Showing papers in "Foundations of Physics in 1983"
TL;DR: In this paper, a new proof of the impossibility of reconciling realism and locality in quantum mechanics is given, which makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems.
Abstract: A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics.
187 citations
TL;DR: In this article, the authors present examples of uniformly moving charge distributions that possess conserved electromagnetic stress tensors, which constitute stable systems with covariantly characterized electromagnetic mass and are dedicated to Paul Dirac for his 80th birthday.
Abstract: Examples of uniformly moving charge distributions that possess conserved electromagnetic stress tensors are exhibited. These constitute stable systems with covariantly characterized electromagnetic mass. This note, on a topic to which Paul Dirac made a significant contribution in 1938, is dedicated to him for his 80th birthday.
95 citations
TL;DR: In this paper, a comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics, and a sharp distinction is made between events, operational propositions, and the properties of physical systems.
Abstract: A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.
88 citations
TL;DR: In this paper, a formalism developed in previous papers for the description of continual observations of some quantities in the framework of quantum mechanics is re-obtained and generalized, starting from a more axiomatic point of view.
Abstract: A formalism developed in previous papers for the description of continual observations of some quantities in the framework of quantum mechanics is reobtained and generalized, starting from a more axiomatic point of view. The statistics of the observations of continuous state trajectories is treated from the beginning as a generalized stochastic process in the sense of Gel'fand. An effect-valued measure and an operation-valued measure on the σ-algebra generated by the cylinder sets in the space of trajectories are introduced. The properties of the characteristic functional for the “operation-valued stochastic process” are discussed and, through a suitableansatz, a significant class of such processes is explicitly constructed, which contains the examples of the preceding papers as particular cases.
86 citations
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TL;DR: Differential geometry, the contemporary heir of the infinitesimal calculus of the 17th century, appears today as the most appropriate language for the description of physical reality as discussed by the authors.
Abstract: Differential geometry, the contemporary heir of the infinitesimal calculus of the 17th century, appears today as the most appropriate language for the description of physical reality. This holds at every level: The concept of “connexion,” for instance, is used in the construction of models of the universe as well as in the description of the interior of the proton. Nothing is apparently more contrary to the wisdom of physicists; all the same, “it works.” The pages that follow show the conceptual role played by this geometry in some examples—without entering into technical details. In order to achieve this, we shall often have to abandon the complete mathematical rigor and even full definitions; however, we shall be able to give a precise description of the connection of ideas thanks to some elements of group theory.
83 citations
TL;DR: In this paper, the usefulness of the Wigner distribution function in collision theory is described, and it is shown how to apply it to specific collision problems, such as collision avoidance.
Abstract: This year marks the 50th anniversary of the birth of the celebrated Wigner distribution function. Many advances made in various areas of science during the 50 year period can be attributed to the physical insights that the Wigner distribution function provides when applied to specific problems. In this paper the usefulness of the Wigner distribution function in collision theory is described.
83 citations
TL;DR: In this article, it is argued that such rescalings naturally lead to the presence of torsion in the space-time derivative of a spinor, and it is further shown that, in standard general relativity, a circularly polarized gravitational wave produces a rotation effect along rays intersecting it similar to, and apparently consistent with, the local torsions of the Einstein-Cartan-Sciama-Kibble theory.
Abstract: Conformal rescalings of spinors are considered, in which the factor Ω, ine
AB ↦Ωe
AB, is allowed to be complex. It is argued that such rescalings naturally lead to the presence of torsion in the space-time derivative▽
a. It is further shown that, in standard general relativity, a circularly polarized gravitational wave produces a (nonlocal) rotation effect along rays intersecting it similar to, and apparently consistent with, the local torsion of the Einstein-Cartan-Sciama-Kibble theory. The results of these deliberations are suggestive rather than conclusive.
68 citations
TL;DR: In this article, a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes has been proposed, and the relation between current conservation and unitarity is used to establish relations between pair production and annihilation amplitudes and scattering.
Abstract: The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents.
67 citations
TL;DR: In this article, a new aether model based on a stochastic covariant distribution of subquantum motions (corresponding to a “vacuum state” alive with fluctuations and randomness) is discussed with respect to the present experimental and theoretical discussion of nonlocality in EPR situations.
