A brief review of the attempts to define “elements of reality” in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post- selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.

The main goal of quantum logic is the bottom-up reconstruction of quantum mechanics in Hilbert space. Here we discuss the question whether quantum logic is an empirical structure or a priori valid. There are good reasons for both possibilities. First, with respect to the possibility of a rational reconstruction of quantum mechanics, quantum logic follows a priori from quantum ontology and can thus not be considered as a law of nature. Second, since quantum logic allows for a reconstruction of quantum (...) mechanics, self-referential consistency requires that the empirical content of quantum mechanics must be compatible with the presupposed quantum ontology. Hence, quantum ontology contains empirical components that are also contained in quantum logic. Consequently, in this sense quantum logic is also a law of nature. (shrink)

The Three Papers comprising this series, together with my earlier [34] also published in this journal, constitute an attempt to set out the major issues in the theoretical domain of reduction and to develop a general theory of theory reduction. The fourth paper, [34], though published separately from this trio, is integral to the presentation and should be read in conjunction with these papers. Even so, the presentation is limited in scope – roughly, to intertheoretic reduction among empirical theories – (...) and informal in presentation – not least because a satisfying formal account of theories has yet to be offered. And despite the length, the treatment is still condensed; often corroborating and/or intuitively helpful detail has had to be consigned to footnotes or omitted. I approach the problem from within my own naturalistic realist philosophy of science and formal analysis of abstract hierarchy in theory. The sources for the former are [25], [29], [31], and [32] and those for the latter essentially [27] and [30]. Hierarchical notions played a significant role in the already published [34]. (shrink)

The Copenhagen interpretation, which informs the textbook presentation of quantum mechanics, depends fundamentally on the notion of ontological wave-particle duality and a viewpoint called “complementarity.” In this paper, Bohr's own interpretation is traced in detail and is shown to be fundamentally different from and even opposed to the Copenhagen interpretation in virtually all its particulars. In particular, Bohr's interpretation avoids the ad hoc postulate of wave function ‘collapse' that is central to the Copenhagen interpretation. The strengths and weakness of both (...) interpretations are summarized. ‡I thank Edward Mackinnon, Henry Folse, and Greg Anderson for valuable comments on the penultimate draft. The final responsibility for the paper rests with the author. †To contact the author, please write to: Bhaktivedanta Institute, 2334 Stuart Street, Berkeley, CA; e-mail: [email protected]. I have been unable to achieve a sharp formulation of Bohr's principle of complementarity despite much effort I have expended on it. (Einstein 1949, 674) While imagining that I understand the position of Einstein, as regards the EPR correlations, I have very little understanding of his principal opponent, Bohr. (Bell 1987, 155) Niels Bohr brain-washed a generation of physicists into believing that the problem had been solved fifty years ago. (Gell-Mann 1979, 29) Every sentence I say must be understood not as an affirmation, but as a question. (Niels Bohr, quoted in Jammer 1966, 175) Bohr's interpretation has never been fully clarified. It needs an interpretation itself, and only that will be its defense. (Weizsäcker 1971, 25). (shrink)

In this note I examine some implications of stochastic interpretations of quantum mechanics for the concept of "charge without charge" presented by Wheeler and Misner. I argue that if a stochastic interpretation of quantum mechanics were correct, then certain shortcomings of the "charge without charge" concept could be overcome.

In recent years, the branching spacetime (BST) interpretation of quantum mechanics has come under study by a number of philosophers, physicists and mathematicians. This paper points out some implications of the BST interpretation for two areas of quantum physics: (1) quantum gravity, and (2) stochastic interpretations of quantum mechanics.

Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...) quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

In this paper I examine the role of dispositional properties in the most frequently discussed interpretations of non-relativistic quantum mechanics. After offering some motivation for this project, I briefly characterize the distinction between non-dispositional and dispositional properties in the context of quantum mechanics by suggesting a necessary condition for dispositionality – namely contextuality – and, consequently, a sufficient condition for non-dispositionality, namely non-contextuality. Having made sure that the distinction is conceptually sound, I then analyze the plausibility of the widespread, monistic (...) ontological thesis about the reducibility of dispositional properties to categorical properties in the context of the philosophy of quantum mechanics. I conclude that with the exception of Bohmian mechanics, the other “minimally realist” views of quantum mechanics require essential dispositions, i.e., dispositions of a non-reducible kind. Interestingly, seen behind the lenses of dispositionalism, Bohr’s and Bohm’s interpretations of quantum mechanics are much closer than it is usually recognized, a fact that could teach us something about the way the quantum world is. (shrink)

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the (...) inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle. (shrink)

Philosophical discourse traditionally distinguishes between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated. However, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, many measurement-related problems force us to consider both our knowledge of the states and observables of a system and its states and observables independent of such knowledge. This applies to quantum systems in particular. This contribution presents an example showing the importance (...) of distinguishing between ontic and epistemic levels of description even for classical systems. Corresponding conceptions of ontic and epistemic states and their evolution are introduced and discussed with respect to aspects of stability and information flow. These aspects show why the ontic/epistemic distinction is particularly important for systems exhibiting deterministic chaos. Moreover, this distinction provides some understanding of the relationships between determinism, causation, predictability, randomness, and stochasticity. (shrink)

State-reduction and the notion of actuality are compared to passage through time and the notion of the present; already in classical relativity the latter give rise to difficulties. The solution proposed here is to treat both tense and value-definiteness as relational properties or facts as relations; likewise the notions of change and probability. In both cases essential characteristics are absent: temporal relations are tenselessly true; probabilistic relations are deterministically true. The basic ideas go back to Everett, although the technical development (...) makes use of the decoherent histories theory of Griffiths, Omnès, and Gell-Mann and Hartle. Alternative interpretations of the decoherent histories framework are also considered. (shrink)

We consider the problem of therelationship between the quantum and theclassical domains from the point of view that itis possible to speak of a direct physicaldescription of quantum systems havingphysical properties. We put emphasis, inevidencing it, on the specific quantum conceptof indistinguishability of identical in aconceptual way (and not in a logical way in thevein of ``da Costa's school''). In essence, thesubsequent argumentation deals with therelationship between the classical and thequantum, with the problem of the quantum theoryof measurement. Even in (...) the absence of adefinitive response to this problem, the bestattitude for the time being, as we cannot reducethe classical and the quantum one to the other,seems to be to accept their pacific coexistence,and this is possible with the toleranceprinciple of the ``pragmatic truth'' developedfrom a logical point of view by Newton daCosta.RESUMO. As áreas quântica eclássica enquanto provisórioscoexistentes parallelos. Abordamos oproblema da relação entre as áreasdo quântico e do clássico considerandoque é possível falar de umadescrição física direta de sistemas quânticos tendo propriedades.Insistimos, para isto, sobre o conceitoespecificamente quântico daindicernabilidade dos idênticos de um ponto devista conceptual (não de um ponto de vistalógico à maneira da ``escola da Costa'')como evidenciando isto. O essencial daargumentação a seguir tem como enfoquea relação clássico-quântico, como problema da teoria quântica damedição. Mesmo não tendo umaresposta definitiva para este, a melhor atitudepor enquanto, já que não se podemreduzir um ao outro o clássico e oquântico, nos parece ser esta de aceitar suacoexistência pacífica, o que épossível com o princípio detolerância da ``verdade pragmática''desenvolvida logicamente por Newton da Costa. (shrink)

Faced with strong arguments to the effect that Leibniz''sPrinciple of the Identity of Indiscernibles (PII) is not a necessary truth, many supporters of the Principle have staged a strategic retreat to the claim that it is contingently true in this, the actual, world. The purpose of this paper is to examine the status of the various forms of PII in both classical and quantum physics, and it is concluded that this latter view is at best doubtful, at worst, simply wrong.

