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arXiv:1507.08576

Non-local beables

Lee Smolin

Published Jul 30, 2015• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1507.08576

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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.
A simple dynamical model over a discrete classical state space is presented. In a certain limit, it reduces to one in a class of models subsuming Bell's field-theoretic version of Bohmian mechanics. But it exhibits the massive parallelism native to quantum mechanics only as an emergent phenomenon, in contrast with Bell's and other hidden variable theories. While still non-local in its dynamics, the model thus restores our ability to regard a system as a combination of separate, localized parts, at the price of admitting non-Markovian dynamics.
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.
I review the hypothesis that neither space nor quantum mechanics is fundamental, and both are emergent from a more fundamental description that is neither. This fundamental description is a completion of quantum mechanics based on relational hidden variables. Here, relational means that they give a fuller description, not of an individual particle but of a network of relations among particles. This completion of quantum mechanics does not live in space, rather space is an emergent description of an underlying network of relations. Since locality is, in this sense, emergent, locality can be disordered, and one of the effects of this is quantum nonlocality. This summarizes a line of thought that weaves through many of my papers on quantum foundations, from the early 1980s to the present.
When discussing quantum ontology, the debate has recently focused on comparing and contrasting wavefunction realism and its rivals. Among them one finds the primitive ontology approach, which is often conflated with the local beables program. In this paper I wish to clarify what I take to be the distinction between the notion of primitive ontology and the one of local beable. I argue that the primitive ontology is the local beable which allows for a dynamical, constructive explanation which preserves symmetries.
Recently 't Hooft demonstrated that ‘ For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization’ . An extension is presented here which covers quantum systems that are characterized by a complete set of mutually commuting Hermitian operators ( beables ). We introduce the symmetry of beables: any complete set of beables is as good as any other one which is obtained through a real general linear group transformation. The quantum numbers of a specific set are related to symmetry breaking initial and boundary conditions in a deterministic model. The Hamiltonian, in particular, can be taken as the emergent beable which provides the best resolution of the evolution of the model universe.
An apparently emerging consensus holds that Everettian Quantum Mechanics (EQM), in the Spacetime State Realism (SSR) version of Wallace and Timpson, involves ontological non-locality (i.e., non-separability) but is fully compatible with the dynamical notion of locality usually taken to be required by relativity. The claim of dynamical locality is based on the fact that the local beables postulated by the theory (namely, Reduced Density Matrices, RDMs, associated with localized regions) are not affected by interventions outside their past light cones. However, the theory's non-separability means that it posits non-local beables (namely RDMs for non-localized regions) in addition to the local ones. We argue here that the involvement of non-local beables introduces complications for extant formulations of dynamical locality and at least suggests, contrary to the emerging consensus, that SSR EQM should perhaps not be considered compatible with relativistic causality after all.