In papers published in the 25 years following his famous 1964 proof, John Bell refined and reformulated his views on locality and causality. Although his formulations of local causality were in terms of probability, he had little to say about that notion. But assumptions about probability are implicit in his arguments and conclusions. Probability does not conform to these assumptions when quantum mechanics is applied to account for the particular correlations Bell argues are locally inexplicable. This account involves no superluminal action and there is even a sense in which it is local, but it is in tension with the requirement that the direct causes and effects of events be nearby. Introduction I never met John Bell, but his writings have supplied me with a continual source of new insights as I read and reread them over 40 years. As I worked toward a rather different understanding of quantum mechanics he was foremost in my mind as a severe but honest critic of such attempts. We all would love to know what Einstein would have made of Bell's theorem. I confess that the deep regret I feel that Bell cannot respond to this paper is sometimes assuaged by a sense of relief. Locality and Local Causality In his seminal 1964 paper [1], John Bell expressed locality as the requirement that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past. [2, p. 14] This seems to require that the result of a measurement would have been the same, no matter what operations had been performed on such a distant system. But suppose the result of a measurement were the outcome of an indeterministic process. Then the result of the measurement might have been different even if exactly the same operations (if any) had been performed on that distant system. So can no indeterministic theory satisfy the locality requirement? Bell felt no need to address that awkward question in his 1964 paper [1], since he took the EPR argument to establish that any additional variables needed to restore locality and causalitywould have to determine a unique result of ameasurement.
In papers published in the 25 years following his famous 1964 proof, John Bell refined and reformulated his views on locality and causality. Although his formulations of local causality were in terms of probability, he had little to say about that notion. But assumptions about probability are implicit in his arguments and conclusions. Probability does not conform to these assumptions when quantum mechanics is applied to account for the particular correlations Bell argues are locally inexplicable. This account involves no superluminal action and there is even a sense in which it is local, but it is in tension with the requirement that the direct causes and effects of events be nearby. Introduction I never met John Bell, but his writings have supplied me with a continual source of new insights as I read and reread them over 40 years. As I worked toward a rather different understanding of quantum mechanics he was foremost in my mind as a severe but honest critic of such attempts. We all would love to know what Einstein would have made of Bell's theorem. I confess that the deep regret I feel that Bell cannot respond to this paper is sometimes assuaged by a sense of relief. Locality and Local Causality In his seminal 1964 paper [1], John Bell expressed locality as the requirement that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past. [2, p. 14] This seems to require that the result of a measurement would have been the same, no matter what operations had been performed on such a distant system. But suppose the result of a measurement were the outcome of an indeterministic process. Then the result of the measurement might have been different even if exactly the same operations (if any) had been performed on that distant system. So can no indeterministic theory satisfy the locality requirement? Bell felt no need to address that awkward question in his 1964 paper [1], since he took the EPR argument to establish that any additional variables needed to restore locality and causalitywould have to determine a unique result of ameasurement.
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.
John Stewart Bell’s famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell’s discovery, its meaning and implications remain controversial. Many workers assert that Bell’s theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with “hidden” variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently—as establishing an “essential conflict” between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell’s own views more widely known and to explain Bell’s little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell’s formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates ‘local causality’) became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about themathematical form of the local causality condition and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, in both its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action at a distance, can be articulated in the Everett interpretation. Introduction John S. Bell's last word on his celebrated nonlocality theorem and its interpretation appeared in his 1990 paper ‘La nouvelle cuisine’, first published in the year of his untimely death. Bell was careful here to distinguish between the issue of ‘no superluminal signalling’ in quantum theory (both quantum field theory and quantum mechanics) and a principle he first introduced explicitly in 1976 and called ‘local causality’ [1]. In relation to the former, Bell expressed concerns that amplify doubts he had already expressed in 1976. These concerns touch on what is now widely known as the no-signalling theorem in quantum mechanics, and ultimately have to do with Bell's distaste for what he saw as an anthropocentric element in orthodox quantum thinking. In relation to local causality, Bell emphasised that his famous factorizability (no-correlations) condition is not to be seen ‘as the formulation of local causality, but as a consequence thereof’ and stressed how difficult he found it to articulate this consequence. He left the question of any strict inconsistency between violation of factorizability and special relativity theory unresolved, a not insignificant shift from his thinking up to the early 1980s.
It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.
Relativistic theory and experiments teach us that causal influences are constrained by the speed of light. Deterministic theories incorporate this lesson in functional terms: whether an event occurs or not is functionally determined by events that occur in its immediate causal past. In this paper we suggest a natural generalization of this constraint that applies to probabilistic theories: the probability that an event occurs is to be functionally determined by the probability of the event-occurrences in its immediate causal past. This constraint differs from Bell's criterion of local causality and turns out to imply it only under an additional assumption that requires history to be, in a sense, irrelevant. Bell-inequality-violating quantum phenomena are thus arguably not in tension with relativity, locality, "statistical independence", nor with a supposed "realism". What they instead show is that history is, in a sense, relevant.
Many of the heated arguments about the meaning of 'Bellʼs theorem' arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976.His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism.His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality.This is contrary to Bellʼs own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name).While there are other forms of Bellʼs theorems-which I present to explain the relation between Jarrett-completeness, 'fragile locality', and EPR-completeness-I maintain that Bellʼs two versions are the essential ones.Although the two Bellʼs theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities.For realists, the notion of local causality, ruled out by Bellʼs 1976 theorem, is motivated implicitly by Reichenbachʼs principle of common cause and explicitly by the principle of relativistic causality, and it is the latter which must be forgone.Operationalists pay no heed to Reichenbachʼs principle, but wish to keep the principle of relativistic causality, which, bolstered by an implicit 'principle of agent-causation', implies their notion of locality.Thus for operationalists, Bellʼs theorem is the 1964 one, and implies that it is determinism that must be forgone.I discuss why the two 'camps' are drawn to these different conclusions, and what can be done to increase mutual understanding.