This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
TWO INTERPRETATIONS OF SPATIO-TEMPORAL COUNTERFACTUALSne general (and straightforward) observation which can be made based on chapters 3 and 4 is that there is more than one way to employ Lewis's semantic framework for counterfactual conditionals in the analysis of quantum entangled states.The main reason is that, as we indicated at the end of chapter 2, there may be various ways to define the similarity relation between possible worlds, and this relation is indispensable for the evaluation of counterfactual statements.To characterize the relation of similarity it is necessary to decide which facts from the actual world are salient with respect to the affinity of possible worlds with it, and which are not.We have already reiterated (and this assessment is unanimously, if mostly tacitly, accepted by all who make use of Lewis's semantics in quantum mechanics) that in the context of the quantummechanical phenomena there is no room for law-breaking possible worlds; therefore Lewis's requirement that the number of unlawful events ("miracles") be minimized cannot act as a criterion of similarity between possible worlds.Only singular, individual and contingent facts can set one possible world apart from another, and only such facts can be taken into account when comparing possible worlds with respect to their affinity with the actual world.But it has already been argued that not all facts taking place in the actual world should count towards similarity.It is imperative, then, to make clear how to tell apart those facts that count from those that do not. "ASYMMETRY BY FIAT" SOLUTION REVIVEDIt seems evident that two dominant intuitions regarding the evaluation of quantum counterfactuals have emerged from the extensive discussion in the two previous chapters.However, it will be much more convenient to describe them in terms of extensions to one of Lewis's alternative approaches to counterfactuals rather than in terms of the similarity relation.As we recall (sec.2.3.3),Lewis indicates that the problem with the temporal asymmetry of counterfactuals can find its solution not only within his O 1 It should be stressed, however, that some authors question the assumed asymmetry of counterfactual dependence.For example H. Price, who defends the idea of backward causation, argues that when evaluating counterfactuals we should hold fixed not the past of the antecedent-event, but rather what is epistemologically accessible to us (see Price 1996, pp.169-170, 178-179).2 It is a matter of choice whether to include or exclude the surface of the light cones in the respective "pasts" of e.We will follow the convention according to which, in the first case, the surface of the forward light cone is excluded from the past, but in the second case the surface of the backward light cone is included in it.
his book's main question-Is quantum mechanics non-local?-stilllooms large.But now we at least know that there can be no hope for a simple and unqualified "yes" or "no" answer to this riddle.There is such an enormous variety of interpretations of what constitutes a violation of the locality intuition, not to mention miscellaneous "degrees of severity" of these violations, that it would be utterly hopeless to expect a quick, onceand-for-all resolution to this problem.Yet we have made some progress.Along the quest to find the best counterfactual formulation of the condition of locality we have uncovered two possible interpretations of counterfactual conditionals which seem to be appropriate for describing quantummechanical phenomena that are in the center of our analysis.We should now take an important step forward and utilize these alternative interpretations to propose a precise formulation of the locality condition that could serve as a tenable explication for various intuitions associated with this notion.As we have already seen throughout this book, philosophers of physics and physicists alike often content themselves with pretty nebulous characterizations of the locality condition, of which the following are a representative sample:An event cannot be influenced by events in space-like separated regions.In particular, the outcome obtained in a measurement cannot be influenced by measurements performed in space-like separated regions; and analogously, possessed elements of physical reality referring to a system cannot be changed by actions taking place in space-like separated regions (Ghirardi & Grassi 1994).Since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system (Greenberger et al. 1990, p. 1132) For many purposes these descriptions may be considered sufficient, but without a thorough investigation into the possible meanings associated with terms such as "influence", "changed by", "in consequence of", etc. we T
In the paper the proof of the non-locality of quantum mechanics, given recently by H. Stapp and D. Bedford, and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it appeals to the unwarranted principle of Elimination of Eliminated Conditions (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Next the question is considered whether the validity of the proof in the GHZ case can be restored by adopting the assumption of partial realism. It is argued that although this assumption makes the crucial step of the original reasoning valid, it nevertheless renders another important transition unjustified, therefore the entire reasoning collapses.
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.
This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.
In this tribute to Henry P. Stapp, I outline the historical development of the problem of non-locality in quantum mechanics starting from the EPR argument through Bell’s theorem up to Stapp’s own contributions. My focus is on Stapp’s 1997 proof of quantum non-locality that uses the logic of counterfactuals. On the basis of my own version of the proof presented in 2010, I give its informal analysis, emphasizing the role of Einstein’s criterion of reality in the derivation. I conclude that the proof achieves its objective, and I briefly point at its significance for the philosophical mind-body problem.