We describe a series of experimental analogies between fluid mechanics and quantum mechanics recently discovered by a team of physicists. These analogies arise in droplet systems guided by a surface wave. We argue that these experimental facts put ancient theoretical work by Madelung on the analogy between fluid and quantum mechanics into new light. After re-deriving Madelung’s result starting from two basic fluid mechanical equations, we discuss the relation with the de Broglie–Bohm theory. This allows to make a direct link (...) with the droplet experiments. It is argued that the fluid mechanical interpretation of quantum mechanics, if it can be extended to the general N-particle case, would have a considerable advantage over the Bohm interpretation: it could rid Bohm’s theory of its non-local character. (shrink)

The presented enhanced version of Eriksen’s theorem defines an universal transform of the Foldy–Wouthuysen type and in any external static electromagnetic field reveals a discrete symmetry of Dirac’s equation, responsible for existence of a highly influential conserved quantum number—the charge index distinguishing two branches of DE spectrum. It launches the charge-index formalism obeying the charge-index conservation law. Via its unique ability to manipulate each spectrum branch independently, the CIF creates a perfect charge-symmetric architecture of Dirac’s quantum mechanics, which resolves all (...) the riddles of the standard DE theory. Besides the abstract CIF algebra, the paper discusses: the novel accurate charge-symmetric definition of the electric-current density; DE in the true-particle representation, where electrons and positrons coexist on equal footing; flawless “natural” scheme of second quantization; and new physical grounds for the Fermi–Dirac statistics. As a fundamental quantum law, the CICL originates from the kinetic-energy sign conservation and leads to a novel single-particle physics in strong-field situations. Prohibiting Klein’s tunneling in Klein’s zone via the CICL, the precise CIF algebra defines a new class of weakly singular DE solutions, strictly confined in the coordinate space and experiencing the total reflection from the potential barrier. (shrink)

In Crull it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky, is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in (...) quantum mechanics, such as the measurement problem or the emergence of classicality. (shrink)

Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) to (...) the notion of a subset. Hence the Boolean logic of subsets has a dual logic of partitions. Then the dual progression is from that logic of partitions to the quantum logic of direct-sum decompositions (i.e., the vector space version of a set partition) of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the logic to express measurement by any self-adjoint operators rather than just the projection operators associated with subspaces. In this introductory paper, the focus is on the quantum logic of direct-sum decompositions of a finite-dimensional vector space (including such a Hilbert space). The primary special case examined is finite vector spaces over ℤ₂ where the pedagogical model of quantum mechanics over sets (QM/Sets) is formulated. In the Appendix, the combinatorics of direct-sum decompositions of finite vector spaces over GF(q) is analyzed with computations for the case of QM/Sets where q=2. (shrink)

Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what has often been alleged, platonists do not fully accommodate these features of the application of mathematics. At best, platonism provides partial ways of handling the issues. I then sketch an alternative, anti-realist account of the application of mathematics, and argue that this account manages to accommodate these features of the application (...) process. In this way, a better account of mathematical applications is, in principle, available. (shrink)

Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata, and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world (...) and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations. (shrink)

Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, (...) but to a set of sub-problems. (shrink)

I argue that quantum optical experiments that purport to refute Bohr’s principle of complementarity fail in their aim. Some of these experiments try to refute complementarity by refuting the so called particle–wave duality relations, which evolved from the Wootters–Zurek reformulation of BPC. I therefore consider it important for my forgoing arguments to first recall the essential tenets of BPC, and to clearly separate BPC from WZPC, which I will argue is a direct contradiction of BPC. This leads to a need (...) to consider the meaning of particle–wave duality relations and to question their fundamental status. I further argue that particle and wave complementary concepts are on a different footing than other pairs of complementary concepts. (shrink)

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

In this paper we analyze the definition of quantum superpositions within orthodox Quantum Mechanics and their relation to physical reality. We will begin by discussing how the metaphysical presuppositions imposed by Bohr on the interpretation of QM have become not only interpretational dogmas which constrain the limits of the present Orthodox Line of Research, but also how these desiderata implicitly preclude the possibility of developing a physical representation of quantum superpositions. We will then continue analyzing how most interpretations of QM (...) argue against the existence of superpositions. Firstly, we will focus on those interpretations which attempt to recover a classical representation about ''what there is'', and secondly, we will concentrate on the arguments provided by Dieks and Griffiths who, staying close to the orthodox formalism, also attempt to ''get rid of the ghost of Schrodinger's cat''. Contrary to the OLR, we will argue -based on our definition of Meaningful Physical Statements - that from a representational realist perspective which stays close to the orthodox Hilbert space formalism, quantum superpositions are not only the key to the most important -present and future- technological and experimental developments in quantum information processing but also, they must be considered as the kernel of any interpretation of QM that attempts to provide a physical representation of reality. We will also argue that the price to pay for such representational realist development must be the abandonment of the idea that 'Actuality = Reality'. (shrink)

