Showing papers in "Foundations of Physics in 1997"
TL;DR: In this paper, the dynamical equations of quantum mechanics are rewritten in the form of dynamical equation for the measurable, positive marginal distribution of the shifted, rotated, and squeezed quadrature introduced in the so-called "symplectic tomography" and a comparison with the well-known quasi-probabilities approach is given.
Abstract: The dynamical equations of quantum mechanics are rewritten in the form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated, and squeezed quadrature introduced in the so-called “symplectic tomography”. Then the possibility of a purely classical description of a quantum system as well as a reinterpretation of the quantum measurement theory is discussed and a comparison with the well-known quasi-probabilities approach is given. Furthermore, an analysis of the properties of this marginal distribution, which contains all the quantum information, is performed in the framework of classical probability theory. Finally, examples of the harmonic oscillator's states dynamics are treated.
218 citations
TL;DR: Ungar et al. as discussed by the authors introduced and explored gyrogroup theory and its applications, exposing the fascinating interplay between Thomas precession of special relativity theory and hyperbolic geometry.
Abstract: Gyrogroup theory and its applications is introduced and explored, exposing the fascinating interplay between Thomas precession of special relativity theory and hyperbolic geometry. The abstract Thomas precession, called Thomas gyration, gives rise to grouplike objects called gyrogroups [A, A. Ungar, Am. J. Phys.59, 824 (1991)] the underlying axions of which are presented. The prefix gyro extensively used in terms like gyrogroups, gyroassociative and gyrocommutative laws, gyroautomorphisms, and gyrosemidirect products, stems from their underlying abstract Thomas gyration. Thomas gyration is tailor made for hyperbolic geometry. In a similar way that commutative groups underlie vector spaces, gyrocommutative gyrogroups underlie gyrovector spaces. Gyrovector spaces, in turn, provide a most natural setting for hyperbolic geometry in full analogy with vector spaces that provide the setting for Euclidean geometry. As such, their applicability to relativistic physics and its spacetime geometry is obvious.
86 citations
TL;DR: The theory, experimental evidence and fundamental physical consequences concerning the existence of families of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ < ∞ are presented in this paper.
Abstract: We present the theory, the experimental evidence and fundamental physical consequences concerning the existence of families of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞, which are solutions of the homogeneuous wave equation, the Maxwell equations, and Dirac, Weyl, and Klein-Gordon equations.
57 citations
TL;DR: In this article, a probabilistic common cause of superluminal correlations between events represented by projections in local observable algebras pertaining to spacelike separated spacetime regions V1 and V2 is formulated in terms of relativistic quantum field theory.
Abstract: Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V1) andA(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events inA(V1) andA(V2) have a genuinely probabilistic common cause, then the local algebrasA(V1) andA(V2) must be statistically independent in the sense of C*-independence.
48 citations
TL;DR: In this article, two spaces with nontrivial translational translational Chern-Simons forms are discussed, first within the classical Einstein-Cartan Dirac theory and second in the quantum heat kernel approach to the Dirac operator, in contrast to what has been assumed previously.
Abstract: Thetranslation Chern-Simons type three-formcoframe∧torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan fourform. Following Chandia and Zanelli, two spaces with nontrivial translational Chern-Simons forms are discussed. We then demonstrate, first within the classical Einstein-Cartan-Dirac theory and second in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.
43 citations
TL;DR: The concept of TI is extended to the cases when systems are described without the use of probability concept and can be considered, when nonzero, as a quantitative SB measure in the system under study.
Abstract: A connection between two fundamental concepts of information and symmetry breaking (SB) is established A concept called transform information (TI) is introduced The known information measures (Hartley, von Neumann-Shannon-Wiener, Fisher informations, Renyi entropies) can be derived as (or mathematically expressed by) the particular forms of TI for certain transforms of a physical systems (when they are described by the probability measures) As TI is zero when the system is invariant under respective transform, it can be considered, when nonzero, as a quantitative SB measure in the system under study The classical information measures that are derived from TI also can be perceived as SB measures This fact is a base for assigning a sense to information The concept of TI is extended to the cases when systems are described without the use of probability concept
38 citations
TL;DR: In this article, it was shown that the set of points on the unit sphere in cartesian n!-space is surjective with the set this article of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and the symmetry group of this subset of matrices.
Abstract: The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n!-space is surjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices.
30 citations
26 citations
26 citations
TL;DR: In this paper, it was shown that covariant electromagnetic Two-Body Dirac equations (in Breit-like form) are just what is needed to correct the covariant Eddington Gaunt equation without resorting to Breit's version of retardation.
