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.

A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the formal aspect has been improved by the use of certain mathematical theories, such as the theory of equipped spaces, and group theory. The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.

A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich–Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.

In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path which lies at the heart of the deBroglie-Bohm “ pilot-wave” interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths. This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as (...) GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton–Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized. (shrink)

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins (...) and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied. (shrink)

We use a new, distinctly “geometrical” interpretation of non-relativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D blockworld ontology. We argue for a geometrical interpretation whose fundamental ontology is one of spacetime relations as opposed to constructive entities whose time-dependent behavior is governed by dynamical laws. Our view rests on two formal results: Kaiser (1981 & 1990), Bohr & Ulfbeck (1995) and Anandan, (2003) showed independently that the Heisenberg commutation relations of NRQM follow from (...) the relativity of simultaneity (RoS) per the Poincaré Lie algebra. And, Bohr, Ulfbeck & Mottelson (2004a & 2004b) showed that the density matrix for a particular NRQM experimental outcome may be obtained from the spacetime symmetry group of the experimental configuration. This shows how the blockworld view is not only consistent with NRQM, not only an implication of our geometrical interpretation of NRQM, but it is necessary in a non-trivial way for explaining quantum interference and “non-locality” from the spacetime perspective. Together the formal results imply that contrary to accepted wisdom, NRQM, the measurement problem and so-called quantum non-locality do not provide reasons to abandon the 4D blockworld implication of RoS. But rather, the deep non-commutative structure of the quantum and the deep structure of spacetime as given by the Minkowski interpretation of special relativity (STR) are deeply unified in a 4D spacetime regime that lies between Galilean spacetime (G4) and Minkowski spacetime (M4). Taken together the aforementioned formal results allow us to model NRQM phenomena such as interference without the need for realism about 3N Hilbert space, establishing that the world is really 4D and that configuration space is nothing more than a calculational device. Our new geometrical interpretation of NRQM provides a geometric account of quantum entanglement and so-called non-locality free of conflict with STR and free of interpretative mystery. In section 2 we discuss the various tensions between STR and NRQM with respect to the dimensionality of the world. Section 3 is devoted to an explication of the Kaiser et al. results and their philosophical implications. Likewise, the Bohr et al. results and their implications are the subject of section 4. In section 5, we present our geometric interpretation of quantum entanglement and “non-locality.”. (shrink)

We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how (...) QM, obtained from relativistic quantum field theory per RBW, explains the twin-slit experiment and conclude by resolving the standard conceptual problems of QM, i.e., the measurement problem, entanglement and non-locality. (shrink)

One of the most challenging and fascinating issue in mathematical and theoretical physics concerns the possibility of identifying the logic underlying the so-called quantum universe, i.e., Quantum Mechanics and Quantum Gravity. Besides the sheer difficulty of the problem, inherent in the actual formulation of Quantum Mechanics—and especially of Quantum Gravity—to be used for such a task, a crucial aspect lies in the identification of the appropriate axiomatic logical proposition calculus to be associated to (...) such theories. In this paper the issue of the validity of the conventional principle of non-contradiction is called into question and is investigated in the context of non-relativistic Quantum Mechanics. In the same framework a modified form of the principle, denoted as 3-way PNC is shown to apply, which relates the axioms of quantum logic with the physical requirements placed by the Heisenberg Indeterminacy Principle. (shrink)

Traditionally, being a realist about something means believing in the independent existence of that something. In this line of thought, a scientific realist is someone who believes in the objective existence of the entities postulated by our best scientific theories. In metaphysical terms, what does that mean? In ontological terms, i.e., in terms of what exists, scientific realism can be understood as involving the adoption of a scientifically informed ontology. But according to some philosophers, a realistic attitude must go beyond (...) ontology. The way in which this requirement has been understood involves providing a metaphysics for the entities postulated by science, that is, answering questions about the nature of what ontology admits to exist. We discuss how two fashionable approaches face the challenge of providing a metaphysics for science: a form of naturalism and the Viking/Toolbox approach. Finally, we present a third way, which adopts the best of both approaches: the meta-Popperian method, which focuses on discarding the wrong alternatives, or better saying, the metaphysical profiles incompatible with certain theories. We present the meta-Popperian method, a metametaphysical method capable of objectively assessing which metaphysical profiles are incompatible with certain scientific theories. For this, we will use quantum mechanics as a case study, presenting some previously obtained results. As our focus is on methodological questions about the relationship between metaphysics and science; with this method, we can see how science can be used to avoid error in metaphysical issues. In our opinion, this would be a way to develop a productive relationship between science and metaphysics. (shrink)