Abstract: The introduction by Dirac of a new aether model based on a stochastic covariant distribution of subquantum motions (corresponding to a “vacuum state” alive with fluctuations and randomness) is discussed with respect to the present experimental and theoretical discussion of nonlocality in EPR situations. It is shown (1) that one can deduce the de Broglie waves as real collective Markov processes on the top of Dirac's aether; (2) that the quantum potential associated with this aether's modification, by the presence of EPR photon pairs, yields a relativistic causal action at a distance which interprets the superluminal correlations recently established by Aspect et al.; (3) that the existence of the Einstein-de Broglie photon model (deduced from Dirac's aether) implies experimental predictions which conflict with the Copenhagen interpretation in certain specific testable interference experiments.
62 citations
TL;DR: In this article, the causes and consequences of this practice are explored mathematically, and it is found that such an identification imposes severe constraints on the admissible states of the physical system.
Abstract: In orthodox quantum mechanics, it has virtually become the custom to identify properties of a physical system with operationally testable propositions about the system. The causes and consequences of this practice are explored mathematically in this paper. Among other things, it is found that such an identification imposes severe constraints on the admissible states of the physical system.
53 citations
TL;DR: In this paper, the nonlinear integro-differential equation, obtained from the coupled Maxwell-Dirac equations by eliminating the potential Aμ, is solved by iteration rather than perturbation.
Abstract: The nonlinear integro-differential equation, obtained from the coupled Maxwell-Dirac equations by eliminating the potential Aμ, is solved by iteration rather than perturbation. The energy shift is complex, the imaginary part giving the spontaneous emission. Both self-energy and vacuum polarization terms are obtained. All results, including renormalization terms, are finite.
TL;DR: In this article, the profound influence of the Wigner distribution function has been discussed in many areas of physics during its fifty years of existence, and the importance of this function is discussed.
Abstract: We discuss the profound influence which the Wigner distribution function has had in many areas of physics during its fifty years of existence.
TL;DR: In this paper, a generalized form of the Wheeler-Feynman absorber theory in an open expanding universe with a singularity at T = 0 is considered, and it is shown that the application of a four-vector reflection boundary condition at the singularity leads to the observed dominance of retarded radiation.
Abstract: The problem of the direction of electromagnetic time, i.e., the complete dominance of retarded electromagnetic radiation over advanced radiation in the universe, is considered in the context of a generalized form of the Wheeler-Feynman absorber theory in an open expanding universe with a singularity atT=0. It is shown that the application of a four-vector reflection boundary condition at the singularity leads to the observed dominance of retarded radiation; it also clarifies the role of advanced and retarded waves in the emission of very weakly absorbed radiation such as neutrinos.
TL;DR: The exact agreement between the Sommerfeld and Dirac results for the energy levels of the relativistic hydrogen atom (the "Sommerfeld Puzzle") is analyzed and explained in this paper.
Abstract: The exact agreement between the Sommerfeld and Dirac results for the energy levels of the relativistic hydrogen atom (the “Sommerfeld Puzzle”) is analyzed and explained.
TL;DR: In this paper, it was shown that the generalized Bell inequalities are conditions that must be satisfied by the probability functions of certain three-variable systems if they are to be expressible in terms of a single, nonnegative function.
Abstract: It is shown that the Bell inequalities are conditions that must be satisfied by the probability functions of certain three-variable systems if they are to be expressible in terms of a single, nonnegative function. The generalized Bell inequalities, or CHSH inequalities, play a similar role for four-variable systems. The physical significance of the results is discussed.
TL;DR: The Mansouri-Sexl and Sjodin point of view on clock synchronization in special relativity is maintained against various criticisms, taking into account also the recent view of stochastic electrodynamics as mentioned in this paper.
Abstract: The Mansouri-Sexl and Sjodin point of view on clock synchronization in special relativity is maintained against various criticisms, taking into account also the recent point of view of stochastic electrodynamics. Light speed invariance is also discussed in an intuitive way.
TL;DR: In this article, a natural one-to-one correspondence between continuous subspaces of nonrelativistic quantum and classical mechanics is established, thus exhibiting a close interrelation between physical uniformities for quantum states and compactifications of phase space.