We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist.We analyze that (...) claim by employing the traditional square of opposition.We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them. (shrink)

Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...) context of thermodynamics and statistical mechanics. The chapter then reviews the main strategies available for resolving the conflict between reversible microdynamics and irreversible macrodynamics, working within the context of the quantitative, time‐irreversible evolution laws that seem to apply to large‐scale phenomena. Finally, it offers a broad the discussion covering other arrows of time within physics. (shrink)

PhD dissertation addressing what can be called conceptual-mathematical anomalies in quantum electrodynamics. This work can be seen as following the line of philosophy of physics studies of quantum field theory that started to emerge in a systematic way in the early eighties of last century. One example is Teller’s work on standard quantum electrodynamics.In this work, by following a historical approach, I will return to the standard version of quantum electrodynamics, which is the only one available when we want to (...) get numbers out to compare with experimental results. This work spins around two main vectors. One is the divergence of the S-matrix series expansion, the other is the spatio-temporal description of physical processes in the theory. (shrink)

This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation (...) invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issue of unifying quantum mechanics and special relativity. (shrink)

Theory and Reality is about the connection between true theories and the world. A mathematical framefork for such connections is given, and it is shown how that framework can be used to infer facts about the structure of reality from facts about the structure of true theories, The book starts with an overview of various approaches to metaphysics. Beginning with Quine's programmatic "On what there is", the first chapter then discusses the perils involved in going from language to metaphysics. It (...) criticises contemporary intuition-driven metaphysics, comments on naturalistic approaches, and then presents the main proposition put forward in the thesis: we should base metaphysics on model theory. In chapters 2 to 5, mathematical treatments are given of concepts that we need: theories, metaphysics, necessitation and semantics. These are used in chapters 6 and 7 to prove that, seen from a certain informative view point, any true theory will give rise to an isomorphism between that theory and the world. This conclusion is similar to Wittgenstein's in the Tractatus, but differs in that it places the structural relationship on the level of whole theories, rather than single propositions. (shrink)

Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful tool to understand the role of the phase as the mechanism responsible for the dynamical evolution displayed by quantum systems. This role is analyzed and discussed here in the context of quantum interference, considering to this end two well-known scenarios, namely Young’s two-slit experiment and Wheeler’s delayed choice experiment. A numerical implementation of the first scenario is used to show how interference in a coherent superposition of two counter-propagating (...) wave packets can be seen and explained in terms of an effective model consisting of a single wave packet scattered off an attractive hard wall. The outcomes from this model are then applied to the analysis of Wheeler’s delayed choice experiment, also recreated by means of a reliable realistic simulation. Both examples illustrate quite well how the Bohmian formulation helps to explain in a natural way aspects of the quantum theory typically regarded as paradoxical. In other words, they show that a proper understanding of quantum phase dynamics immediately removes any trace of unnecessary artificial wave-particle arguments. (shrink)

Is quantum mechanics about ‘states’? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to ‘classical’ instantiations of a probability calculus. Its providing a general framework for prediction accounts for its distinctive traits, which one should be careful not to mistake for reflections of any strange ontology. The suggestion is also made that quantum theory unwittingly emerged, in Schrödinger’s formulation, as a ‘lossy’ by-product of a (...) quantum-mechanical variant of the Hamilton-Jacobi equation. As it turns out, the effectiveness of quantum theory qua predictive algorithm makes up for the computational impracticability of that master equation. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Discusses Armstrong's and Roman Ingarden's ontology, criticises substance ontology, and defends tropes and a field ontology.