In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general (...) very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory). (shrink)

A derivation by Fröhner of non-relativistic quantum mechanics via Fourier analysis applied to probability theory is not extendable to relativistic quantum mechanics because Schrödinger's positive definite probability density ψ*ψ is lost (Dirac's spin 1/2 case being the exception). The nature of the Fourier link then changes; it points to a redefinition of the probability scheme as an information carrying telegraph, the code of which is Born's as extended by Dirac and by Feynman. Hermitian symmetry (...) of the transition amplitude 〈ϕ∣ψ〉 between Dirac representations expresses reciprocity of preparation and measurement (the quantal coding and decoding), two equally active interventions of the physicist; as “the measurement perturbs the system” retrodiction implies retroaction evidenced in “delayed choice.” Reciprocity of knowledge and organization vindicates Wigner's claim that “reciprocal to the action of matter upon mind there exists a direct action of mind upon matter”: psychokinesis, branded by Jaynes as “a psychiatric disorder of the Copenhagen school.” As for factlike irreversibility, it is expressed by the enormity of the change rate from information to negentropy: while gain in knowledge is normal psychokinesis is paranormal. Stapp's recent discussion of psychokinesis in a quantum context should be resumed in association with an EPR correlation; an experimental test is proposed. (shrink)

1. Introduction Dirac's theory of the electron was the first widely accepted relativistic quantum theory, and it later provided the basis for constructing the modern electromagnetic theory of quantum electrodynamics. Whereas Dirac's theory in its simplest form describes relativistic freely-propagating massive non-chiral particles of spin-½, QED describes how such particles interact with one another electromagnetically, via a dynamical quantum field.

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation (...) that recover both of them in the non-relativistic limit. (shrink)

A recently proposed approach to relativistic quantum mechanics is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may (...) be a bit more surprising. (shrink)

Currently there are at least four sizeable projects going on to establish the gravitational acceleration of massive antiparticles on earth. While general relativity and modern quantum theories strictly forbid any repulsive gravity, it has not yet been established experimentally that gravity is attraction only. With that in mind, the Elementary Process Theory (EPT) is a rather abstract theory that has been developed from the hypothesis that massive antiparticles are repulsed by the gravitational field of a body of ordinary matter: (...) the EPT essentially describes the elementary processes by which the smallest massive systems have to interact with their environments for repulsive gravity to exist. In this paper we model a nonrelativistic, one-component massive system that evolves in time by the processes as described by the EPT in an environment described by classical fields: the main result is a semi-classical model of a process at Planck scale by which a non-relativistic onecomponent system interacts with its environment, such that the interaction has both gravitational and electromagnetic aspects. Some worked-out examples are provided, among which the repulsion of an antineutron by the gravitational field of the earth. The general conclusion is that the semi-classical model of the EPT corresponds to non-relativistic classical mechanics. Further research is aimed at demonstrating that the EPT has a model that reproduces the successful predictions of general relativity. (shrink)

The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it (...) is the ergodic demand what ultimately leads to the matrix formulation of quantum mechanics. The paper thus represents a step forward in the quest for an elucidation of the fundamentals of quantum mechanics. (shrink)

Theoretical physicists and philosophers of science tackle the conceptual problems of quantum mechanics from a variety of mathematical and philosophical angles in 18 papers, most from a conference at the University of Western Ontario in the autumn of 1994. Nearly half treat the largely uncharted territory of relativistic quantum mechanics and quantum field theory. Others provide innovative approaches to longstanding problems about measurement, irreversibility, nonlocality, contextualism, and the classical limit of quantum mechanics. (...) No index. Annotation copyright by Book News, Inc., Portland, OR. (shrink)

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandoned. Here we propose a nonlinear scalar (...) field theory able to reproduce the PWI for the Schrödinger and Klein–Gordon guiding waves. Our model relies on a relativistic ‘phase harmony’ condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the N particles cases in presence of entanglement and external (classical) electromagnectic fields. (shrink)