Abstract: Uniformities describing the distinguishability of states and of observables are discussed in the context of general statistical theories and are shown to be related to distinguished subspaces of continuous observables and states, respectively. The usual formalism of quantum mechanics contains no such physical uniformity for states. Using recently developed tools of quantum harmonic analysis, a natural one-to-one correspondence between continuous subspaces of nonrelativistic quantum and classical mechanics is established, thus exhibiting a close interrelation between physical uniformities for quantum states and compactifications of phase space. General properties of the completions of the quantum state space with respect to these uniformities are discussed.
TL;DR: In this article, a new approach to measurement theory is presented, which is motivated by direct laboratory procedures as they are carried out in practice, and is developed within the quantum logic framework.
Abstract: We present a new approach to measurement theory. Our definition of measurement is motivated by direct laboratory procedures as they are carried out in practice. The theory is developed within the quantum logic framework. This work clarifies an important problem in the quantum logic approach; namely, where the Hilbert space comes from. We consider the relationship between measurements and observables, and present a Hilbert space embedding theorem. We conclude with a discussion of charge systems.
TL;DR: In this paper, a model theory is constructed that exhibits quantization on a cosmic scale, incorporating a fundamental length, of cosmic size, and preserving the weak, geometrical equivalence principle.
Abstract: A model theory is constructed that exhibits quantization on a cosmic scale. A holistic rationale for the theory is discussed. The theory incorporates a fundamental length, of cosmic size, and preserves the weak, geometrical equivalence principle. The momentum operator is an integral, nonlocal, naturally contravariant operator, in contrast to the usual quantum case. In the limit of high quantum numbers the theory reduces to classical physics, giving rise to a world which is quantized both on the microscopic and cosmic scale, each of which passes over to the usual macroscopic, continuous, classical, world in the highn limit. The theory is applied to two experimental situations, absorption lines in high-z quasars and elliptical rings around normal galaxies, with suggestive but not definitive results.
TL;DR: In this article, a probabilistic basis for these methods is presented in terms of the four-space formulation of relativistic quantum mechanics (FSF), and applications are presented to illustrate use of the many-body formalism.
Abstract: The complexity of the field theoretic methods used for analyzing relativistic bound state problems has forced researchers to look for simpler computational methods. Simpler methods such as the relativistic harmonic oscillator method employed in the description of extended hadrons have been investigated. They are considered phenomenological, however, because they lack a theoretical basis. A probabilistic basis for these methods is presented here in terms of the four-space formulation of relativistic quantum mechanics (FSF). The single-particle FSF is reviewed and its physical meaning is examined. The many-body single-parameter formalism is then developed. Applications are presented to illustrate use of the many-body formalism and demonstrate the ease with which relativistic bound state problems can be handled. A multiple-parameter formalism is constructed in the Appendix.
TL;DR: In the fifty-one years since its publication Dirac's magnetic monopole conjecture has stimulated a theoretical outpouring rich in variety as mentioned in this paper, the experimental techniques with which monopoles have been sought and the limits on monopole properties these searches have established.
Abstract: In the fifty-one years since its publication Dirac's magnetic monopole conjecture has stimulated a theoretical outpouring rich in variety. We review here the experimental techniques with which monopoles have been sought and we will describe the limits on monopole properties these searches have established.
TL;DR: A particle of molecular dimensions which can exist in two states is associated with a membrane pore through which molecules of a gas can pass as mentioned in this paper, but the gas molecules from two identical phases on either side of the membrane may pass only when the particle is in one particular state.
Abstract: A particle of molecular dimensions which can exist in two states is associated with a membrane pore through which molecules of a gas can pass. The gas molecules from two identical phases on either side of the membrane may pass only when the particle is in one particular state. If certain restrictions are imposed on the system, then the particle appears to act like a Maxwell's Demon(1) which “handles” the gas molecules during their passage through the pore.
TL;DR: In this article, three cosmologies which predict a variable Newtonian gravitational constant are discussed from theoretical and observational points of view, both from a theoretical and an observational point of view.
Abstract: In 1937 Dirac presented an argument, based on the socalled large dimensionless numbers, which led him to the conclusion that the Newtonian gravitational constantG changes with epoch. Towards the end of the last century Ernst Mach had given plausible arguments to link the property of inertia of matter to the large scale structure of the universe. Mach's principle also leads to cosmological models with a variable gravitational constant. Three cosmologies which predict a variableG are discussed in this paper both from theoretical and observational points of view.