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The point is not to (...) clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting. (shrink)

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...) to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics. (shrink)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

We investigate variations of the Zitterbewegung frequency of electron due to an external static and uniform magnetic field employing the expectation value quantum approach, and compare our results with the classical model of spinning particles. We demonstrate that these two so far compatible approaches are not in agreement in the presence of an external uniform static magnetic field, in which the classical approach breaks the usual symmetry of free particles and antiparticles states, i.e. it leads to CP violation. Hence, regarding (...) the Zitterbewegung frequency of electron, the classical approach in the presence of an external magnetic field is unlikely to correctly describe the spin of electron, while the quantum approach does, as expected. We also show that the results obtained via the expectation value are in close agreement with the quantum approach of the Heisenberg picture derived in the literature. However, the method we use is capable of being compared with the classical approach regarding the spin aspects. The classical interpretation of spin produced by the altered Zitterbewegung frequency, in the presence of an external magnetic field, are discussed. (shrink)

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. From a probability principle P1 and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a (...) generalization of P2, a principle P3. All three principles are shown to be without alternative. It is thus shown that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed. (shrink)

Motivated by a recent proof of free choices in linking equations to the experiments they describe, I clarify some relations among purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. I relate conditional probabilities associated with projection-valued measures to conditional density operators identical, in some cases but not in others, to the usual reduced density operators. While a fatal (...) obstacle precludes associating conditional density operators with general non-projective measures, tensor products of general positive operator-valued measures (POVMs) are associated with conditional density operators. This association together with the free choice of probe particles allows a postulate of state reductions to be replaced by a theorem. An application shows an equivalence between one form of quantum key distribution and another with respect to certain eavesdropping attacks. (shrink)

We give a common mathematical characterization of relevant stochastic evolution schemes built up in the literatute to attack the quantum measurement problem. This characterization is based on two hypotheses, namely, (i) the trace conservation with probability one and (ii) the existence of a complex phase determining a linear support for the stochastic process driving the random evolution.

The Maxwell equations are shown to be the one-photon spin-one quantum equations. All Maxwell equations (without sources) are derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. The wavefunction is a linear combination of the electric and magnetic fields. The procedure is not unique, there are ambiguities of adding a scalar field. A quaternionic representation of the Maxwell equations (with sources) is constructed, a covariant reformulation of which is presented. Whittaker (...) potentials are analysed. Conservation laws are derived using a method of “pseudo-Lagrangians.”. (shrink)

In this series of articles the early life and work of the young Julian Schwinger are explored. In this first article, Schwinger's childhood, growing-up, and early education are discussed.

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C2 is generated by two Pauli matrices iσ2 and iσ3; C3 is generated by the three Pauli matrices σ1, σ2, σ3; C4 is generated by four Dirac matrices γ0, γ1, γ2, γ3 and C5 is generated by five Dirac matrices iγ0, iγ1, iγ2, iγ3, iγ5. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained (...) with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation. (shrink)

In this, the first of a two-part paper, a conceptual purification of physics is advocated, whereby the idea of the field is completely eliminated in favor of particulate dynamical laws. Previous work concerning a specific formulation of such purely mechanical laws is reviewed and is shown to imply the possibility of existence of electrons and positrons within nuclei or “elementary” particles in stable bound states characterized by real mass-energy and imaginary momentum. The second part of the paper will examine the (...) qualitative implications and the sufficiency of such concepts for physical description.Newton, Introduction to thePrincipia. (shrink)

The aim of this paper is to undermine structural realism by testing the soundness of its three main theses. The first section presents the epistemic and ontic forms of structural realism. The following section defends that if scientific theories represent the structure of the world, structural realism needs a general account of representation. Representation is the crux of structural realism. Section 3 argues that structure/ontology distinction collapses. Mathematical structures are ontologyladen. Lastly, section 4 is devoted to analyse whether there is (...) a retention of mathematical structure across theory change. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

Emergent properties (EPs) are not causally reducible to the properties of a complex system’s elements. If a system’s properties cannot be reduced to those of any of its components, then that system is effectively a singular entity (SE). EPs are thus not properties of known complexes, but of SEs. A precise description of the parameters necessary to observe a physical system as an SE is thus necessary to establish under what conditions properties are understood as emergent. That description is provided (...) in terms of the temporal dynamics of systems and their internal/external interactions. (shrink)

In this paper, I argue that symmetry principles in physics (in particular, in quantum mechanics) have a methodological character, rather than an ontological or an epistemological one. First, I provide a framework to address three related issues regarding the notion of symmetry: (i) how the notion can be characterized; (ii) one way of discussing the nature of symmetry principles, and (iii) a tentative account of some types of symmetry in physics. To illustrate how the framework functions, I then consider the (...) case of the early formulation of quantum mechanics, examining the different roles played by symmetry in this context. Finally, I raise difficulties for ontological and purely episte. (shrink)

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary account of the nature of quantum information. (...) Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

This essay is a discussion of the philosophical and foundational issues that arise in non-relativistic quantum theory. After introducing the formalism of the theory, I consider: characterizations of the quantum formalism, empirical content, uncertainty, the measurement problem, and non-locality. In each case, the main point is to give the reader some introductory understanding of some of the major issues and recent ideas.

