Quantum Mechanics on Spacetime I: Spacetime State Realism

Wallace, David; Timpson, Christopher G.

doi:10.1093/bjps/axq010

Cited by 149 publications

(80 citation statements)

References 23 publications

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“…Since QFT is probably best understood as describing the assignment of fundamental quantities to regions of spacetime (Wallace and Timpson, 2010), it is plausible that the best candidates for the "individuals" posited by the theory are spacetime points, or spacetime regions. For this reason it seems to me that spacetime theories, and not basic quantum mechanics, should be the locus of philosophical debate about the nature of identity and individuality in modern physics.…”

Section: Discussionmentioning

confidence: 99%

Identity, Superselection Theory, and the Statistical Properties of Quantum Fields

Baker¹

2013

Philos. of Sci.

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The permutation symmetry of quantum mechanics is widely thought to imply a sort of metaphysical underdetermination about the identity of particles. Despite claims to the contrary, this implication does not hold in the more fundamental quantum field theory, where an ontology of particles is not generally available. Although permutations are often defined as acting on particles, a more general account of permutation symmetry can be formulated using superselection theory. As a result, permutation symmetry applies even in field theories with no particle interpretation. The quantum mechanical account of permutations acting on particles is recovered as a special case.

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Section: Discussionmentioning

confidence: 99%

Identity, Superselection Theory, and the Statistical Properties of Quantum Fields

Baker¹

2013

Philos. of Sci.

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“…More recently, Wallace and Timpson (2010) have advanced an ontology for QFT that fits under the heading of broad field interpretations. On their view, spacetime state realism, there is a fundamental quantity assigned to each region of spacetime, represented by the local state of that region.…”

Section: Field Interpretationsmentioning

confidence: 99%

“…So the real physical content of the theory is given by equivalence classes of the Heisenberg observables under these transformations. And these equivalence classes are isomorphic to the local states described in Wallace and Timpson (2010)-making Heisenberg operator realism a mere notational variant of spacetime state realism. Arntzenius (2012, 116-120) criticizes this argument on the grounds that Wallace and Timpson's transformations do not deserve to be called symmetries, because they fail to leave the theory's dynamical laws unchanged.…”

Section: Field Interpretationsmentioning

confidence: 99%

The Philosophy of Quantum Field Theory

Baker

2016

Oxford Handbooks Online

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If we divide our physical theories (somewhat artificially) into theories of matter and theories of spacetime, quantum field theory (QFT) is our most fundamental empirically successful theory of matter. As such, it has attracted increasing attention from philosophers over the past two decades, beginning to eclipse its predecessor theory of quantum mechanics (QM) in the philosophical literature. Here I survey some central philosophical puzzles about the theory's foundations. Inequivalent representationsPerhaps the deepest new conceptual problem prompted by QFT, and certainly the one most thoroughly explored by philosophers, is the problem of inequivalent representations.1 From ordinary QM we are familiar with the use of an algebra of operators to stand for the canonical observable quantities (position and momentum, or their field-theoretic equivalents 2 ). The minimal operator algebra for these canonical observables, called the algebra of observables A, can be represented by operators on a Hilbert space H. This is done by assigning an operator π(A) from the bounded operators on H to every operator A ∈ A. The mapping π is called a Hilbert space representation of A. Given plausible assumptions, there is a unique 1 To my knowledge, Huggett and Weingard (1996) were the first to discuss this problem in a published article, although Arageorgis (1995) had already explored it in some depth in his seminal dissertation.2 In bosonic field theories, the canonical observables are the field operators φ(x) and their conjugate momenta π(x), while in fermionic theories only even polynomials of the fields and their momenta are observables.

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“…Timpson emphasised that the model's primary feature is not dynamical locality, but rather separability, which allows composite states to be reduced to their subsystems [13,14]. Here, we re-cast the model of Deutsch and Hayden in the framework of ontological models, which does not assume the many-worlds interpretation and is therefore vulnerable to Bell's theorem.…”

Section: Introductionmentioning

confidence: 99%

A Separable, Dynamically Local Ontological Model of Quantum Mechanics

Pienaar

2015

Found Phys

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A model of reality is called separable if the state of a composite system is equal to the union of the states of its parts, located in different regions of space. Spekkens has argued that it is trivial to reproduce the predictions of quantum mechanics using a separable ontological model, provided one allows for arbitrary violations of 'dynamical locality'. However, since dynamical locality is strictly weaker than local causality, this leaves open the question of whether an ontological model for quantum mechanics can be both separable and dynamically local. We answer this question in the affirmative, using an ontological model based on previous work by Deutsch and Hayden. Although the original formulation of the model avoids Bell's theorem by denying that measurements result in single, definite outcomes, we show that the model can alternatively be cast in the framework of ontological models, where Bell's theorem does apply. We find that the resulting model violates local causality, but satisfies both separability and dynamical locality, making it a candidate for the 'most local' ontological model of quantum mechanics. INTRODUCTION"We are all made of algebra-stuff: the elements of local reality are faithfully described not by real variables or stochastic real variables but by the elements of a certain algebra that can be represented by Hermitian matrices. [...] A failure to understand this can result in various misconceptions about quantum physics in general, and about its locality in particular. "Can we explain quantum phenomena in terms of an underlying model of reality? Traditionally, such explanations took the form of hidden variable models. Bell's theorem places a severe constraint on these models, demonstrating that (given certain reasonable assumptions) no hidden variable model can reproduce the predictions of quantum mechanics and at the same time satisfy local causality [2,3]. Since Bell's work, hidden variable models have been generalised and extended to the framework of ontological models, introduced by Harrigan & Spekkens [4,5]. While the framework is not general enough to capture all possible interpretations of quantum mechanics, it is sufficiently general to permit a clear exposition of the various definitions of locality that are central to understanding the implications of Bell's theorem.We will focus on ontological models set in relativistic space-time, in which one can ascribe a real, physical state, called the ontic state, to the physical systems located in any spatial region at one time (more generally, on a space-like hyper-surface). Given a foliation of spacetime into a family of time-slices (or hyper-surfaces), the ontic state evolves with respect to the global time parameter according to some dynamical laws. Measurements performed in a region of space-time produce outcomes with probabilities that depend only on the ontic state in the region where the measurement is performed. We do not make any assumptions about the kinematics and evolution of the ontic states, other than that they reproduc...

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Quantum Mechanics on Spacetime I: Spacetime State Realism

Cited by 149 publications

References 23 publications

Identity, Superselection Theory, and the Statistical Properties of Quantum Fields

Identity, Superselection Theory, and the Statistical Properties of Quantum Fields

The Philosophy of Quantum Field Theory

A Separable, Dynamically Local Ontological Model of Quantum Mechanics

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