The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the (...) determination of coordinate and momentum is always positive (non zero).A “functional” formulation of classical mechanics was suggested. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta for not too long time intervals. Corrections to the Newton trajectories are computed. An interpretation of quantum mechanics is attempted in which both classical and quantum mechanics contain fundamental randomness. Instead of an ensemble of events one introduces an ensemble of observers. (shrink)

We show: (1) It is possible to produce the three familiar statistics without referring to the problem of distinguishability; (2) what really distinguishes elementary particles is the correlation existing among them; (3) correlations existing among quantum particles, positive for bosons and negative form fermions, are completely different in character.

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) (...) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories. (shrink)

The consequences of the following definition of indistinguishability are analyzed. Indistinguishable classical or quantum particles are identical classical or quantum particles in a state characterized by a probability measure, a statistical operator respectively, which is invariant under any permutation of the particles. According to this definition the particles of classical Maxwell-Boltzmann statistics are indistinguishable.

The point of departure for this article is Werner Heisenberg’s remark, made in 1929: “It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which (...) seems entirely adequate for the treatment of atomic processes.” The cost of this discovery, at least in Heisenberg’s and related interpretations of quantum mechanics, is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future. (shrink)

We examine the problem of the existence (in classical and/or quantum physics) of longitudinal limitations of measurability, defined as limitations preventing the measurement of a given quantity with arbitrarily high accuracy. We consider a measuring device as a generalized communication system, which enables us to use methods of information theory. As a direct consequence of the Shannon theorem on channel capacity, we obtain an inequality which limits the accuracy of a measurement in terms of the average power (...) necessary to transmit the information content of the measurement itself. This inequality holds in a classical as well as in a quantum framework. (shrink)

Bewildering features of modern physics, such as relativistic space-time structure and the peculiarities of so-called quantum statistics, challenge traditional ways of conceiving of objects in space and time. Interpreting Bodies brings together essays by leading philosophers and scientists to provide a unique overview of the implications of such physical theories for questions about the nature of objects. The collection combines classic articles by Max Born, Werner Heisenberg, Hans Reichenbach, and Erwin Schrodinger with recent contributions, including several papers that (...) have never before been published. -/- The book focuses on the microphysical objects that are at the heart of quantum physics and addresses issues central to both the "foundational" and the philosophical debates about objects. Contributors explore three subjects in particular: how to identify a physical object as an individual, the notion of invariance with respect to determining what objects are or could be, and how to relate objective and measurable properties to a physical entity. The papers cover traditional philosophical topics, common-sense questions, and technical matters in a consistently clear and rigorous fashion, illuminating some of the most perplexing problems in modern physics and the philosophy of science. (shrink)

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a ‘quantum connection’ stubbornly (...) persists in the literature, even though it has also been criticized frequently. Here we shall argue that although this criticism is justified, the proposed alternative solutions have often been wrong and have not put the paradox in its right perspective. In fact, the Gibbs paradox is unrelated to fundamental issues of particle identity; only distinguishability in a pragmatic sense plays a role , and in principle the paradox always is there as long as the concept of a particle applies at all. In line with this we show that the paradox survives even in quantum mechanics, in spite of the quantum mechanical symmetrization postulates. (shrink)

A proposition is associated in classical mechanics with a subset of phase space, in quantum logic with a projection in Hilbert space, and in both cases with a 2-valued observable or test. A theoretical statement typically assigns a probability to such a pure test. However, since a pure test is an idealization not realizable experimentally, it is necessary — to give such a statement a practical meaning — to describe how it can be approximated by feasible tests. This (...) gives rise to a search for a formal representation of feasible tests, which leads via mixed tests (weighted means of pure tests) to vague tests (convex sets of mixed tests). A model is described in which the latter form a continuous lattice; the pure and mixed tests are the maximal elements and the feasible tests form a basis. Each type of test has its own logic; this is illustrated by the passage from mixed tests to pure tests, which corresponds to the transition from L to classical logic. (shrink)