If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and final boundary conditions in non-relativistic quantum mechanics leads to the idea that the properties of macroscopic quantum systems, relevantly measuring instruments, are uniquely determined by the boundary conditions. An important element in reaching that conclusion is that preparations and (...) measurements belong in a special class because they involve many subsystems, at least some of which do not form superpositions of their physical properties before the boundary conditions are imposed. It is suggested that the primary role of the formalism of standard quantum mechanics is to provide the consistency condition on the boundary conditions rather than the properties of quantum systems. Expressions are proposed for assigning a set of (unmeasured) physical properties to a quantum system at all times. The physical properties avoid the logical inconsistencies implied by the no-go theorems because they are assigned differently from standard quantum mechanics. Since measurement outcomes are determined by the boundary conditions, they help determine, rather than are determined by, the physical properties of quantum systems. (shrink)

We review a proposal of how to complete non-relativistic Quantum Mechanics to a physically meaningful, mathematically precise and logically coherent theory. This proposal has been dubbed ETH-Approach to Quantum Mechanics, “E” standing for “Events,” “T” for “Trees,” and “H” for “Histories.” The ETH-Approach supplies the last one of three pillars Quantum Mechanics can be constructed upon in such a way that its foundations are solid and stable. Two of these pillars are well known. (...) The third one has been proposed quite recently; it implies a general non-linear stochastic law for the time-evolution of states of individual physical systems. (shrink)

The relational approach to tense holds that the now, passage, and becoming are to be understood in terms of relations between events. The debate over the adequacy of this framework is illustrated by a comparative study of the sense in which physical theories, (in)deterministic and (non)relativistic, can lend expression to the metaphysics at issue. The objective is not to settle the matter, but to clarify the nature of this metaphysics and to establish that the same issues are at stake (...) in the relational approach to value-definiteness and probability in quantum mechanics. They concern the existence of a unique present, respectively actuality, and a notion of identity over time that cannot be paraphrased in terms of relations. (shrink)

This thesis inquires what it means to interpret non-relativistic quantum mechanics (QM), and the philosophical limits of this interpretation. In pursuit of a scientific-realist stance, a metametaphysical method is expanded and applied to evaluate rival interpretations of QM, based on the conceptual distinction between ontology and metaphysics, for objective theory choice in metaphysical discussions relating to QM. Three cases are examined, in which this metametaphysical method succeeds in indicating what are the wrong alternatives to interpret QM in (...) metaphysical terms. The first two cases failed in doing so due to different kinds of underdetermination. In the third case, unlike underdetermination, where there are many choices to be made, a “null-determination” is proposed where there may be no metaphysical choices in the available metaphysical literature. Considering what has been discussed, an agnostic philosophic position is adopted concerning the possibility of interpreting QM from a scientific-realistic point of view. (shrink)

What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism . We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism , a (...) view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, although, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature, even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden. (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)

We argue that the experimental verification of Newtonian mechanics and of non-relativistic quantum mechanics do not imply that space is continuous. This provides evidence against the realist interpretation of the most mathematical parts of physics.

This paper discusses a claim by Clifton and Halvorson (2001) that, contrary to non-relativistic quantum mechanics, local operations can never destroy entanglement in relativistic quantum field theory. The impossibility of achieving local disentanglement would raise a threat for the mutual independence between microscopic subsystems. Here, we observe that Clifton and Halvorson no-go result rests on an unnecessarily strong notion of local operations, which we label absolutely local operations, and we argue that a weaker notion, namely (...) that of relatively local operations, is sufficient to guarantee that acting on one subsystem does not have non-local effects on another spacelike separated subsystem. We then show that one can achieve local disentanglement in relativistic quantum field theory by means of relatively local operations. In fact, we prove that, under the split property, there exists a class of disentangling relatively local operations. (shrink)

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.

Modern particle physics suggests an intriguing vision of physical reality: we are to imagine the symmetries of the world as fundamental, whereas the material constituents of the world are ontologically derivative of them. This paper develops a novel ontology for non-relativistic quantum mechanics which gives precise metaphysical content to this vision.

The purpose of the paper is to explore different aspects of the covariance of non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations the geometric phase associated with Schrödinger evolution is (...) non-invariant, and the significance of this result is briefly analysed. The covariance properties of Schrödinger dynamics are then brought to bear on certain versions of the modal interpretation of quantum mechanics. The conclusion that it is only relational properties that can be considered coordinate- or gauge-independent elements of reality is reinforced by appeal to the theory of quantum reference frames due to Aharonov and Kauffher. , Cambridge University Press ; pp. 45-70.). (shrink)