The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a (...) metamathematical interpretation of ideas sometimes considered disparate, heuristic, or simply ill-defined: the collapse of the wave function, for example; Everett's many worlds'-construal of quantum measurement; and a natural product space of contextual (nonlocal) hidden variables. (shrink)

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s. We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect measurement, which influenced his discussion (...) of the "reduction of the wave packet" and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical measurement. (shrink)

In this essay I examine various aspects of the nearcentury-long debate concerning the conceptualfoundations of quantum mechanics and the problems ithas posed for physicists and philosophers fromEinstein to the present. Most crucial here is theissue of realism and the question whether quantumtheory is compatible with any kind of realist orcausal-explanatory account which goes beyond theempirical-predictive data. This was Einstein's chiefconcern in the famous series of exchanges with NielsBohr when he refused to accept the truth orcompleteness of a doctrine (orthodox QM) (...) which ruledsuch questions to be strictly inadmissible. I discussthe later history of quantum-theoretical debate withparticular reference to the issue of nonlocality,i.e., the phenomenon of superluminal(faster-than-light) interaction betweenwidely-separated particles. Then I show how thestandard `Copenhagen' interpretation of QM hasinfluenced current anti-realist orontological-relativist approaches to philosophy ofscience. Indeed, there are clear signs that somephilosophers have retreated from a realist positionvery largely in response to just these problems. So itis important to ask exactly why – on what scientificor philosophical grounds – any preferred alternative(causal-realist) construal should have been ruled outas a matter of orthodox QM wisdom. Moreconstructively, my paper presents various arguments infavour of one such alternative, the `hidden-variables'theory developed since the early 1950s by David Bohmand consistently marginalised by proponents of theCopenhagen doctrine. (shrink)

In this paper I put forward a new micro realistic, fundamentally probabilistic, propensiton version of quantum theory. According to this theory, the entities of the quantum domain - electrons, photons, atoms - are neither particles nor fields, but a new kind of fundamentally probabilistic entity, the propensiton - entities which interact with one another probabilistically. This version of quantum theory leaves the Schroedinger equation unchanged, but reinterprets it to specify how propensitons evolve when no probabilistic transitions occur. Probabilisitic transitions occur (...) when new "particles" are created as a result of inelastic interactions. All measurements are just special cases of this. This propensiton version of quantum theory, I argue, solves the wave/particle dilemma, is free of conceptual problems that plague orthodox quantum theory, recovers all the empirical success of orthodox quantum theory, and at the same time yields as yet untested predictions that differ from those of orthodox quantum theory. (shrink)

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.

It is widely accepted that consciousness or, more generally, mental activity is in some way correlated to the behavior of the material brain. Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness. Several approaches answering this question affirmatively, proposed in recent decades, will be surveyed. It will be pointed out that they make different epistemological assumptions, refer to different neurophysiological (...) levels of description, and use quantum theory in different ways. For each of the approaches discussed, problematic and promising features will be equally highlighted. (shrink)

The main aim of this work is to contribute tothe elucidation of the concept of informationby comparing three different views about thismatter: the view of Fred Dretske's semantictheory of information, the perspective adoptedby Peter Kosso in his interaction-informationaccount of scientific observation, and thesyntactic approach of Thomas Cover and JoyThomas. We will see that these views involvevery different concepts of information, eachone useful in its own field of application. This comparison will allow us to argue in favorof a terminological `cleansing': it (...) is necessaryto make a terminological distinction among thedifferent concepts of information, in order toavoid conceptual confusions when the word`information' is used to elucidate relatedconcepts as knowledge, observation orentropy. (shrink)

Aristotelian ideas have in the past been applied with mixed fortunes to quantum mechanics. One of the most persistent criticisms is that Aristotle’s notions of potentiality and actuality are burdened with a teleological character long ago abandoned in the natural sciences. Recently this criticism has been met with a model of the actualization of quantum potentialities in light of Aristotle’s doctrine of ‘spontaneous events’. This presumably restores the nowadays acceptable idea of efficient causation in place of Aristotle’s original doctrine of (...) the ‘four causes’. In this article I challenge the model by arguing that when properly scrutinized Aristotle’s final cause poses no problems for an Aristotelian reading of quantum mechanics. Final causes in fact provide a better ontology for quantum mechanics than spontaneous causation. The idea of ‘spontaneity’ is unanalyzable and therefore of little use in quantum mechanics. In addition, it is ontologically sterile in the context of quantum measurement, as shown by a historical and conceptual review of the role of efficient causation in experimental physics. (shrink)

