This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...) the profound nature of quantum concepts. First edition Hb (1987): 0-521-33495-0 First edition Pb (1988): 0-521-36869-3. (shrink)

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (shrink)

Precis of my book by this title, for a symposium.

Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the world (...) supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis's metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws. (shrink)

There is a common form of problem, to be found in many areas of philosophy, concerning the relationship between our perspective on reality and reality itself. We make statements (or form judgements) about how things are from a given standpoint or perspective. We make the statement ‘it is raining’ from the standpoint of the present time, for example, or the statement‘it is here’ from the standpoint of where we are, or the statement ‘I am glad’ from the standpoint of a (...) subject. In each of these cases, the statement has a certain ‘aspect’ or perspectival character in virtue of which its truth is capable of varying from one standpoint to another. Thus the statement ‘it is raining’ is tensed, the statement ‘it is here’ is ‘spatiocentric’ and the statement ‘I am glad’ is first-personal. The problem we then face is to determine whether this aspect is a feature of the reality which is described or merely a feature of the statement by which it is described. Is reality itself somehow tensed or spatiocentric or firstpersonal or is it merely that we describe a tenseless or spatially uncentered or impersonal reality from a tensed or spatiocentric or first-personal point of view? (shrink)

The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the (...) law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. (shrink)

Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...) space-time points. The role of the wave function then is to govern the motion of the matter. (shrink)

Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...) well as ordinary material degrees of freedom. This paper lays out and compares some options that primitive ontologists have for making sense of the quantum state. (shrink)

Background and assumptions. Persistence and philosophy of time ; Atomism and composition ; Scope ; Some matters of methodology -- Persistence, location, and multilocation in spacetime. Endurance, perdurance, exdurance : some pictures ; More pictures ; Temporal modification and the "problem of temporary intrinsics" ; Persistence, location and multilocation in generic spacetime ; An alternative classification -- Classical and relativistic spacetime. Newtonian spacetime ; Neo-Newtonian (Galilean) spacetime ; Reference frames and coordinate systems ; Galilean transformations in spacetime ; Special relativistic (...) spacetime ; Length contraction and time dilation ; Invariant properties of special relativistic spacetime -- Persisting objects in classical spacetime. Enduring, perduring, and exduring objects in Galilean spacetime ; The argument from vagueness ; From minimal D-fusions to temporal parts ; Motivating a sharp cutoff ; Some objections and replies ; Implications -- Persisting objects in Minkowski spacetime. Enduring, perduring, and exduring objects in Minkowski spacetime ; Flat and curved achronal regions in Minkowski spacetime ; Early reflections on persisting objects in Minkowski spacetime : Quine and Smart ; "Profligate ontology"? ; Is achronal universalism tenable in Minkowski spacetime? ; "Crisscrossing" and immanent causation -- Coexistence in spacetime. The notion of coexistence ; Desiderata ; Coexistence in Galilean spacetime ; Coexistence in Minkowski spacetime : CASH ; Alexandrov-Stein present and Alexandrov-Stein coexistence ; AS-Coexistence v. CASH : symmetry, multigrade, and objectivity ; As-coexistence v. CASH : relevance ; The mixed past of coexistence ; No need in the extended now -- Strange coexistence? Coexistence and existence@ ; The asymmetry thesis ; The absurdity thesis ; Collective CASH value of coexistence ; Collective existence@ and coexistence in classical spacetime ; Collective existence@ and coexistence in Minkowski spacetime ; Contextuality ; Chronological incoherence ; Some objections -- Shapes and other arrangements in Minkowski spacetime. How rigid is a granite block? ; Perspectives in space ; Perspectives in spacetime ; Are shapes intrinsic to objects? ; The causal objection ; The micro-reductive objection ; Pegs, boards, and shapes ; Perduring objects exist. (shrink)

Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...) analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic and causal. We also establish the (...) consistency of our axioms and discuss the philosophical implications. (shrink)

Although considerations based on contemporary space-time theories, such as special and general relativity, seem highly relevant to the debate about persistence, their significance has not been duly appreciated. My goal in this paper is twofold: (1) to reformulate the rival positions in the debate (i.e., endurantism [three-dimensionalism] and perdurantism [four-dimensionalism, the doctrine of temporal parts]) in the framework of special relativistic space-time; and (2) to argue that, when so reformulated, perdurantism exhibits explanatory advantages over endurantism. The argument builds on the (...) fact that four-dimensional entities extended in space as well as time are relativistically invariant in a way three-dimensional entities are not. (shrink)

It is a central aspect of our ordinary concept of time that history unfolds and events come into being. It is only natural to take this seriously. However, it is notoriously difficult to explain further what this `becoming' consists in, or even to show that the notion is consistent at all. In this article I first argue that the idea of a global temporal ordering, involving a succession of cosmic nows, is not indispensable for our concept of time. Our experience (...) does not support the existence of global simultaneity and arguments from modern physics further support the conclusion that time should not be seen as a succession of cosmic nows. Accordingly, I propose that if we want to make sense of becoming we should attempt to interpret it as something purely local. Second, I address the question of what this local becoming consists in. I maintain that processes of becoming are nothing but the successive happening of events, and that this happening of events consists entirely in the occurring of these events at their own spacetime locations. This leads to a consistent view of becoming, which is applicable even to rather pathological spacetimes. (shrink)

Yuri Balashov sets out major rival views of persistence--endurance, perdurance, and exdurance--in a spacetime framework and proceeds to investigate the implications of Einstein's theory of relativity for the debate about persistence. His overall conclusion--that relativistic considerations favour four-dimensionalism over three-dimensionalism--is hardly surprising. It is, however, anything but trivial. Contrary to a common misconception, there is no straightforward argument from relativity to four-dimensionalism. The issues involved are complex, and the debate is closely entangled with a number of other philosophical disputes, including (...) those about the nature and ontology of time, parts and wholes, material constitution, causation and properties, and vagueness. (shrink)