Experimental evidence of the last decades has made the status of ``collapses of the wave function'' even more shaky than it already was on conceptual grounds: interference effects turn out to be detectable even when collapses are typically expected to occur. Non-collapse interpretations should consequently be taken seriously. In this paper we argue that such interpretations suggest a perspectivalism according to which quantum objects are not characterized by monadic properties, but by relations to other systems. Accordingly, physical systems may (...) possess different properties with respect to different ``reference systems''. We discuss some of the relevant arguments, and argue that perspectivalism both evades recent arguments that single-world interpretations are inconsistent and eliminates the need for a privileged rest frame in the relativistic case. (shrink)

I wish to discuss some rather incomplete ideas concerning difficulties that arise in some parts of quantum mechanics. In general there have been no serious difficulties when we are dealing with a finite number of particles, but very essential difficulties arise as soon as we treat a system having an infinite number of degrees of freedom; for example, the theory of holes, which, because of the pair generation, requires an indefinite number of particles; also the Dirac non-relativistic (...) theory of light and the Pauli-Heisenberg relativistic quantum electro-dynamics, these being equivalent to systems consisting of an infinite number of particles. (shrink)

The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help (...) us in deciding matters concerning that problem, since that is a metaphysical problem rather than a quantum mechanical one. We argue further that weak PII is unmotivated on metaphysical grounds. We examine three metaphysical theses (bundle theory, counting, empiricism) that may provide reasons for one to sustain PII, and we conclude that weak PII gets no independent motivation from them. (shrink)

Applying the resolution–scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Itô process driven by the solutions of a Riccati equation. We verify that the corresponding Fokker–Planck equation is solved for a probability density corresponding to the squared modulus of the solution of the Schrödinger equation for the same problem. Inspired by the treatment of the one-dimensional case, we identify a generalization to time dependent problems in (...) any number of dimensions. The Itô process is then driven by a function which is identified as establishing the link between non-differentiable dynamics and standard quantum mechanics. This is the basis for the scale relativistic interpretation of standard quantum mechanics and, in the case of applications to chaotic systems, it leads us to identify quantum-like states as characterizing the entire system rather than the motion of its individual constituents. (shrink)

As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system’s dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct (...) state histories along some other, a phenomenon that David Albert has dubbed “non-narratability.” In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another. (shrink)

We study the non-relativistic (NR) limit of relativistic spacetimes in relation with the topology of the Universe. We first show that the NR limit of the Einstein equation is only possible in Euclidean topologies, i.e., for which the covering space is \(\mathbb {E}^3\). We interpret this result as an inconsistency of general relativity in non-Euclidean topologies and propose a modification of that theory which allows for the limit to be performed in any topology. For this, a second reference (...) non-dynamical connection is introduced in addition to the physical spacetime connection. The choice of reference connection is related to the covering space of the spacetime topology. Instead of featuring only the physical spacetime Ricci tensor, the modified Einstein equation features the difference between the physical and the reference Ricci tensors. This theory should be considered instead of general relativity if one wants to study a universe with a non-Euclidean topology and admitting a non-relativistic limit. (shrink)

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus—‘naturalised’ metaphysics supports both the acceptability (...) of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand. (shrink)

Our purpose in this paper is to delineate an ontology for quantum mechanics that results adequate to the formalism of the theory. We will restrict our aim to the search of an ontology that expresses the conceptual content of the recently proposed modal-Hamiltonian interpretation, according to which the domain referred to by non-relativistic quantum mechanics is an ontology of properties. The usual strategy in the literature has been to focus on only one of the interpretive (...) problems of the theory and to design an interpretation to solve it, leaving aside the remaining difficulties. On the contrary, our aim in the present work is to formulate a “global” solution, according to which different problems can be adequately tackled in terms of a single ontology populated of properties, in which systems are bundles of properties. In particular, we will conceive indistinguishability between bundles as a relation derived from indistinguishability between properties, and we will show that states, when operating on combinations of indistinguishable bundles, act as if they were symmetric with no need of a symmetrization postulate. (shrink)

This paper explores the consequences of the orthodox resolution of the measurement problem for the axiomatic base of non-relativistic elementary quantum mechanics. It is argued that the standard resolution of the measurement problem generates a paradox whose dissolution may be achieved through an enrichment of the axiomatic foundations of quantum mechanics. These results are also linked to some recent creative proposals by Nancy Cartwright concerning the nature of the so-called reduction of the wave packet.

