We investigate whether standard counterfactual analyses of causation (CACs) imply that the outcomes of space-like separated measurements on entangled particles are causally related. Although it has sometimes been claimed that standard CACs imply such a causal relation, we argue that a careful examination of David Lewis’s influential counterfactual semantics casts doubt on this. We discuss ways in which Lewis’s semantics and standard CACs might be extended to the case of space-like correlations. 1 Introduction2 Measurement Outcomes and Counterfactual Analyses of Causation3 Lewis’s Analysis 1 of Counterfactuals (‘Asymmetry-by-Fiat’) 3.1 Analysis 1 3.2 A frame-relative reading of Analysis 1 3.3 Frame-invariant readings of Analysis 1 3.4 Discussion4 Lewis’s Analysis 2 of Counterfactuals (‘Closest Worlds’)5 Extending the Everyday Concept of Cause6 Conclusion
We investigate whether standard counterfactual analyses of causation (CACs) imply that the outcomes of space-like separated measurements on entangled particles are causally related. Although it has sometimes been claimed that standard CACs imply such a causal relation, we argue that a careful examination of David Lewis’s influential counterfactual semantics casts doubt on this. We discuss ways in which Lewis’s semantics and standard CACs might be extended to the case of space-like correlations. 1 Introduction2 Measurement Outcomes and Counterfactual Analyses of Causation3 Lewis’s Analysis 1 of Counterfactuals (‘Asymmetry-by-Fiat’) 3.1 Analysis 1 3.2 A frame-relative reading of Analysis 1 3.3 Frame-invariant readings of Analysis 1 3.4 Discussion4 Lewis’s Analysis 2 of Counterfactuals (‘Closest Worlds’)5 Extending the Everyday Concept of Cause6 Conclusion
Abstract The existence of non-local correlations between outcomes of measurements in quantum entangled systems strongly suggests that we are dealing with some form of causation here. An assessment of this conjecture in the context of the collapse interpretation of quantum mechanics is the primary goal of this paper. Following the counterfactual approach to causation, I argue that the details of the underlying causal mechanism which could explain the non-local correlations in entangled states strongly depend on the adopted semantics for counterfactuals. Several relativistically-invariant interpretations of spatiotemporal counterfactual conditionals are discussed, and the corresponding causal stories describing interactions between parts of an entangled system are evaluated. It is observed that the most controversial feature of the postulated causal connections is not so much their non-local character as a peculiar type of circularity that affects them.
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.
Is time necessary for causation? We argue that, given a counterfactual theory of causation, it is not. We defend this claim by considering cases of counterfactual dependence in quantum mechanics. These cases involve laws of nature that govern entanglement. These laws make possible the evaluation of causal counterfactuals between space-like separated entangled particles. There is, for the proponent of a counterfactual theory of causation, a possible world in which causation but not time exists that can be reached by "stripping out" time from the actual world, leaving (some) quantum mechanical laws intact.
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.
In this dissertation, I will argue that quantum field theory can be interpreted as a description of causal interactions. I will first discuss previous theories of physical causation, and come to the conclusion that they are inapplicable in quantum field theory. As a consequence, I will start to develop a new theory of causation by first analysing the concept ‘causation’ into the most basic and widely shared intuitions, in order to find out later whether these intuitions can be reduced to physics. I will then have a closer look on the intuition that causation is a directed relation, which is commonly regarded as incompatible with the symmetries of physics. I will present a new argument to the effect that causation and quantum field theory are compatible with respect to the directionality of causation. After that, I will analyse the theoretical description of interactions in quantum field theory, and in particular group structure, locality and local conservation laws will crystallise as the central concepts that a causal interpretation might be based on. Subsequently, I will discuss and present replies to what I believe are the most relevant objections to a causal interpretation of physics, namely, Haag’s theorem, the measurement problem and entanglement. In the final chapter of this dissertation, I will conjoin the results of the previous chapters to a new theory of causation for quantum field theory. The main result will be that a causal process is a quantum field theoretical interaction, i.e., the exchange of energy from an initial to a final state via a force.
In his seminal paper, Bell [Physics Physique Fizika 1, 195 (1964)] considers the correlations that result from space-like separated measurements on a pair of entangled particles. He uses relativity theory to motivate the Bell causal structure, then shows the existence of quantum correlations that cannot be explained classically within this causal structure. Classical explanations of such quantum correlations are possible in alternative causal structures, for instance, those that allow superluminal causal influences, but, as shown in [New Journal of Physics 17 033002 (2015)], all such alternative explanations require fine tuning (causation without correlation). Here we discuss the existence of spurious quantum correlations --- correlations that look quantum in one causal structure, but have a natural classical explanation in another. More precisely, there are causal structures that admit non-classical quantum correlations, but for which the same correlations have a classical explanation in another causal structure without fine tuning. The realisation in the other causal structure can also be achieved without breaking any natural constraints on the causal structure that follow from relativity theory. However, similarly to non-classical quantum correlations in the Bell causal structure, we find other causal structures with non-classical quantum correlations that do not have a classical causal explanation in any alternative causal structure without fine tuning.