The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic in one sense, are less (...) relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another. (shrink)

This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling (...) principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness. (shrink)

This chapter outlines a metaphysics of science in the sense of a naturalized metaphysics. It considers in the first place the interplay of physics and metaphysics in Newtonian mechanics, then goes into the issues for the metaphysics of time that relativity physics raises, shows that what one considers as the referent of quantum theory depends on metaphysical considerations and finally explains how the stance that one takes with respect to objective modality and laws of nature shapes the options that are (...) available for an ontology of quantum physics. In that way, this chapter seeks to make a case for a natural philosophy that treats physics and metaphysics as inseparable in the enquiry into the constitution of the world, there being neither a neo-positivist way of deducing metaphysics from the formalisms of physical theories, nor a neo-rationalist realm of investigation for metaphysics that is independent of physics. (shrink)

It is a frequent assumption that—via superluminal information transfers—superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a ‘no-go’ theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational. Concerning Bell’s theorem, we argue that Bell employed (...) both interpretations, and that he finally adopted the operational position which is associated often with ontological quantum theory, e.g., de Broglie–Bohm theory. This position we refer to as “effective non-signalling”. By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as “axiomatic non-signalling”. In search of a decisive communication-theoretic criterion for differentiating between “axiomatic” and “effective” non-signalling, we employ the operational framework offered by Shannon’s mathematical theory of communication, whereby we distinguish between Shannon signals and non-Shannon signals. We find that an effective non-signalling theorem represents two sub-theorems: Non-transfer-control theorem, and Non-signification-control theorem. Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. Effective non-signalling prevents the instantaneous, i.e., superluminal, transfer of message-encoded information through the controlled use—by a sender-receiver pair —of informationally-correlated detection events, e.g., in EPR-type experiments. An effective non-signalling theorem allows for nonlocal quantum information transfer yet—at the same time—effectively denies superluminal signalling and communication. (shrink)

This paper aims to implement Bell’s notion of local causality into a framework, called local physical theory, which is general enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will then arise as the classical case of our definition. First, we investigate what is needed for a local physical theory to be locally causal. Then we compare local causality with Reichenbach’s common cause principle and relate both to the Bell (...) inequalities. We find a nice parallelism: both local causality and the common cause principle are more general notions than captured by the Bell inequalities. Namely, Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively. (shrink)

This paper argues that there is no conflict between quantum theory and relativity, and that quantum theory itself helps us explain puzzling “non-local” correlations in a way that contradicts neither Bell’s intuitive locality principle nor his local causality condition. The argument depends on understanding quantum theory along pragmatist lines I have outlined elsewhere, and on a more general view of how that theory helps us explain. The key counterfactuals that hold in such cases manifest epistemic rather than causal connections between (...) distant events. Quantum theory exploits the possibility of private informational links between an agent and events he neither observes nor brings about, in ways that are strikingly independent of the spatiotemporal relations between them. This possibility has interesting implications for theories of chance in a relativistic world. (shrink)

There is widespread belief in a tension between quantum theory and special relativity, motivated by the idea that quantum theory violates J. S. Bell’s criterion of local causality, which is meant to implement the causal structure of relativistic space-time. This paper argues that if one takes the essential intuitive idea behind local causality to be that probabilities in a locally causal theory depend only on what occurs in the backward light cone and if one regards objective probability as what imposes (...) constraints on rational credence along the lines of David Lewis’ Principal Principle, then one arrives at the view that whether or not Bell’s criterion holds is irrelevant for whether or not local causality holds. The assumptions on which this argument rests are highlighted, and those that may seem controversial are motivated. (shrink)

Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their (...) differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories. (shrink)