Our purpose in this paper is to delineate an ontology for quantum mechanics that results adequate to the formalism of the theory. We will restrict our aim to the search of an ontology that expresses the conceptual content of the recently proposed modal-Hamiltonian interpretation, according to which the domain referred to by non-relativistic quantum mechanics is an ontology of properties. The usual strategy in the literature has been to focus on only one of the interpretive (...) problems of the theory and to design an interpretation to solve it, leaving aside the remaining difficulties. On the contrary, our aim in the present work is to formulate a “global” solution, according to which different problems can be adequately tackled in terms of a single ontology populated of properties, in which systems are bundles of properties. In particular, we will conceive indistinguishability between bundles as a relation derived from indistinguishability between properties, and we will show that states, when operating on combinations of indistinguishable bundles, act as if they were symmetric with no need of a symmetrization postulate. (shrink)

Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and (...) methodology for interpreting such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity. (shrink)

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an (...) external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter. (shrink)

A century after the advent of quantum mechanics and general relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell’s inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava–Lifshitz gravity. Here, we explore a recent proposal for a “real ensemble” non-local description of (...) class='Hi'>quantum mechanics, in which “particles” can copy each others’ observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as \ time)\, where \. Interestingly, this convergence is controlled by the absolute value of energy, suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem. (shrink)

The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of ‘absolute space’. When applied to classical mechanics, under the guise of an extended symmetry group, this procedure is known to lead to an equation of motion with inertial-like forces that are sourced by the mass distribution of the system itself. In this paper we follow a similar procedure and reformulate the Schrödinger equation of non-relativistic (...) quantum mechanics in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system, leaving no room for the notion of absolute space. (shrink)

I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level model to that of the high-level model that approximately (...) commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity. (shrink)

We discuss some methodological aspects of the relation between physics and metaphysics by dealing specifically with the case of non-relativistic quantum mechanics. Our main claim is that current attempts to productively integrate quantum mechanics and metaphysics are best seen as approaches of what should be called ‘the metaphysics of science’, which is developed by applying already existing metaphysical concepts to scientific theories. We argue that, in this perspective, metaphysics must be understood as an autonomous discipline. (...) It results that this metaphysics cannot hope to derive any kind of justification from science. Thus, one of the main motivations of such project, which is the obtaining of a scientifically respectable justification for the attribution of a single true metaphysical profile to the posits of a scientific theory, is doomed because of the emergence of metaphysical underdetermination from the outset. If metaphysics floats free from physics, which is a premise of such project of integration between these two areas, then it is always possible to attribute more than one metaphysical profile to dress physical entities. (shrink)

A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of (...) quantum mechanics that emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. (shrink)

Statistical mechanics is often taken to be the paradigm of a successful inter-theoretic reduction, which explains the high-level phenomena (primarily those described by thermodynamics) by using the fundamental theories of physics together with some auxiliary hypotheses. In my view, the scope of statistical mechanics is wider since it is the type-identity physicalist account of all the special sciences. But in this chapter, I focus on the more traditional and less controversial domain of this theory, namely, that of explaining (...) the thermodynamic phenomena.What are the fundamental theories that are taken to explain the thermodynamic phenomena? The lively research into the foundations of classical statistical mechanics suggests that using classical mechanics to explain the thermodynamic phenomena is fruitful. Strictly speaking, in contemporary physics, classical mechanics is considered to be false. Since classical mechanics preserves certain explanatory and predictive aspects of the true fundamental theories, it can be successfully applied in certain cases. In other circumstances, classical mechanics has to be replaced by quantum mechanics. In this chapter I ask the following two questions: I) How does quantum statistical mechanics differ from classical statistical mechanics? How are the well-known differences between the two fundamental theories reflected in the statistical mechanical account of high-level phenomena? II) How does quantum statistical mechanics differ from quantum mechanics simpliciter? To make our main points I need to only consider non-relativistic quantum mechanics. Most of the ideas described and addressed in this chapter hold irrespective of the choice of a (so-called) interpretation of quantum mechanics, and so I will mention interpretations only when the differences between them are important to the matter discussed. (shrink)

A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincare transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of non-relativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; (...) a motion in H becomes the usual Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations. (shrink)

I argue that a particle ontology naturally emerges from the basic dynamical equations of non-relativistic quantum mechanics, when the quantum continuity equation is realistically interpreted. This was recognized by J.J. Sakurai in his famous textbook “Modern Quantum Mechanics”, and then dismissed on the basis of the Heisenberg position–momentum uncertainty principle. In this paper, I show that the reasons of this rejection are based on a misunderstanding of the physical import of the uncertainty principle. As (...) a consequence, a particle ontology can be derived from the quantum formalism without the need of additional ad hoc assumptions, and therefore it cannot be regarded as “extra-structure”. (shrink)