The status of a causal approach to EPR-Bell nonlocal correlations in terms of a counterfactual framework for causation is considered. It is argued that when the relativistic spacetime structure of the events is taken into due account, the adoption of this approach is best motivated by the assumption of a preferred frame of reference, an assumption that seems even more in need of justification than the causal theory itself.
The status of a causal approach to EPR-Bell nonlocal correlations in terms of a counterfactual framework for causation is considered. It is argued that when the relativistic spacetime structure of the events is taken into due account, the adoption of this approach is best motivated by the assumption of a preferred frame of reference, an assumption that seems even more in need of justification than the causal theory itself.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
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.
This work presents a minimal reinterpretation of quantum entanglement based solely on the causal structure inherent in relativistic spacetime. No new physical entities, parameters, or modifications to existing theories are introduced.The discussion remains entirely within the established frameworks of general relativity and quantum mechanics, with particular emphasis on Lorentz invariance and relativistic causality. The central idea is that the causal structure of spacetime is unique and invariant, while spatial separation corresponds to different references (foliations) to this structure rather than its duplication.Within this viewpoint, quantum entanglement is understood as a local readout of correlations already encoded in a shared causal structure, without invoking nonlocal influences or superluminal information transfer. This document is intended as a conceptual clarification and archival record rather than a proposal of a new theory.It is provided to preserve a logically consistent interpretation that may be of interest for future foundational discussions.
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.
By moving to the context of relativistic space-time structure, this chapter completes the argument of Chapter 4 that we can use quantum theory locally to explain correlations that violate Bell inequalities with no instantaneous action at a distance. Chance here must be relativized not just to time but to a space-time point, so that an event may have more than one chance at the same time—it may even be certain relative to one space-time point but ‘at the same time’ completely uncertain relative to another. This renders Bell’s principle of Local Causality either inapplicable or intuitively unmotivated. Counterfactual dependence between the outcomes of measurements on systems assigned an entangled state is not causal since neither outcome is subject to intervention: but it may still be appealed to in a non-causal explanation of one in terms of the other.
Gisin has provided an argument for the conclusion that no covariant nonlocal model can reproduce the operational statistics observed in Bell experiments. Gisin's argument applies only to deterministic models and we argue that proposed generalizations of the argument beyond determinism based solely on statistical notions are unconvincing, as they lack the resources to formulate a satisfactory notion of no-retrocausality. We introduce the framework of frame-indexed causal models in order to extend Gisin's argument to the genuinely probabilistic case. Frame-indexed causal models associate potentially different causal models with different reference frames while requiring corresponding operational variables to agree runwise. Within this framework, we establish two no-go results based on Gisin's argument. First, we show that no empirically adequate frame-indexed causal model can jointly satisfy Independent Settings, No-Retrocausality, and Causal Lorentz Invariance. Second, it is established that this result continues to hold when Causal Lorentz Invariance is weakened to Lorentz Invariance of Causal Connections, which requires only the skeleton of the causal structure to remain invariant, thereby allowing the direction of causal influence to depend on the choice of reference frame. These results are discussed in the context of relativistic interpretations of quantum theory and nonclassical causal inference.