Abstract: G. Breit's original paper of 1929 postulates the Breit equation as a correction to an earlier defective equation due to Eddington and Gaunt, containing a form of interaction suggested by Heisenberg and Pauli. We observe that manifestly covariant electromagnetic Two-Body Dirac equations previously obtained by us in the framework of Relativistic Constraint Mechanics reproduce the spectral results of the Breit equation but through an interaction structure that contains that of Eddington and Gaunt. By repeating for our equation the analysis that Breit used to demonstrate the superiority of his equation to that of Eddington and Gaunt, we show that the historically unfamiliar interaction structures of Two-Body Dirac equations (in Breit-like form) are just what is needed to correct the covariant Eddington Gaunt equation without resorting to Breit's version of retardation.
25 citations
TL;DR: In this article, the Coulomb problem in the framework of off-shell electrodynamics was studied and a straightforward solution of the classical equations of motion, for a test event traversing the field induced by a fixed event (an event moving uniformly along the time axis at a fixed point in space) was presented.
Abstract: Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10−6 seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics.
TL;DR: In this article, the authors consider a spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane.
Abstract: We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection amplitude and show that there is an infinite ladder of resonances; analyzing the resonance pole trajectories, we show that half of them turn into true embedded eigenvalues provided the flux through the loop is an integer or half-integer multiple of the flux unit hc/e. We also describe a general method to solve the scattering problem on graphs of which the present model is a simple particular case. Finally, we discuss ways in which a state localized initially at the loop decays.
TL;DR: In this paper, the authors reviewed old and recent ideas concerning the nature of time, starting from Mach's refusal of Newton's absolute time, and concluded that the slowing down of moving clocks is a real phenomenon.
Abstract: Old and recent ideas concerning the nature of time are reviewed, starting from Mach's refusal of Newton's absolute time. Many experiments show that the slowing down of moving clocks is a real phenomenon. Such must then also be the so-called “twin paradox,” which owes its name to its evident incompatibility with the philosophy of relativism (not to be confused with the theory of relativity). The Lorentz reformulation of special relativity started by postulating physical effects of the ether, but accepted Einstein's clock synchronization. Only because of this Lorentz could not understand the advantages of an easily deducible different theory. As stressed by Popper, one of the main problems of the usual approach is the introduction of a superdeterministic universe. Recent results obtained by the author show that a theory is possible, based on relative time but on absolute simultaneity, in which the conceptual difficulties of relativity are avoided.
TL;DR: In this paper, it was shown that non-unitary deformations, including q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other non-canonical deformations have a number of problematic properties when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of numerical predictions, loss loss of the axions of special relativity, and others.
Abstract: The most majestic scientific achievement, of this century in mathematical beauty, axiomatic consistency, and experimental verifications has been special relativity with its unitary structure at the operator level, and canonical structure at the classical levels, which has turned out to be exactly valid for point particles moving in the homogenenous and isotropic vacuum (exterior dynamical problems). In recent decades a number of authors have studied nonunitary and noncanonical theories, here generally calleddeformations for the representation of broader conditions, such as extended and deformable particles moving within inhomogeneous and anisotrophic physical media (interior dynamical problems). In this paper we show that nonunitary deformations, including, q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other deformations, even thoughmathematically correct, have a number of problematic aspects ofphysical character when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the classical noncanonical counterparts of the above nonunitary deformations are equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicted by similar problematic aspects because Riemannian spaces are noncanonical deformations of Minkowskian spaces, thus having noninvariant space-time units. We then point out that new mathematical methods, calledisotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known asrelativistic hadronic mechanics which: (1) is as axiomatically consistent as relativistic quantum mechanics, (2) preserves the abstract axioms of special relativity, and (3) results in a completion of the conventional mechanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unification of the special and general relativity via the isominkowskian geometry in which the two relativities are differentiated via the invariant basic unit, while preserving conventional Riemannian metrics, Einstein's field equations, and related experimental verifications; a novel operator form of gravity verifying the axioms of relativistic quantum mechanics under the universal isopoincare symmetry; a new structure model of hadrons with conventional massive particles as physical constituents which is compatile with composite quarks and with established unitary classifications; and other novels applications in nuclear physics, astrophysics, theoretical biology, and other fields. The paper ends with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of recycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first time in this paper thanks to mathematical advances that recently appeared in a special issue of theRendiconti Circolo Matematico Palermo, and in other journals identified in the Acknowledgements.