There has been considerable recent philosophical debate over the implications of many particle quantum mechanics for the metaphysics of individuality (cf. Huggett [1997]). In this paper I look at things from a rather different perspective: by investigating the significance of permutation symmetry. I consider how various philosophical positions link up to the physical postulate of the indistinguishability of permuted states-permutation invariance-and how this postulate is used to explain quantum statistics. I offer an explanation of the statistics that relies on the (...) neglected parallel between permutations and covariant spatial transformation. And I explore the parallel, showing that a further kind of symmetry explains why permutations are invariant when spatial symmetries are not. (shrink)

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin-statistics connection and the Symmetrization Postulate. In light of recent theories (such as q-deformed commutators) that allow for ‘small’ violations of the spin-statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation (...) symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of Permutation Invariance and the Symmetrization Postulate 3.2 The configuration-space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q-mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions. (shrink)

In this paper I put forward a suggestion for identifying causality in micro-systems with the specific quantum field theoretic interactions that occur in such systems. I first argue — along the lines of general transference theories — that such a physicalistic account is essential to an understanding of causation; I then proceed to sketch the concept of interaction as it occurs in quantum field theory and I do so from both a formal and an informal point of view. Finally, I (...) present reasons for thinking that only a quantum field theoretic account can do the job — in particular I rely on a theorem by D. Currie and to the effect that interaction cannot be described in (a Hamiltonian formulation of) Classical Mechanics. Throughout the paper I attempt to suggest that the widespread scepticism about the ability of quantum theory to support a theory of causality is mistaken and rests on several misunderstandings. (shrink)

An epistemological interpretation of quantum mechanics hinges on the claim that the distinctive features of quantum mechanics can be derived from some distinctive features of an observational basis. Old and new variations of this theme are listed. The program has a limited success in non-relativistic quantum mechanics. The crucial issue is how far it can be extended to quantum field theory without introducing significant ontological postulates. A C*-formulation covers algebraic quantum field theory, but not the standard model. Julian Schwinger’s anabatic (...) methodology extended a strict measurement-based formulation of quantum mechanics through field theory. His extension also excluded the quark hypothesis and the standard model. Quarks and local gauge invariance are postulates that go beyond the limits of an epistemological interpretation of quantum mechanics. The ontological significance ascribed to these advances depends on the role accorded ontology. (shrink)

Conventional wisdom has it that chaotic behavior is either strongly suppressed or absent in quantum models. Indeed, some researchers have concluded that these considerations serve to undermine the correspondence principle, thereby raising serious doubts about the adequacy of quantum mechanics. Thus, the quantum chaos question is a prime subject for philosophical analysis. The most significant reasons given for the absence or suppression of chaotic behavior in quantum models are the linearity of Schrödinger’s equation and the unitarity of the time-evolution described (...) by that equation. Both are shown in this essay to be irrelevant by demonstrating that the crucial feature for chaos is the nonseparability of the Hamiltonian. That demonstration indicates that quantum chaos is likely to be exhibited in models of open quantum systems. A measure for probing such models for chaotic behavior is developed, and then used to show that quantum mechanics has chaotic models for systems having a continuous energy spectrum. The prospects of this result for vindicating the correspondence principle (or the motivation behind it, at least) are then briefly examined. (shrink)

The aim of this article is twofold. Recently, Lewis has presented an argument, now known as the "counting anomaly", that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the fact that (...) the composition principle, which holds true in standard quantum mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of such interpretations. Once this flaw is uncovered, the anomaly vanishes. (shrink)

Indispensability arguments for realism about mathematical entities have come under serious attack in recent years. To my mind the most profound attack has come from Penelope Maddy, who argues that scientific/mathematical practice doesn't support the key premise of the indispensability argument, that is, that we ought to have ontological commitment to those entities that are indispensable to our best scientific theories. In this paper I defend the Quine/Putnam indispensability argument against Maddy's objections.

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)