Recent work on the hole argument in general relativity by Weatherall has drawn attention to the neglected concept of models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot for the claim that some isometries “generate new possibilities” in general (...) relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime. (shrink)

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical (...) state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function. After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function. I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain. (shrink)

According to what has become a standard history of quantum mechanics, von Neumann in 1932 succeeded in convincing the physics community that he had proved that hidden variables were impossible as a matter of principle. Subsequently, leading proponents of the Copenhagen interpretation emphatically confirmed that von Neumann's proof showed the completeness of quantum mechanics. Then, the story continues, Bell in 1966 finally exposed the proof as seriously and obviously wrong; this rehabilitated hidden variables and made serious foundational research possible. It (...) is often added in recent accounts that von Neumann's error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist. We shall attempt to tell a more balanced story. Most importantly, von Neumann did not claim to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann's conclusion was basically that hidden-variables schemes must violate the "quantum principle" that all physical quantities are to be represented by operators in a Hilbert space. According to this conclusion, hidden-variables schemes are possible in principle but necessarily exhibit a certain kind of contextuality. As we shall illustrate, early reactions to Bohm's theory are in agreement with this account. Leading physicists pointed out that Bohm's theory has the strange feature that particle properties do not generally reveal themselves in measurements, in accordance with von Neumann's result. They did not conclude that the "impossible was done" and that von Neumann had been shown wrong. (shrink)

The publication of the EPR paper in 1935 prompted Heisenberg to draft a manuscript on the question of the completability of quantum mechanics. We give here the English translation of this manuscript with a brief introduction and bibliography.

An adequate conjunction-implication pair is given for complete orthomodular lattices. The resulting conjunction is noncommutative in nature. We use the well-known lattice of closed subspaces of a Hilbert space, to give physical meaning to the given lattice operation.

In his paper titled ‘Against “measurement” ’ [Physics World 3(8), 33–40 [1990]], Bell criticised arguments that use the concept of measurement to justify the statistical interpretation of quantum theory. Among these was the text of Gottfried [Quantum Mechanics (Benjamin, New York, [1966])]. Gottfried has replied to this criticism, claiming to show that, for systems with both continuous and discrete degrees of freedom, the statistical interpretation for the discrete variables is implied by requiring that the continuous variables are described classically. In (...) the present paper, Gottfried’s argument is criticised. It is suggested that he takes over aspects of classical physics which are in conflict with the classical limit of the Schrödinger equation. He incorrectly assumes that, in the output from a Stern-Gerlach apparatus, the wave-function of any ion is restricted to one or another of the beams. (shrink)

The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincare symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observables associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localization may be applied to massive as well as massless fields. Localization observables are defined as to obey Lorentz (...) covariant commutation relations and in particular include a time observable conjugated to energy. While position components do not commute in the presence of a nonvanishing spin, they still satisfy quantum relations which generalize the differential laws of classical relativity. We also give of these observables a representation in terms of canonical spatial positions, canonical spin components, and a proper time operator conjugated to mass. These results plead for a new representation not only of space-time localization but also of motion. (shrink)

If a physicist claims to be a realist, he or she must face at least the three problems outlined here: the careful specification of the validity limits of every theory and model used, the coherence relationships that must hold between two theories of the same physical system but on different cognitive levels, and the ambiguity in the ontology of two different formulations of empirically equivalent theories.

The question of the relation between the amplitude of the photon vector potential and its angular frequency is analyzed. The analogy between the relativistic quantum mechanical equations for a massles particle and those governing the photon vector potential appears clearly. Finally, the virtual electromagnetic waves associated with the photon and predicted by de Broglie, Bohr, and other appear naturally as a result of the photon vector potential quantification.

The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such “anecdotal” factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.

The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.