TL;DR: In this article, a generalization of the familiar de Broglie-Bohm interpretation of quantum mechanics is formulated, based on relinquishing the momentum relationship p=∇S and allowing a spread of momentum values at each position.
Abstract: A generalization of the familiar de Broglie-Bohm interpretation of quantum mechanics is formulated, based on relinquishing the momentum relationship p=∇S and allowing a spread of momentum values at each position. The development of this framework also provides a new perspective on the well-known question of joint distributions for quantum mechanics. It is shown that, for an extension of the original model to be physically acceptable and consistent with experiment, it is necessary to impose certain restrictions on the associated joint distribution for particle positions and momenta. These requirements thereby define a new class of possible models. In pursuing this line of reasoning, the main contributions of this paper are (i) to identify the restrictions that must be imposed, (ii) to demonstrate that joint distribution expressions satisfying them do exist, and (iii) to construct a sample model based on one such joint distribution.
TL;DR: In this article, it was shown that effective frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different experimental setups, the choice of which obeys a classical distribution.
Abstract: Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabo showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different experimental setups, the choice of which obeys a classical distribution.
TL;DR: In this paper, the authors claim that physics has been constructed because three "philosophical" principles have been respected, namely realism, locality, and consistency, which lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV).
Abstract: We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that all state vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality.
TL;DR: In this paper, unconditional CP-violation effects, independent from those known before, new unconditional tests of the CPT and T invariances, and new results for correlations are derived.
Abstract: The CP-violation problem and unconditional tests of discrete symmetries T and CPT are investigated in the exact quantum theory (QT) beyond the usually used Lee-Oehme-Yang (LOY) theory, which is based on the famous Weisskopf-Wigner (WW) approximation. New unconditional CP-violation effects, independent from those known before, new unconditional tests of the CPT and T invariances, and new results for correlations are derived. Corresponding general results are obtained for
$$K^0 - \bar K^0 ,{\mathbf{ }}B^0 - \bar B^0 ,{\mathbf{ }}D^0 - \bar D^0 $$
mesons. On the base of these new theoretical results, some proposals for experiments by CP LEAR and ϕ, B factories are given. The new results are interesting not only for the CP-violation problem itself but also for testing violation of the standard quantum dynamics connected with ideas of quantum gravity.
TL;DR: In this paper, the history of q-deformations, their physical shortcomings, and their apparent resolution via an invariant Lie-admissible formulation based on a new mathematics of genotopic type are discussed.
Abstract: In this note we outline the history of q-deformations, indicate their physical shortcomings, suggest their apparent resolution via an invariant Lie-admissible formulation based on a new mathematics of genotopic type, and point out their expected physical significance.
TL;DR: In this paper, the many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result, of a quantum mechanical measurement, and a possible procedure for "interworld" exchange of information and energy, using only state of the art quantum optical equipement, is described.
Abstract: The many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result, of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to this interpretation. A possible procedure for “interworld” exchange of information and energy, using only state of the art quantum optical equipement, is described. A single ion is isolated from its environment in an ion trap. Then a quantum mechanical measurement with two discrete outcomes is performed on another system, resulting in the formation of two parallel worlds. Depending on the outcome of this measurement the ion is excited from only one of the parallel worlds before the ion decoheres through its interaction with the environment. A detection of this excitation in the other parallel world is direct evidence for the many-worlds interpretation. This method could have important practical applications in physics and beyond.
TL;DR: In this paper, it is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω0, mod ωi) rather than as pariah, pseudo-Riemannian spaces.
Abstract: It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω0, mod ωi) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian) connections are scrutinized.
TL;DR: In this paper, a simple classical model of the zitterbewegung was proposed, where spin is proportional to the velocity of the particle, the component parallel top is constant and the orthogonal components are oscillating with 2p frequency.
Abstract: We propose a simple classical model of the zitterbewegung. In this model spin is proportional to the velocity of the particle, the component parallel top is constant and the orthogonal components are oscillating with2p frequency. The quantization of the system gives wave equations for spin,0, 1/2, 1, 3/2,…, etc. respectively. These equations are convenient for massless particles. The wave equation of the spin-1, massless free particle is equivalent to the Maxwell equations and the state functions have a probability interpretation and exhibit conserved current densities. The ground state has zero energy.
TL;DR: In this paper, the connections existing between Clauser-Horne's inequalities and the conditions established by Pitowsky expressing the Kolmogorovian nature of a probability vector are clarified.
