Causarum Investigatio and the Two Bell’s Theorems of John Bell

Wiseman, Howard M.; Cavalcanti, Eric G.

doi:10.1007/978-3-319-38987-5_6

Cited by 56 publications

(139 citation statements)

References 69 publications

(196 reference statements)

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“…Formally, it says that any correlation between two spacelike separated events E 1 and E 2 can only arise from each of them being correlated with events λ in their shared past light cone. Once we take into account those shared influences the joint probability distribution of E 1 and E 2 factorizes [3,5,10]:…”

Section: Strong Localitymentioning

confidence: 99%

Ghostly action at a distance: A non-technical explanation of the Bell inequality

Alford

2016

American Journal of Physics

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We give a simple non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality, also known as local causality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.

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Section: Strong Localitymentioning

confidence: 99%

Ghostly action at a distance: A non-technical explanation of the Bell inequality

Alford

2016

American Journal of Physics

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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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“…2 See Brown and Timpson (2014) and Wiseman and Cavalcanti (2015) for a discussion on the relationship between the deterministic background assumptions of Einstein et al (1935), Bell (1964 and this later work of Bell's. §2.2 The Bell experiments.…”

Section: The Bell Experimentsmentioning

confidence: 99%

“…Bell suggests such beables should satisfy a number of desiderata, but most importantly beables should correspond to something "physical", in order to distinguish variables that can be associated with "real physical" values from those that pertain to abstracta. For Bell, the latter ought to be excluded tout court from any causal considerations.[p57]As an example:2 See Brown and Timpson (2014) and Wiseman and Cavalcanti (2015) for a discussion on the relationship between the deterministic background assumptions of Einstein et al (1935), Bell (1964 and this later work of Bell's. §2.2 The Bell experiments.…”

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confidence: 99%

Using interventions to discover quantum causal structure

Shrapnel¹

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Identifying causal relations plays an indispensable role in science, economics, medicine and everyday life. Interventionist causation associates the discovery of such relations with the possibility of manipulation or intervention. A causes B, if manipulating A in the right way can bring about changes in B. The main technical tool, the causal model, can be seen as a device for telling us how and why certain actions are more effective than others. Such models have found application in almost every scientific discipline.However, despite several decades of sophisticated analysis and a wealth of technical results, interventionist causal methods are known to fail in the quantum case. The quantum domain, with its peculiar, counterintuitive features, is widely considered an inhospitable environment in which to apply our usual causal discovery tools.This causal skepticism presents us with a puzzle. Physicists are now able to manipulate and control quantum systems, and the design and construction of quantum technology relies on an ability to identify when one strategy will work and another will fail. From the perspective of interventionist causation, it seems that a formal account of quantum causal modelling ought to be possible.The main contribution of this thesis is to provide an extension of interventionist methodology to the quantum case. In Chapter 1, I introduce interventionist causation from the perspective of two giants of the field: Judea Pearl and James Woodward. The Causal Markov Condition (CMC) and Faithfulness assumptions are presented, and I draw particular attention to the discovery of casual structure. I touch on some of the well-known problems with interventionist causation per se.In Chapter 2, I put this methodology to work in a quantum mechanical context. Following tradition, we examine one of the Bell experiments in order to determine how the classical interventionist framework fails. Noting that the usual response is to demand that one drops either the CMC or Faithfulness, I suggest that neither approach is particularly satisfactory and argue for an alternative. I discuss some reasons why the interventionist is forced to pursue this different path.In Chapter 3, I motivate the possibility of an interventionist account of quantum causation. I first look at how physicists represent quantum technology in order to make interventionist and counterfactual inferences: via the use of quantum circuit diagrams. Using three examples I demonstrate the manner in which these diagrams can be used to facilitate causal inference.In Chapter 4, I examine some recent attempts at characterising quantum causal models due to work from the quantum foundations community. I present three such accounts and explain why I endorse a fourth, the focus of the next chapter.iii In Chapter 5, I present a new framework that allows for the discovery of interventionist quantum causal structure. I finish the thesis with a summary and some suggestions for further work.iv Declaration by authorThis thesis is composed of my original wor...

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Causarum Investigatio and the Two Bell’s Theorems of John Bell

Cited by 56 publications

References 69 publications

Ghostly action at a distance: A non-technical explanation of the Bell inequality

Ghostly action at a distance: A non-technical explanation of the Bell inequality

A Separable, Dynamically Local Ontological Model of Quantum Mechanics

Using interventions to discover quantum causal structure

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