I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, that is, the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality.My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand.Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime. 1. Introduction2. Formulating Stochastic Einstein Locality2.1. Events and regions2.2. The idea of SEL2.3. Three formulations of SEL2.3.1. The formulations2.3.2. Comparisons2.4. Implications between the formulations2.4.1. Conditions for the equivalence of SELD1 and SELD22.4.2. Conditions for the equivalence of SELS and SELD23. Relativistic Causality in the Bell Experiment3.1. The background3.1.1. The Bell experiment reviewed3.1.2. My previous position3.2. A common common cause? The Budapest school3.2.1. Resuscitating the PCC3.2.2. Known proofs of a Bell inequality need a strong PCC3.2.3. Two distinctions3.2.4. Szabó's model3.2.5. A common common cause is plausible3.2.6. Bell inequalities from a weak PCC: the Bern school3.3. SEL in the Bell experiment3.3.1. PCC and SEL are connected by PPSI3.3.2. The need for other judgments3.3.3. Weak vs. strong SELD4. SEL in Algebraic Quantum Field Theory4.1. The story so far4.2. Questions4.2.1. Our formulations4.2.2. The Budapest and Bern schools5. SEL in Dynamical Spacetimes5.1. SEL for metric structure?5.2. SEL for causal sets?5.2.1. The causal set approach5.2.2. Labelled causal sets; general covariance5.2.3. Deducing the dynamics5.2.4. The fate of SEL
I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, that is, the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality.My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand.Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime. 1. Introduction2. Formulating Stochastic Einstein Locality2.1. Events and regions2.2. The idea of SEL2.3. Three formulations of SEL2.3.1. The formulations2.3.2. Comparisons2.4. Implications between the formulations2.4.1. Conditions for the equivalence of SELD1 and SELD22.4.2. Conditions for the equivalence of SELS and SELD23. Relativistic Causality in the Bell Experiment3.1. The background3.1.1. The Bell experiment reviewed3.1.2. My previous position3.2. A common common cause? The Budapest school3.2.1. Resuscitating the PCC3.2.2. Known proofs of a Bell inequality need a strong PCC3.2.3. Two distinctions3.2.4. Szabó's model3.2.5. A common common cause is plausible3.2.6. Bell inequalities from a weak PCC: the Bern school3.3. SEL in the Bell experiment3.3.1. PCC and SEL are connected by PPSI3.3.2. The need for other judgments3.3.3. Weak vs. strong SELD4. SEL in Algebraic Quantum Field Theory4.1. The story so far4.2. Questions4.2.1. Our formulations4.2.2. The Budapest and Bern schools5. SEL in Dynamical Spacetimes5.1. SEL for metric structure?5.2. SEL for causal sets?5.2.1. The causal set approach5.2.2. Labelled causal sets; general covariance5.2.3. Deducing the dynamics5.2.4. The fate of SEL
Bell's Theorem demonstrates that factorizable theories for the EPR experiment (EPR) cannot reproduce the quantum correlations. Factorizability is motivated by various locality conditions. So to understand the nature of nonlocality in EPR, we first need to understand the conceptual relations between factorizability, these various locality conditions and the nature of the quantum correlations. That is the main focus of my thesis. My main conclusion is that these conceptual relations are more subtle than the literature has usually suggested. Chapter 1 is a general introduction. In Chapter 2, I review the general framework of factorizable stochastic theories for EPR. I argue that factorizability can be motivated by various locality conditions, even in theories that admit time-dependent states and take the measurement interactions to be neither instantaneous, nor simultaneous. In Chapter 3, I focus on Cartwright' s (1989) and Humphreys' (1989) theories of probabilistic causation for singular events, which are based on modifications of traditional causal linear modelling. I argue (against Cartwright) that local models for EPR in the framework of these theories are committed to factorizability; and so they cannot reproduce the EPR correlations. In Chapter 4, I turn to Stochastic-Einstein Locality (SEL). Hellman (1982) proposed that SEL with some provisos characterizes the No-Superluminal-Action (NSA) of the Special Theory of Relativity (STR), and he argued that SEL is not violated in EPR. Butterfield (1994) proposed that SEL (without Hellman's provisos) characterizes the lack of superluminal Lewisian causation, and he argued that SEL is violated in EPR. I argue that SEL (without Hellman's provisos) is motivated by NSA and spatiotemporal separability. Thus, the violation of SEL might arise from the failure of spatiotemporal separability. And this failure is compatible with NSA and superluminal Lewisian causation. Accordingly, Hellman's and Butterfield's views need not be in tension. In Chapter 5, I focus on the implications for nonlocality of Jarrett's (1984) analysis of factorizability into "locality" and "completeness". I argue that although this analysis cannot distinguish between failures of factorizability which are compatible with STR and those which are not, it is significant for clarifying the implications of Bell's theorem for nonlocality. In Chapter 6, I qmsider three arguments that are intended to deny superluminal causal propagation in EPR, and a fourth argument that is intended to establish the opposite conclusion. I argue that in various ways these arguments have gone wrong. Three of these argument rely on implicit assumptions that have been overlooked. Accordingly, two of them reached a reasonable conclusion, i.e. the failure of separability, for the wrong reasons; whereas the third reached a wrong conclusion, i.e. that the failure of the contiguity of causal processes explains the failure of factorizability in EPR. The fourth relies on a wrong assumption, and thus it reaches a too strong conclusion, that the EPR correlations require superluminal action. My main conclusion is that the quantum correlations require nonseparability . In Chapter 7, I focus on decision theory in the context of EPR. In both EPR and the famous Newcomb's problem (NewProb), there are unscreenable-off correlations. I argue that NewProb can be related to EPR, in the sense that a NewProb can be realized by that experiment.
Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a–c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.
This paper is the philosopher-friendly version of our more technical work (Hofer-Szabó and Vecsernyés, 2014). It aims to give a clear-cut definition of Bell's notion of local causality. Having provided a framework, called local physical theory, which integrates probabilistic and spatiotemporal concepts, we formulate the notion of local causality and relate it to other locality and causality concepts. Then we compare Bell's local causality with Reichenbach's Common Cause Principle and relate both to the Bell inequalities. We find a nice parallelism: both local causality and the Common Cause Principle are more general notions than captured by the Bell inequalities. Namely, Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.
Introduction Fifty years after the publication of Bell's theorem, there remains some controversy regarding what the theorem is telling us about quantum mechanics, and what the experimental violations of Bell inequalities are telling us about the world. This chapter represents my best attempt to be clear about what I think the lessons are. In brief: There is some sort of nonlocality inherent in any quantum theory, and, moreover, in any theory that reproduces, even approximately, the quantum probabilities for the outcomes of experiments. But not all forms of nonlocality are the same; there is a distinction to be made between action at a distance and other forms of nonlocality, and I will argue that the nonlocality needed to violate the Bell inequalities need not involve action at a distance. Furthermore, the distinction between forms of nonlocality makes a difference when it comes to compatibility with relativistic causal structure. The Bell locality condition is a condition which, if satisfied, renders possible a completely local account of the correlations between outcomes of spatially separated experiments. Bell's theorem tells us that the probabilities that we compute from quantum mechanics do not admit of such an account. Modulo auxiliary assumptions that, in my opinion, should be noncontroversial, this yields the conclusion that there must be something nonlocal about any theory that yields the quantum mechanical probabilities or anything close to them. One way to violate the Bell locality condition – and this is the way that any deterministic theory must do it – is via straightforward action at a distance. However, we should also consider the possibility of a stochastic theorywith probabilistic laws that involve irreducible correlations. The sort of nonlocality inherent in such a theory involves relations between events that are significantly different from causal relations as usually conceived. Perhaps surprisingly, such a theory, unlike its deterministic cousins, need not invoke a distinguished relation of distant simultaneity. This makes a difference for the situation of the two sorts of theories vis-a-vis relativity. Though a deterministic theory can achieve the appearance of being relativistic, at the level of observable phenomena, it can do so only by introducing a preferred foliation and with it a causal structure at odds with relativistic causal structures. Things are otherwise with dynamical collapse theories.
The paper extends the framework of outcomes in branching space-time (Kowalski and Placek [1999]) by assigning probabilities to outcomes of events, where these probabilities are interpreted either epistemically or as weighted possibilities. In resulting models I define the notion of common cause of correlated outcomes of a single event, and investigate which setups allow for the introduction of common causes. It turns out that a deterministic common cause can always be introduced, but (surprisingly) only special setups permit the introduction of truly stochastic common causes. I analyse next the Bell-Aspect experiment and derive the Bell-CH inequalities. I observe that we postulate there not a common cause for outcomes of a single event but rather a common common cause that accounts for outcomes of many events, where 'events' mean 'measurements with (different) directions of polarization'. Since the inequalities are violated, I claim that no causal story can be told about the Bell correlations, where causality is subliminal and restricted by screening-off condition. Similarly, given certain intuitive principles, no deterministic story can be told about these correlations.
The aim of this paper is to implement Bell’s notion of local causality into a framework, called local physical theory. This framework, based on the axioms of algebraic field theory, is broad enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will arise as the classical case of our definition. Classifying local physical theories by whether they obey local primitive causality, a property rendering the dynamics of the theory causal, we then investigate what is needed for a local physical theory to be locally causal. Finally, comparing local causality with the common cause principles and relating both to the Bell inequalities we find a nice parallelism: Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.