Abstract: This paper consists of two parts. Firstly, we shall clarify the connections existing between Clauser-Horne's inequalities and the conditions established by Pitowsky expressing the Kolmogorovian nature of a probability vector. We shall discuss afterwards three possible interpretations of the experimental violation of these inequalities.
TL;DR: A quantum theory combining an irreversible time evolution semigroup with a time reversal operator is presented in this paper, where the authors show that the quantum theory can be viewed as a quantum version of time reversal.
Abstract: A quantum theory combining an irreversible time evolution semigroup with a time reversal operator is presented.
TL;DR: In this paper, a large Hilbert space is used for the calculation of the nuclear matrix elements governing the light neutrino mass mediated mode of neutrinoless double beta decay (Ovββ-decay) of 76 Ge,100 Mo,116 Cd,128 Te, and136 Xe within the standard pn-QRPA and the renormalized QRPA with proton-neutron pairing (full-RQ-PA) methods.
Abstract: A large Hilbert space is used for the calculation of the nuclear matrix elements governing the light neutrino mass mediated mode of neutrinoless double beta decay (Ovββ-decay) of76 Ge,100 Mo,116 Cd,128 Te, and136 Xe within the proton-neutron quasiparticle random phase approximation (pn-QRPA) and the renormalized QRPA with proton-neutron pairing (full-RQRPA) methods. We have found that the nuclear matrix elements obtained with the standard pn-QRPA for several nuclear transitions are extremely sensitive to the renormalization of the particle-particle component of the residual interaction of the nuclear hamiltonian. Therefore the standard pn-QRPA does not guarantee the necessary accuracy to allow us to extract a reliable limit on the effective neutrino mass. This behavior already known from the calculation of the two-neutrino double beta decay matrix elements, manifests itself in the neutrinoless double-beta decay but only if a large model space is used. The full-RQRPA, which takes into account proton-neutron pairing and considers the Pauli principle in an approximate way, offers a stable solution in the physically acceptable region of the particle-particle strength. In this way more accurate values on the effective neutrino mass have been deduced from the experimental lower limits of the half-lifes of neutrinoless double beta decay.
TL;DR: In this article, the authors analyzed decoherence in continuous measurements with the help of restricted path integrals (RPI) and (equivalently in simple cases) complex Hamiltonians.
Abstract: Decoherence is the name for the complex of phenomena leading to appearance of classical features of quantum systems. In the present paper decoherence in continuous measurements is analyzed with the help of restricted path integrals (RPI) and (equivalently in simple cases) complex Hamiltonians. A continuous measurement results in a readout giving information in the classical form on the evolution of the measured quantum system. The quantum features of the system reveal themselves in the variation of possible measurement readouts. For example, the monitoring energy of a multi-level system may visualize a transition between levels as a process evolving in time but with an unavoidable quantum noise. Decoherence of a continuously measured system is completely determined by the measurement readout, i.e., by the information recorded in its environment. It is shown that the ideology of RPI makes the Feynman version of quantum mechanics closed, contrary to the conventional operator form of quantum mechanics which needs quantum theory of measurement as a necessary additional part.
TL;DR: In this article, it was shown that the projection postulate can be applied in good approximation to such measurements, although corrections to ideal measurements are determined explicitly. But it was not shown how far the experiment of Itanoet et al. can be considered as a test of the quantum Zeno effect.
Abstract: The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account.
TL;DR: In this paper, the authors present an informal review of their recent work whose goal is to develop a mathematical theory of the physical phenomenon of emission and absorption of radiation by systems of nonrelativistic matter such as atoms and molecules.
Abstract: In this paper we present an informal review of our recent work whose goal is to develop a mathematical theory of the physical phenomenon of emission and absorption of radiation by systems of nonrelativistic matter such as atoms and molecules.
TL;DR: In this article, a Weizsacker-type nuclear mass formula is investigated which has the eigenvalue of the quadratic Casimir operator of SU(4) as a Wigner term.
Abstract: It is argued that mass anomalies at the N≈Z line are associated with SU(4) isospin-spin symmetry. Drawing on these arguments, a Weizsacker-type nuclear mass formula is investigated which has the eigenvalue of the quadratic Casimir operator of SU(4) as a Wigner term. This SU(4)-based mass formula yields a better agreement than the one with the usual Wigner term |N—Z|/A. In addition, the SU(4) eigenvalue expression adequately replaces the usual pairing term of the Weizsacker formula giving a lower overall rms deviation than the latter.