TL;DR: The geometry of lattice universes in general is reviewed and particular attention is given to the 3-geometry of a 5-black hole model universe at the momentarily static phase of maximum expansion as an illustration of the insights to be won by considering symmetries and reflections as discussed by the authors.
Abstract: The geometry of lattice universes in general is reviewed, and particular attention is given to the 3-geometry of a 5-black hole model universe at the momentarily static phase of maximum expansion as an illustration of the insights to be won by considering symmetries and reflections. Three models for the black holes in this lattice universe are compared and contrasted. Reasons are given for working with Misner's “flange backup” model. The geometry interior to the individual tetrahedral cell of this lattice is compared and contrasted with the electrostatic field produced by a point charge located in the center of a cavity of the same shape that has perfectly conducting walls.
TL;DR: The inspiring "numerology" uncovered by Dirac, Eddington, Weyl, and Weyl as discussed by the authors can be explained and derived when it is slightly modified so to connect the "gravitational world" with the "strong world" (hadron), rather than with the electromagnetic one.
Abstract: The inspiring “numerology” uncovered by Dirac, Eddington, Weyl,et al. can be explained and derived when it is slightly modified so to connect the “gravitational world” (cosmos) with the “strong world” (hadron), rather than with the electromagnetic one.
TL;DR: In this article, the authors present two alternative structures of the asymptotic state space of quantum electrodynamics, i.e., infraparticle and infravacuum.
Abstract: Scattering states in quantum electrodynamics can not be represented in Fock space (i.e., as states with finitely many incoming and outgoing free photons), since most collisions involve the emission of infinitely many soft photons. At present, there exist two alternative proposals for an appropriately modified structure of the asymptotic state space of quantum electrodynamics. According to the “infraparticle” proposal, each charged particle would be accompanied by an appropriate cloud of infinitely many soft photons, whereas according to the “infravacuum” proposal these clouds would be replaced by a common soft photon background. The second (less popular) idea is illustrated and motivated here by simple model calculations.
TL;DR: In this paper, the Finslerian curvature tensor tensor is used to construct the Lagrangian of the field equations in the static case, and the status of the conservation laws proves to be similar to that in the theory of the Yang-Mills field.
Abstract: The analysis of a previous paper (see Ref. 1), in which the possibility of a Finslerian generalization of the equations of motion of gravitational field sources was demonstrated, is extended by developing the Finslerian generalization of the gravitational field equations on the basis of the complete contractionK = Kljlj of the Finslerian curvature tensorKljhk(x, y). The relevant Lagrangian is constructed by the replacement of the directional variableyi inK by a vector fieldyi(x), so that the notion of osculation may be regarded as the key concept on which the approach is based. The introduction of the auxiliary vector fieldyi(x) is shown to be of physical significance, for the field equations refer not only to the proper field variables but also to a special coordinate system associated withyi(x) through the Clebsch representation of the latter. The status of the conservation laws proves to be similar to that in the theory of the Yang-Mills field. By choosing a special Finslerian metric function we elucidate in detail the structure of the field equations in the static case.
TL;DR: In this article, a model of dissipative quantum dynamics with a nonlinear friction term is applied to systems periodic in time and the model is compared with the standard approaches based on the Floquet theorem.
Abstract: A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. The implication of a nonlinear evolution for Ludwig's axiomatization is briefly outlined.
TL;DR: The Weyl-Dirac theory of gravitation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe as discussed by the authors.
Abstract: The Weyl-Dirac theory of gravitation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe. One is led to a natural gauge giving\({{\dot G} \mathord{\left/ {\vphantom {{\dot G} G}} \right. \kern-
ulldelimiterspace} G} = - 5.5 \times 10^{ - 12} y^{ - 1} \). This is smaller by about a factor of ten than the value obtained on the basis of Dirac's large number hypothesis.
TL;DR: In this article, it was shown that the appearance of accidental degeneracy in the energy levels of a given Hamiltonian is not due to a symmetry group, and the relation between accidental degeneracies and symmetry group merits further probing.
Abstract: It is usually assumed that the appearance of accidental degeneracy in the energy levels of a given Hamiltonian is due to a symmetry group. By considering the elementary problem of a rotator with spin-orbit coupling, when the strength of the latter is equal to the inverse of the moment of inertia, we find that this assumption does not explain the degeneracy of all the levels of the Hamiltonian. Thus the relation between accidental degeneracies and symmetry group merits further probing.