I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. 1. Introduction 2. Newcomb’s Probleme 3. Causal Decision Theory 3.1 Regions of causal influence 3.2 Evidential and effective probabilities 4. The parallel with Bell’s theorem 4.1 Consequences of the analogy 4.1.1 The marble boxes game 4.1.2 Mechanism underlying the marble boxes game 4.1.3 The causalist’s decision 4.1.4 The Bell game 5. Communicated versus Non-communicated Predictions 6. Summary and Conclusion
I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. 1. Introduction 2. Newcomb’s Probleme 3. Causal Decision Theory 3.1 Regions of causal influence 3.2 Evidential and effective probabilities 4. The parallel with Bell’s theorem 4.1 Consequences of the analogy 4.1.1 The marble boxes game 4.1.2 Mechanism underlying the marble boxes game 4.1.3 The causalist’s decision 4.1.4 The Bell game 5. Communicated versus Non-communicated Predictions 6. Summary and Conclusion
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational interpretation of the non-signalling theorem. We here argue that the non-signalling theorem must instead be viewed as an epistemic, operational theorem i.e. one that refers exclusively to what epistemic agents can, or rather cannot, do. That is, we emphasize that the non-signalling theorem is a theorem about the operational inability of epistemic agents to signal information. In other words, as a proper principle, the non-signalling theorem may only be employed as an epistemic, phenomenological, or operational principle. Critically, our argument emphasizes that the non-signalling principle must not be used as an ontic principle about physical reality as such, i.e. as a theorem about the nature of physical reality independently of epistemic agents e.g. human observers. One major reason in favor of our conclusion is that any definition of signalling or of non-signalling invariably requires a reference to epistemic agents, and what these agents can actually measure and report. Otherwise, the non-signalling theorem would equal a general "no-influence" theorem. In conclusion, under the assumption that the non-signalling theorem is epistemic (i.e. "epistemic non-signalling"), the search for deterministic approaches to quantum mechanics, including NHVTs and an emergent quantum mechanics, continues to be a viable research program towards disclosing the foundations of physical reality at its smallest dimensions.
I compare deterministic and stochastic hidden variable models of the Bell experiment, exphasising philosophical distinctions between the various ways of combining conditionals and probabilities. I make four main claims. (1) Under natural assumptions, locality as it occurs in these models is equivalent to causal independence, as analysed (in the spirit of Lewis) in terms of probabilities and conditionals. (2) Stochastic models are indeed more general than deterministic ones. (3) For factorizable stochastic models, relativity's lack of superluminal causation does not favour locality over completeness. (4) If we prohibit all superluminal causation, then the violation of the Bell inequality teaches us a lesson, besides quantum mechanics' familiar ones that quantities can lack precise values and that pairs of quantities can lack joint probabilities: namely, some pairs of events are not screened off by their common past.
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.
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.
Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a \emph{correlation scenario}, and Bell's Theorem then discards those local hidden variable theories in which the sources are independent. However, most correlation scenarios do not arise from Bell scenarios, and we describe examples of (quantum) nonlocality in some of these scenarios, while posing many open problems along the way. Some of our scenarios have been considered before by mathematicians in the context of causal inference.
Bell's theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a correlation scenario , and Bell's theorem then discards those local hidden variable theories in which the sources are independent. However, most correlation scenarios do not arise from Bell scenarios, and we describe examples of (quantum) non-locality in some of these scenarios, while posing many open problems along the way. Some of our scenarios have been considered before by mathematicians in the context of causal inference.