The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system describing in terms of ray trajectories, for a stationary refractive medium, a very wide family of wave-like phenomena (including diffraction and interference) going much beyond the limits of the geometrical optics (“eikonal”) approximation, which is contained as a simple limiting case. Due to the fact, moreover, that the time independent Schrödinger equation is itself a Helmholtz-like equation, the same mathematics holding for a classical optical (...) beam turns out to apply to a quantum particle beam moving in a stationary force field, and leads to a system of Hamiltonian equations providing exact and deterministic particle trajectories and dynamical laws, and containing the laws of Classical Mechanics in the eikonal limit. (shrink)

Quantum physics is often perceived as a weird and abstract theory, which physicists must use in order to make correct predictions. But many recent experiments have shown that the weirdness of the theory simply mirrors the weirdness of phenomena: it is Nature itself, and not only our description of it, that behaves in an astonishing way. This book selects those, among these typical quantum phenomena, whose rigorous description requires neither the formalism, nor an important background in (...) class='Hi'>physics.The first part of the book deals with the phenomenon of single-particle interference, covering the historical questions of wave-particle duality, objective randomness and the boundary between the quantum and the classical world, but also the recent idea of quantum cryptography. The second part introduces the modern theme of entanglement, by presenting two-particle interference phenomena and discussing Bell's inequalities. A concise review of the main interpretations of quantum physics is provided. (shrink)

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than (...) in classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics. (shrink)

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorisation. By interpreting physically this mathematical fact, we show that it provides a natural way to describe (...) the “Heisenberg cut”, as well as a unified mathematical model including both quantum and classical physics, appearing as required incommensurable facets in the description of nature. (shrink)

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born (...) of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers. (shrink)

The discussion of different principles of additivity for probability functions has been largely focused on the personalist interpretation of probability. Very little attention has been given to additivity principles for physical probabilities. The form of additivity for quantum probabilities is determined by the algebra of observables that characterize a physical system and the type of quantum state that is realizable and preparable for that system. We assess arguments designed to show that only normal quantum states are realizable (...) and preparable and, therefore, quantum probabilities satisfy the principle of complete additivity. We underscore the little remarked fact that unless the dimension of the Hilbert space is incredibly large, complete additivity in ordinary non-relativistic quantum mechanics reduces to countable additivity. We then turn to ways in which knowledge of quantum probabilities may constrain rational credence about quantum events and, thereby, constrain the additivity principle satisfied by rational credence functions. (shrink)

Substantivalists claim that spacetime enjoys an existence analogous to that of material bodies, while relationalists seek to reduce spacetime to sets of possible spatiotemporal relations. The resulting debate has been central to the philosophy of space and time since the Scientific Revolution. Recently, many philosophers of physics have turned away from the debate, claiming that it is no longer of any relevance to physics. At the same time, there has been renewed interest in the debate among physicists working (...) on quantum gravity, who claim that the conceptual problems which they face are intimately related to interpretative questions concerning general relativity . My goal is to show that the physicists are correct--there is a close relationship between the interpretative issues of classical and quantum gravity. ;In the first part of the dissertation I challenge the received view that substantivalism has a commanding advantage over relationalism on grounds internal to GR. I argue that this view is based on a misconception of the relationships between realism and substantivalism, and between empiricism and relationalism. This has led to a narrow conception of relationalism. Once this is relinquished it can be seen that none of the standard arguments in favor of substantivalism are cogent. ;In the second part of the dissertation, I consider the way in which considerations arising out of quantum gravity bear upon the substantival-relational debate. I develop a framework in which to discuss the interpretative problems of gauge theories and place GR in this context. From this perspective, I provide a taxonomy of interpretative options, and show how the hole argument arises naturally as a consequence of gauge freedom. This means that certain substantivalist interpretations of GR render the theory indeterministic. In the final chapter, I argue that, far from being a drawback, this presents an opportunity for substantivalists. Examples from quantum mechanics, quantum field theory, and quantum gravity, are used to demonstrate that the ambiguities inherent in quantization can lead to an interpretative interplay between theories. In the case of quantum gravity, this means that substantivalism and relationalism suggest, and are suggested by, distinct approaches to quantizing GR. (shrink)