The best case for thinking that quantum mechanics is nonlocal rests on Bell's Theorem, and later results of the same kind. However, the correlations characteristic of Einstein–Podolsky–Rosen (EPR)–Bell (EPRB) experiments also arise in familiar cases elsewhere in quantum mechanics (QM), where the two measurements involved are timelike rather than spacelike separated; and in which the correlations are usually assumed to have a local causal explanation, requiring no action-at-a-distance (AAD). It is interesting to ask how this is possible, in the light (...) of Bell's Theorem. We investigate this question, and present two options. Either (i) the new cases are nonlocal too, in which case AAD is more widespread in QM than has previously been appreciated (and does not depend on entanglement, as usually construed); or (ii) the means of avoiding AAD in the new cases extends in a natural way to EPRB, removing AAD in these cases too. There is a third option, viz., that the new cases are strongly disanalogous to EPRB. But this option requires an argument, so far missing, that the physical world breaks the symmetries which otherwise support the analogy. In the absence of such an argument, the orthodox combination of views—action-at-a-distance in EPRB, but local causality in its timelike analogue—is less well established than it is usually assumed to be. 1 Introduction1.1 Background1.2 Outline of the argument2 The Experiments2.1 Standard EPRB2.2 Sideways EPRB2.3 Comparing the experiments2.4 The need for beables3 The Symmetry Considerations3.1 The action symmetry3.2 Time-symmetry in SEPRB4 The Basic Trilemma4.1 An intuitive defence of Option III?5 Avoiding the Trilemma?6 The Classical Objection7 Defending Option III7.1 The free will argument7.2 Independence and consistency8 Entanglement and Epistemic Perspective. (shrink)

Wood and Spekkens argue that any causal model explaining the EPRB correlations and satisfying the no-signalling constraint must also violate the assumption that the model faithfully reproduces the statistical dependences and independences—a so-called ‘fine-tuning’ of the causal parameters. This includes, in particular, retrocausal explanations of the EPRB correlations. I consider this analysis with a view to enumerating the possible responses an advocate of retrocausal explanations might propose. I focus on the response of Näger, who argues that the central ideas of (...) causal explanations can be saved if one accepts the possibility of a stable fine-tuning of the causal parameters. I argue that in light of this view, a violation of faithfulness does not necessarily rule out retrocausal explanations of the EPRB correlations. However, when we consider a plausible retrocausal picture in some detail, it becomes clear that the causal modelling framework is not a natural arena for representing such an account of retrocausality. _1_ Causal Models, Quantum Mechanics, and Faithfulness _2_ Fine-Tuning _2.1_ Fine-tuning in a retrocausal model _3_ Possible Responses _4_ Quantum Causal Models and Retrocausality _4.1_ A more detailed retrocausal account _4.2_ A model of the EPRB probabilities _4.3_ Mapping to a causal model _5_ Conclusion. (shrink)

A fair amount of recent scholarship has been concerned with correcting a supposedly wrong, but wide-spread, assessment of the consequences of the empirical falsification of Bell-type inequalities. In particular, it has been claimed that Bell-type inequalities follow from “locality tout court” without additional assumptions such as “realism” or “hidden variables”. However, this line of reasoning conflates restrictions on the spatio-temporal relation between causes and their effects (“locality”) and the assumption of a cause for every event (“causality”). It thus fails to (...) recognize a substantial restriction of the class of theories that is falsified through Bell-type inequalities. (shrink)

The paper argues that a causal explanation of the correlated outcomes of EPR-type experiments is desirable and possible. It shows how Bohmian mechanics and the GRW mass density theory offer such an explanation in terms of a non-local common cause.