This paper reviews four attempts throughout the history of quantum mechanics to explicitly employ dispositional notions in order to solve the quantum paradoxes, namely: Margenau's latencies, Heisenberg's potentialities, Maxwell's propensitons, and the recent selective propensities interpretation of quantum mechanics. Difficulties and challenges are raised for all of them, and it is concluded that the selective propensities approach nicely encompasses the virtues of its predecessors. Finally, some strategies are discussed for reading similar dispositional notions into two other well-known interpretations of quantum (...) mechanics, namely the GRW interpretation and Bohmian mechanics. (shrink)

The paper argues that the formulation of quantum mechanics proposed by Ghirardi, Rimini and Weber (GRW) is a serious candidate for being a fundamental physical theory and explores its ontological commitments from this perspective. In particular, we propose to conceive of spatial superpositions of non-massless microsystems as dispositions or powers, more precisely propensities, to generate spontaneous localizations. We set out five reasons for this view, namely that (1) it provides for a clear sense in which quantum systems in entangled states (...) possess properties even in the absence of definite values; (2) it vindicates objective, single-case probabilities; (3) it yields a clear transition from quantum to classical properties; (4) it enables to draw a clear distinction between purely mathematical and physical structures, and (5) it grounds the arrow of time in the time-irreversible manifestation of the propensities to localize. (shrink)

The two theories that revolutionized physics in the twentieth century, relativity and quantum mechanics, are full of predictions that defy common sense. Recently, we used three such paradoxical ideas to prove “The Free Will Theorem” (strengthened here), which is the culmination of a series of theorems about quantum mechanics that began in the 1960s. It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if (...) the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. Our argument combines the well-known consequence of relativity theory, that the time order of space-like separated events is not absolute, with the EPR paradox discovered by Einstein, Podolsky, and Rosen in 1935, and the Kochen-Specker Paradox of 1967 (See [2].) We follow Bohm in using a spin version of EPR and Peres in using his set of 33 directions, rather than the original configuration used by Kochen and Specker. More contentiously, the argument also involves the notion of free will, but we postpone further discussion of this to the last section of the article. Note that our proof does not mention “probabilities” or the “states” that determine them, which is.. (shrink)

In this paper, it is argued that the prima facie conflict between special relativity and the quantum-mechanical collapse postulate is only apparent, and that the seemingly incompatible accounts of entangled systems undergoing collapse yielded by different reference frames can be regarded as no more than differing accounts of the same processes and events. Attention to the transformation properties of quantum-mechanical states undergoing unitary, non-collapse evolution points the way to a treatment of collapse evolution consistent with the demands of relativity. r (...) 2002 Elsevier Science Ltd. All rights reserved. (shrink)

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...) case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

The question of how to interpret spontaneous collapse theories of quantum mechanics is an open one. One issue involves what link one should use to go from wave function talk to talk of ordinary macroscopic objects. Another issue involves whether that link should be taken ontologically seriously. In this paper, I ague that the link should be taken ontologically seriously; I argue against an ontology consisting solely of the wave function. I then consider three possible links: the fuzzy link, the (...) accessible mass density link, and the mass density simpliciter link. I show that the first two links have serious anomalies which render them unacceptable. I show that the mass density simpliciter link, in contrast, is viable. (shrink)

J. M. E. McTaggart’s anti-passage argument (the argument that time is “unreal) has misled philosophers of time for almost a century. The present paper shows that the clearest formulation of this argument, that of D. H. Mellor in Real Time II, is unsound when its premises are interpreted so that it is valid and invalid when it so interpreted that it is sound). This argument need mislead us no longer. -/- The crucial item in the interpretation of the premises is (...) the copula ‘is’, as in ‘E is past’. The copula may be either tensed or tenseless. While this ambiguity of the copula has been noted before, its implications for McTaggart’s argument had not been adequately exploited. This paper does that job. (shrink)

This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends (...) on a resolution of the measurement problem. Two alleged proofs that nature is indeterministic, relying, in turn, on Gleason's theorem and Conway and Kochen's recent 'free will theorem', are shown to be wanting qua proofs of indeterminism. We are thus left with the conclusion that the determinism question remains open. (shrink)

The starting point of the present paper is Bell’s notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen’s analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are the correct understanding of the notions of sufficiency, completeness and redundancy involved; and the fact that the apparatus settings and measurement outcomes have very different (...) theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell’s condition of local causality. (shrink)

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.

With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are dynamically stable. (...) This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality. (shrink)

Advocates of the Everett interpretation of quantum mechanics have long claimed that other interpretations needlessly invoke "new physics" to solve the measurement problem. Call the argument fashioned that gives voice to this claim the Redundancy Argument, or ’Redundancy’ for short. Originating right in Everett’s doctoral thesis, Redundancy has recently enjoyed much attention, having been advanced and developed by a number of commentators, as well as criticized by a few others.[1] Although versions of this argument can target collapse theories of quantum (...) mechanics, it is usually conceived with no-collapse "hidden variable" interpretations in mind, e.g., modal and Bohmian interpretations. In particular, the argument is an attack against theories committed to both realism about the quantum state and realism about entities – what Bell 1987 calls "beables" – that supplement this state. Particles, fields, value states, and more have been suggested as possible ontology to supplement the quantum state. Redundancy is the argument that this supplementation is methodologically otiose, the superfluous pomp that Newton scorned. (shrink)