In this work we try to study theories of causation based upon causal processes and causal interactions in the context of classical and quantum physics. Our central aim is to find out whether such causal theories are compatible with the world picture suggested by contemporary theories of physics. In the first part, we review, compare and try to place among more general taxonomical schemes, the causal theories by Russell (the causal lines approach), Reichenbach (mark method, probabilistic (...) causality and the principle of common cause), Salmon (mark method, structure, invariant and conserved quantities approaches) and Dowe (conserved quantity theory). In the second part of the work, we deal with some problems that process theories of causation face whenever one tries to define, rigorously, causal concepts (e.g. “causal process” or “conjunctive common cause”) in the context of classical relativistic physical theories (van Dam – Wigner particle theory, the free Klein-Gordon field, classical electromagnetic theory) as well as quantum theories (algebraic relativistic quantum field theory). In this vein, special attention has been given to the locality problem in physical theories as it emerges from the structure of local classical the quantum theories (semantic locality), the relation between global and local conditions for physical systems (global and local determinism) as well as the problem of action at a distance, which is of central importance for the theories of causation under examination (Bell’s inequalities, EPR paradox, Reeh-Schlieder theorem and local independence conditions). We argue for three different theses: first, there are physical theories in the context of which it is impossible even to formulate the necessary physical hypotheses that allow us to define basic causal concepts and causal principles; second, there are physical theories which allow us to formulate these hypotheses only ad hoc; finally, in some cases it is necessary to revise basic causal principles and concepts bequeathed by the philosophical tradition. (shrink)

The quantum harmonic oscillator is described in terms of two basic sets of coordinates: linear coordinates x, px and angular coordinates eiφ, Pφ (action-angle variables). The angular “coordinate” eiφ is assumed unitary, the conjugate momentum pφ is assumed Hermitian, and eiφ and pφ are assumed to be a canonical pair. Two transformations are defined connecting the angular coordinates to the linear coordinates. It is found that x, px can be physical, i.e., Hermitian and canonical, only under constraints on the (...) pφ eigenvalue spectrum. The conclusion is that eiφ can be a unitary operator. A parallel analysis of the classical harmonic oscillator is done with equivalent results. (shrink)

In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot (...) get by without attributing energy to the electromagnetic field, matter may still have electromagnetic potential energy. Indeed, if we take the matter to be represented by the Dirac field, then it will possess potential energy. Thus, potential energy reappears. Upon field quantization, the potential energy of the Dirac field becomes an interaction term in the Hamiltonian operator of quantum electrodynamics. (shrink)

This historico-critical analysis of the concept of mass is the third in Jammer's series of studies of fundamental physical concepts. His fascinating account traces its intricate historical evolution from early notions of matter and the medieval concept of mass as quantitas materiae to the dynamic conceptions of mass. The concept is followed through the three stages of conceptualization ; systematization ; and formalization. Jammer further treats mass in relation to the electromagnetic theories; special and general relativity; quantum mechanics and (...) the theory of elementary particles; and the modern "space-theories" of matter. He concludes that no final clarification of the concept has yet been attained, despite the efforts of both physicists and philosophers. This difficult material is handled with great scholarship and control, skillfully interpreted, and concisely presented --B. J. H. (shrink)

Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. (...) We first take a look at the algebraic description of both classical and quantum observables in terms of Jordan–Lie algebras and show how the two algebraic structures are the precise mathematical manifestation of the twofold role of observables. Then, we turn to the geometric reformulation of quantum kinematics in terms of Kähler manifolds. A key achievement of this reformulation is to show that the twofold role of observables is the constitutive ingredient defining what an observable is. Moreover, it points to the fact that, from the restricted point of view of the transformational role of observables, classical and quantum kinematics behave in exactly the same way. Finally, we present Landsman’s general framework of Poisson spaces with transition probability, which highlights with unmatched clarity that the crucial difference between the two kinematics lies in the way the two roles of observables are related to each other. (shrink)

Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. (...) We first take a look at the algebraic description of both classical and quantum observables in terms of Jordan–Lie algebras and show how the two algebraic structures are the precise mathematical manifestation of the twofold role of observables. Then, we turn to the geometric reformulation of quantum kinematics in terms of Kähler manifolds. A key achievement of this reformulation is to show that the twofold role of observables is the constitutive ingredient defining what an observable is. Moreover, it points to the fact that, from the restricted point of view of the transformational role of observables, classical and quantum kinematics behave in exactly the same way. Finally, we present Landsman’s general framework of Poisson spaces with transition probability, which highlights with unmatched clarity that the crucial difference between the two kinematics lies in the way the two roles of observables are related to each other. (shrink)

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

We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field, with the purpose of revealing the mechanism that takes it from the initially classical description to the final quantum-mechanical one. The combined effect of the zpf and the radiation reaction force results, after a characteristic time lapse, in the loss of the initial conditions and the concomitant irreversible transition of the dynamics to a stationary regime controlled by the field. In this (...) regime, the canonical variables x, p become expressed in terms of the dipolar response functions to a set of field modes. A proper ordering of the response coefficients leads to the matrix representation of quantum mechanics, as was proposed in the early days of the theory, and to the basic commutator x^,p^=iħ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left[ {\hat{x}},{\hat{p}}\right] =i\hbar $$\end{document}. Further, the connection with the corresponding Fokker–Planck equation valid in the Markov approximation, allows one to obtain the radiative corrections of qed. These results reaffirm the essentially electrodynamic and stochastic nature of the quantum phenomenon, as proposed by stochastic electrodynamics. (shrink)

Koopman-von Neumann in the 30’s gave an operatorial formulation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for classical path-integral) to distinguish it from the quantum mechanical one, which we will indicate with QPI. In the CPI two Grassmannian partners of time make their natural appearance and in this manner time becomes something like a three dimensional supermanifold. Next (...) we introduce a metric in this supermanifold and show that a particular choice of the supermetric reproduces the CPI while a different one gives the QPI. (shrink)

We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather (...) that the classical notion is overdetermined. (shrink)

The standard interpretation of quantum physics (QP) and some recent generalizations of this theory rest on the adoption of a rerificationist theory of truth and meaning, while most proposals for modifying and interpreting QP in a “realistic” way attribute an ontological status to theoretical physical entities (ontological realism). Both terms of this dichotomy are criticizable, and many quantum paradoxes can be attributed to it. We discuss a new viewpoint in this paper (semantic realism, or briefly SR), which (...) applies both to classical physics (CP) and to QP. and is characterized by the attempt of giving up verificationism without adopting ontological realism. As a first step, we construct a formalized observative language L endowed with a correspondence truth theory. Then, we state a set of axioms by means of L which hold both in CP and in QP. and construct a further language Lv which can express bothtestable andtheoretical properties of a given physical system. The concepts ofmeaning andtestability do not collapse in L and Le hence we can distinguish between semantic and pragmatic compatibility of physical properties and define the concepts of testability and conjoint testability of statements of L and Le. In this context a new metatheoretical principle (MGP) is stated, which limits the validity of empirical physical laws. By applying SR (in particular. MGP) to QP, one can interpret quantum logic as a theory of testability in QP, show that QP is semantically incomplete, and invalidate the widespread claim that contextuality is unavoidable in QP. Furthermore. SR introduces some changes in the conventional interpretation of ideal measurements and Heisenberg’s uncertainty principle. (shrink)

Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as (...) a method of abstracting away from the messy details of microphenomena, not only in physics, but in other sciences as well. (shrink)

