:2010.14303•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jun 1, 2021•18 citations
The call to supplement the quantum wave function with local beables is almost as old as quantum mechanics. But what exactly is the problem with the wave function as the representation of a quantum system? I canvass three potential problems with the wave function: the well-known problems of incompleteness and dimensionality, and the lesser known problem of non-locality introduced recently by Myrvold. Building on Myrvold's insight, I show that the standard ways of introducing local beables into quantum mechanics are unsuccessful. I consider whether we really need local beables, and assess the prospects for a new theory of local beables.
Introduction: The Theory of Local Beables John Bell's most celebrated contribution to the foundations of physics is his famous theorem. The theorem demonstrates that any physical theory capable of generating the predictions of the standard quantum-mechanical algorithm, in particular the prediction of violations of Bell's inequality for experiments done at spacelike separation, cannot be local. The sense of “locality” used here is the same sense that Einstein had in mind when he pointed out that the standard interpretation of the quantum algorithm was committed to “spooky action at a distance” To this day, the import of Bell's theorem is not universally appreciated. I have written about this elsewhere [1], and others in this volume will take up that task. It is properly the main focus during this 50th anniversary of that great achievement. But it is also important to recall and celebrate Bell's other achievements. In many of his later writings, including “The Theory of Local Beables,” “Quantum Mechanics for Cosmologists,” “On the Impossible Pilot Wave,” “Beables for Quantum Field Theory,” “Six Possible Worlds of Quantum Mechanics,” “Are There Quantum Jumps?” and “Against ‘Measurement,”’ 1 Bell turned his attention to the more general problem of physically construing the mathematical formalism used to derive these predictions. This activity is often denominated “interpreting quantum theory” as if there were some precise physical theory that might somehow be supplemented with an “interpretation” Once the issue is framed this way it is easy to ask: But if I already have a theory in hand, what can be gained by supplementing it with an “interpretation”? Many physicists, at this juncture, are happy to conclude that “interpretations” are not a matter of physics at all – maybe they are only of interest to philosophers – and that therefore the whole enterprise of “interpreting quantum theory” is not within the purview of physics per se. What then is in the purviewof physics proper?One answer to this question goes under the banner “instrumentalism”: all physics as such, is concerned about is predicting the outcomes of experiments .
In [2], a detailed argument is presented on a version of pilot-waves, given by at Theory of Exclusively Local Beables. What the author of [2] considers to be his crucial proposal is described in the title of section 3 as 'complicated, ugly, and highly contrived'. The reason for such a proposal is claimed to be the widespread perception among quantum physicists, according to which 'those sympathetic to the pilot-wave ontology no doubt expected that, for a system of N particles moving in three spatial dimensions, the theoretical description would be of N wave-particle pairs - each pair consisting of a point particle guided in some way by an associated wave propagating in 3-space. But Schroedinger's wave function for such an N-particle system was emphatically not a set of N (interacting) waves, each propagating in 3-space. It was, rather, a single wave propagating in the 3N-dimensional configuration space for the system', [2, p. 5]. In the present paper it is argued that the mentioned widespread expectation need not be seen as being betrayed by what actually happens. In particular, the construction in section 3 of [2] may be avoidable.
Abstract This chapter considers and responds to the objection that a wave function in a high-dimensional space cannot ultimately constitute the low-dimensional macroscopic objects of experience. It discusses two forms this objection takes: one based on the putative fact that our evidence for quantum theories consists of low-dimensional objects, and another based on the putative fact that quantum theories are about low-dimensional objects, that they have primitive ontologies of local beables. Even admitting that there may be something straightforward and comprehensible about the fundamental ontologies for quantum theories proposed by the wave function realist, the philosophers who raise these objections see a problem with these ontologies in that they cannot serve as the constitutive foundation for the world as we experience it. And this undermines the promise of wave function realism to serve as a framework for the interpretation of quantum theories.
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).