This paper addresses arguments that “separability” is an assumption of Bell’s theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as “holism”) will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately.In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (...) (b) the definition of Bell’s locality condition does not rely on separability in any way; (c) the proof of Bell’s theorem does not use separability as an assumption. If, inspired by considerations of non-separability, the assumptions of Bell’s theorem are weakened, what remains no longer embodies the locality principle. Teller’s argument for “relational holism” and Howard’s arguments concerning separability are criticised in the light of these results. Howard’s claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem. (shrink)

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies).To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the (...) derivation of Bell’s theorem. Determinism as such does not undermine that independence . Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold. (shrink)

The paper has two aims: (1) it sets out to show that it is well motivated to seek for an account of quantum non-locality in the framework of ontic structural realism (OSR), which integrates the notions of holism and non-separability that have been employed since the 1980s to achieve such an account. However, recent research shows that OSR on its own cannot provide such an account. Against this background, the paper argues that by applying OSR to the primitive ontology theories (...) of quantum physics, one can accomplish that task. In particular, Bohmian mechanics offers the best prospect for doing so. (2) In general, the paper seeks to bring OSR and the primitive ontology theories of quantum physics together: on the one hand, in order to be applicable to quantum mechanics, OSR has to consider what the quantum ontology of matter distributed in space-time is. On the other hand, as regards the primitive ontology theories, OSR provides the conceptual tools for these theories to answer the question of what the ontological status of the wave-function is. (shrink)

We reconsider the problem of the compatibility of quantum nonlocality and the requests for a relativistically invariant theoretical scheme. We begin by discussing a recent important paper by T. Norsen on this problem and we enlarge our considerations to give a general picture of the conceptually relevant issue to which this paper is devoted.

I argue for a realist interpretation of the quantum state. I begin by reviewing and critically evaluating two arguments for an antirealist interpretation of the quantum state, the first derived from the so-called ‘measurement problem’, and the second from the concept of local causality. I argue that existing antirealist interpretations do not solve the measurement problem. Furthermore, I argue that it is possible to construct a local, realist interpretation of quantum mechanics, using methods borrowed from quantum field theory and based (...) on John S. Bell’s concept of ‘local beables’. -/- If the quantum state is interpreted subjectively, then the probabilities it associates with experimental outcomes are themselves subjective. I address the prospects for developing a subjective Bayesian interpretation of quantum mechanical probabilities based on the Quantum de Finetti Representation Theorem. Epistemic interpretations of the quantum state can be divided into those that are epistemic with respect to underlying ontic states, and those that are epistemic with respect to measurement outcomes. The Pusey Barrett and Rudolph (PBR) theorem places serious constraints on the former family of interpretations. I identify an important explanatory gap in the latter sort of interpretation. In particular, if the quantum state is a subjective representation of beliefs about future experimental outcomes, then it is not clear why those experimenters who use quantum mechanics should be better able to negotiate the world than those who do not. -/- I then turn to the task of articulating a positive argument for the thesis of quantum state realism. I begin by articulating a minimal set of conditions that any realist interpretation must meet. One assumption built into the PBR result is that systems prepared in a given quantum state have a well-defined set of physical properties, which may be completely or incompletely described by the quantum state. Antirealist interpretations that reject this assumption are therefore compatible with the PBR result. A compelling case for quantum state realism must therefore be made on more general grounds. I consider two concrete examples of phenomena described by quantum mechanics that strongly suggest that the quantum state is genuinely representational in character. (shrink)

John S. Bell introduced the notion of beable, as opposed to the standard notion of observable, in order to emphasize the need for an unambiguous formulation of quantum mechanics. In the paper I show that Bell formulated in fact two different theories of beables. The first is somehow reminiscent of the Bohr views on quantum mechanics but, at the same time, is curiously adopted by Bell as a critical tool against the Copenhagen interpretation, whereas the second, more mature formulation was (...) among the sources of inspiration of the so-called Primitive Ontology (PO) approach to quantum mechanics, an approach inspired to scientific realism. In the first part of the paper it is argued that, contrary to the Bell wishes, the first formulation of the theory fails to be an effective recipe for addressing the ambiguity underlying the standard formulation of quantum mechanics, whereas it is only the second formulation that successfully paves the way to the PO approach. In the second part, I consider how the distinction between the two formulations of the Bell theory of beables fares vis-a-vis the complex relationship between the theory of beables and the details of the PO approach. (shrink)