This work first explicates the philosophy of classical and quantum fields and particles. I am interested in determining how science can have a metaphysical dimension, and then with the claim that the quantum revolution has an important metaphysical component. I argue that the metaphysical implications of a theory are properties of its models, as classical mechanics determines properties of atomic diversity and temporal continuity with its representations of distinct, continuous trajectories. ;It is often suggested that (...) class='Hi'>classical statistical physics requires that many particle states be represented so that permuting properties leads to distinct states; this implies that individuals can be reidentified across possible worlds in a non-qualitative way. I show there is no evidence for this conclusion, an important result, for it is claimed that quantum particles are not individuals. This claim is based on the misconception about classical statistics, but also on a conflation of notions of identity; I show that, while transworld identity is incompatible with quantum mechanics, other classical notions may be consistently ascribed. I also give a field-particle distinction that applies usefully in both quantum and classical domains. In the former the distinction helps defeat claims of underdetermined by data, in the latter it helps provide a minimal field metaphysics. ;Next I tackle renormalisation: I show how divergences occur in approximate, perturbative calculations, and demonstrate how finite, empirically verified, answers are obtained. These techniques seem to show that the predictions are not logical consequences of the exact theory. I use the techniques of the renormalisation group to establish that perturbative renormalised quantum field theory does indeed approximate the consequences of field theory. ;Finally, I discuss the idea that renormalisation proves that there can be no quantum theory of everything, only a patchwork of effective theories. The preceding chapter shows that renormalisation demonstrates only that the picture is consistent, and this is insufficient to show that physics must be phenomenological. (shrink)

This is an extended essay review of Tanya and Jeffrey Bub’s Totally Random: Why Nobody Understands Quantum Mechanics: A serious comic on entanglement. We review the philosophical aspects of the book, provide suggestions for instructors on how to use the book in a class setting, and evaluate the authors’ artistic choices in the context of comics theory. Although Totally Random does not defend any particular interpretation of quantum mechanics, we find that, in its mode of presentation, Totally Random (...) is a beautiful expression and illustration of the information-theoretic interpretation and its value. (shrink)

We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so-called transformers of information, basic processes are information processes and statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of flows of information in cognitive (...) and social systems, since a p-adic metric gives a quite natural description of the ability to form associations. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, (...) which is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Based on the hypothesis that the (non-reversible) arrow of time is intrinsic in any system, no matter how small, the consequences are discussed. Within the framework of local quantum physics it is shown how such a semi-group action of time can consistently be extended to that of the group of spacetime translations in Minkowski space. In presence of massless excitations, however, there arise ambiguities in the theoretical extensions of the time translations to the past. The corresponding loss of (...) quantum information on states upon time is determined. Finally, it is explained how the description of operations in classical terms combined with constraints imposed by the arrow of time leads to a quantum theoretical framework. These results suggest that the arrow of time is fundamental in nature and not merely a consequence of statistical effects on which the Second Law is based. (shrink)

We give a partial answer to the question whether the Schrödinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrödinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of (...) Nelson’s stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables. The main motivation of this paper is to provide a step for constructing a Newtonian theory which would approximately reproduce quantum mechanics both in unitary evolution and measurement regimes. (shrink)

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is (...) proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added. (shrink)

We formulate from first principles a theory of stochastic processes in configuration space. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schrödinger equation, which is derived here (...) with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section. (shrink)

According to certain interpretations of quantum mechanics, the behavior of some physical systems is random—that is, certain current states of physical systems are related to other current states and the set of possible future states in a probabilistic, rather than a deterministic, fashion. This account of physical systems seems to conflict with the claim that there is an omnipotent God—that is, a God Who can efficaciously bring about any logically possible creaturely state, and Who can cause efficacious secondary causes—and (...) so raises problems for classical theism. After explaining these problems, I provide a solution to them based upon a version of hylomorphism, which I call Theistic Hylomorphism with Randomness. On this view, it can be affirmed that the physical world is both random and in determinate states, and divine omnipotence can be upheld in a random world. After presenting this version of hylomorphism and showing how it defeats the problems for classical theism raised by quantum mechanics, I defend it against three objections. (shrink)

The present essay aims at broadening the recent discussion on the issue of holism vs. particularism in quantum physics. I begin with a clarification of the relation between the holism/particularism debate and the discussion of supervenience relation. I then defend particularism in physics (including quantum physics) by considering a new classification of properties of physical systems. With such a classification, the results in the Bell theorem are shown to violate spatial separability but not physical particularism.