The thought of Bernard Lonergan provides an epistemological position that is both true to the exigencies of modern science and yet open to the possibility of God and revealed religion. In this paper I outline Lonergan's “transcendental method,” which describes the basic pattern of operations involved in any act of human knowing, and discuss how Lonergan uses this cognitional theory as a basis for an epistemological position of critical realism. Then I explain how his approach handles some philosophical problems raised (...) by classical and modern science and show how his thought provides an intelligible link between the scientific and religious horizons. (shrink)

Nobel Laureate in physics Wolfgang Pauli studied philosophy and the history of ideas intensively, especially in his later years, to form an accurate ontology vis-à-vis quantum theory. Pauli's close contacts with the Swiss psychiatrist C.G. Jung gave him special qualifications for also understanding the basic problems of empirical knowledge. After Pauli's sudden death in 1958, this work was maintained mainly in his posthumously published correspondence, which so far extends only to 1939. Because Pauli's view differs essentially from the direction physics (...) research took after the deaths of the founding fathers of quantum theory, this article attempts to describe the main features in Pauli's revolutionary thought, which is based on nature's “epistemological lesson” as revealed by Pauli's atomic research. Pauli's conclusions have important implications for various issues in Western culture, not least with the limits of science and the relation of science to religion. (shrink)

Nothing seems more possible to me than that people some day will come to the definite opinion that there is no copy in the… nervous system which corresponds to a particular thought, or a particular idea, or, memory.WittgensteinIn a recent essay it was emphasized that brain and mind appear to the mind as complementary and reciprocally recursive domains of a hermeneutic circle (Fischer, 1987). An outstanding and not yet recognized feature of this hermeneutic circle is that interpretation within this circle (...) is not rule-governed and hence appears self-organized: individual features of the world (or the brain) become intelligible in terms of the whole context (of the mind)… while the entire context becomes intelligible through individual features (or brain functions). How, or from where then is significance arising? (shrink)

Inspite of the great success in many disciplines the program of reductionism has failed its genuine purpose. Systemtheory however has yielded a new concept of reductionism which we call reductionism by correspondence and which may imply a new understanding of the mind-body problem. The crucial operations of reductionism by correspondence are called idealization, interpretation and classification. They are used to optimize the description of a system. Nevertheless they lead to certain deficiencies which cannot be avoided in principle. We are therefore (...) driven to the assumption that natural systems can only be described as probabilistic systems. From this point of view nothing is said about the direction of the reduction. (shrink)

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask whether (...) the resulting interpretation of quantum mechanics is empirically testable. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as an (...) average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of . It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L. (shrink)

In this essay, I offer a critical evaluation of Hilary Putnam's writings on epistemology and philosophy of science, in particular his engagement with interpretative problems in quantum mechanics. I trace the development of his thinking from the late 1960s when he adopted a strong causal-realist position on issues of meaning, reference, and truth, via the "internal realist" approach of his middle-period writings, to the various forms of pragmatist, naturalized, or "commonsense" epistemology proposed in his latest books. My contention is that (...) Putnam's retreat from a full-fledged realist outlook has been prompted in large part by his belief that it cannot possibly be reconciled with the implications of quantum mechanics for our understanding of processes and events in the subatomic domain. However, I suggest, this response should be seen as premature given the range of as-yet unresolved problems with quantum mechanics on the orthodox (Copenhagen) interpretation and also the existence of an alternative account - David Bohm's hidden-variables theory - which perfectly matches the established predictive-observational results while providing a credible realist ontology. I also examine Putnam's case for adopting a nonstandard (three-valued) "quantum logic" in relation to the thinking of other philosophers - Michael Dummett among them - who have espoused a more global or doctrinaire version of anti-realism. I conclude that Putnam's early (causal-realist) position is by no means untenable in light of the various arguments that he now takes as counting decisively against it. (shrink)

Timelines is an inquiry into the nature of time, both as an apparent feature of the external physical world and as a fundamental feature of our experience of ourselves in the world. The principal argument of Timelines is that our coventional ideas about time are largely mistaken and that what we think of as independent physical time is actually our calibration of a certain relation between events. Namely, the relation between time-keeping events and the causal sequential differences of physical processes (...) which are real and independent of us. (shrink)

Merleau-Ponty’s remarks on quantum mechanics offer a unique perspective on the relationship between scientific results and their interpretation. This article elaborates Merleau-Ponty’s phenomenological perspective on quantum mechanics by considering the main texts in which he explicitly attends to this topic: namely, La Nature: notes cours du Collège de France and The Visible and the Invisible.