Showing papers in "International Journal of Theoretical Physics in 1988"

Bell's Theorem Does Not Eliminate Fully Causal Hidden Variables

Abstract: Bell's theorem applies only to a hybrid universe in which hidden variables determine only part of the outcomes of experiments When applied to a fully causal hidden variable theory, in which detector settings as well as their interaction with particles during observation are determined by the variables, Bell's analysis must be modified The result is that a fully causal hidden variable model can be produced for which a properly chosen spread of hidden variables gives precisely the same prediction as standard quantum theory

An Overview of the Transactional Interpretation of Quantum Mechanics

Abstract: The transactional interpretation of quantum mechanics (TI) is summarized and various points concerning the TI and its relation to the Copenhagen interpretation (CI) are considered. Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantum mechanical interpretations to experimental tests and results are discussed.

An Overview of the Transactional Interpretation

Abstract: The transactional interpretation of quantum mechanics is summarized and various points concerning the transactional interpretation and its relation to the Copenhagen interpretation are considered. Questions concerning mapping the transactional interpretation onto the Copenhagen interpretation, of advanced waves as solutions to proper wave equations, of collapse and the quantum formalism, and of the relation of quantum mechanical interpretations to experimental tests and results are discussed.

Existence of the Gravitomagnetic Interaction

Abstract: The point of view expressed in the literature that gravitomagnetism has not yet been observed or measured is not entirely correct. Observations of gravitational phenomena are reviewed in which the gravitomagnetic interaction—a post-Newtonian gravitational force between moving matter—has participated and which has been measured to 1 part in 1000. Gravitomagnetism is shown to be ubiquitous in gravitational phenomena and is a necessary ingredient in the equations of motion, without which the most basic gravitational dynamical effects (including Newtonian gravity) could not be consistently calculated by different inertial observers.

“Superconducting” causal nets

Abstract: The world is described as a relativistic quantum neural net with a quantum condensation akin to superconductivity. The sole dynamical variable is an operator representing immediate causal connection. The net enjoys a quantum principle of equivalence implying local LorentzSL(2,C) invariance and causality. The past-future asymmetry of its cell is similar to that of the neutrino. A net phase transition is expected at temperatures on the order of theW mass rather than the Planck mass, and near gravitational singularities.

Realistic quantum probability

Abstract: A mathemetical framework for a realistic quantum probability theory is presented. The basic elements of this framework are measurements and amplitudes. Definitions of the various concepts are motivated by guidelines from the path integral formalism for quantum mechanics. The operational meaning of these concepts is discussed. Superpositions of amplitude functions are investigated and superselection sectors are shown to occur in a natural way. It is shown that this framework includes traditional nonrelativistic quantum mechanics as a special case. Proofs of most of the theorems will appear elsewhere.

Exact solutions to Einstein field equations

Abstract: In a recent paper Reboucas and d'Olival obtain an ordinary differential equation for a Bianchi type II metric with a rotating timelike congruence of geodesics, and obtain a particular solution of the differential equation. This paper completely integrates the differential equation.

Abstract quantum theory and space-time structure. I. Ur theory and Bekenstein-Hawking entropy

Abstract: We discuss the close connection between a quantum theory of binary alternatives and the local Lorentzian structure of space-time, and outline v. Weizsacker's concept of the “ur”-the quantized binary alternative. Then space-time is introduced mathematically as a symmetric space of the invariance group of the ur. It is physically interpreted as “the” cosmological space-time, the universe. In our model spacelike structures rest on the concept of “hypermembranes”—dynamical manifolds of codimension 1 in space-time. For a given number of urs asmallest length is introduced in this cosmic model by group-theoretic arguments. Already before introducing a dynamics the concept of isolated noncomposite objects can be given. They can be understood as simple models either for elementary particles or for black holes. Identifying the maximal localized states of many urs with a localized state of a particle, we get a good description of the large cosmological numbers and also alower bound for a neutrino mass. A simple counting of the particle states given from the ur-theoretic ansatz allows an easy explanation of the Bekenstein-Hawking entropy.

Dynamical Structures for k-Vector Fields

Abstract: A new class of dynamical structures that generalize electrodynamics is presented. In this construction the 1-jets of solutions are represented by a class ofk-vector fields that extend the notion of a Poisson structure to multivectors of degree greater than two. These objects function as tangent vectors to solutions. Although the dynamical equations are systems of partial differential equations, the formalism is very similar to mechanics.

Connections between Abstract Quantum Theory and Space-Time Structure II. A Model of Cosmological Evolution

Abstract: By ur-theoretic and general relativistic arguments, a new cosmological model is introduced which avoids most well-known cosmoiogical “problems.”

Fuzzy quantum spaces and compatibility

Abstract: Using ideas from fuzzy set theory, we generalize the notion of a quantum (probability) space introduced by Suppes to so-called fuzzy quantum spaces and we study the compatibility problem.

Gauge symmetries of electroweak interactions

Abstract: By considering the symmetries associated with baryon number and lepton number conservation as gauge symmetries, the underlying gauge symmetry of weak electromagnetic interactions is shown to beSU(2) L ×U(1)×U(1)Baryon×U(1)Lepton. If right-handed currents exist on a par with the observed left-handed ones, then the full symmetry of electroweak interactions that emerges isSU(2)L×SU(2)R×U(1)Baryon×U(1)Lepton. These symmetries offer a rich spectrum of massive neutral gauge bosons, one of which is the massive neutral boson of the standardSU(2) L ×U(1) Y model.

Feynman Rules for Probability Amplitudes

Abstract: Starting with very simple assumptions, Feynman rules for the quantum mechanical amplitudes and the associated probabilities are derived. These rules emerge as the only consistent rules for manipulating complex amplitudes assigned to processes. The probability of a process to which an amplitudex has been assigned is determined asp(x)=|x|α, 0<α≤2. If virtual processes are allowed,α=2.

Characteristic exponents of impulsive differential equations in a banach space

Abstract: The notion of general exponent of impulsive homogeneous differential equations is defined. A formula for the solution of impulsive nonhomogeneous differential equations is obtained and is used to establish a dependence between the existence of bounded solutions of such equations and the general exponent of the respective homogeneous equation.

Canonical quantization and chromodynamics in a spherical cavity

Abstract: The canonical quantization formalism is applied to the Lagrange density of chromodynamics, which includes gauge fixing and Faddeev-Popov ghost terms in a general covariant gauge. We develop the quantum theory of the interacting fields in the Dirac picture, based on the Gell-Mann and Low theorem and the Dyson expansion of the time evolution operator. The physical states are characterized by their invariance under Becchi-Rouet-Stora transformations. Subsequently, confinement is introduced phenomenologically by imposing, on the quark, gluon, and ghost field operators, the linear boundary conditions of the MIT bag model at the surface of a spherically symmetric and static cavity. Based on this formalism, we calculate, in the Feynman gauge, all nondivergent Feynman diagrams of second order in the strong coupling constantg. Explicit values of the matrix elements are given for low-lying quark and gluon cavity modes.

Reconstruction of abstract quantum theory

Abstract: Understanding quantum theory as a general theory of prediction, we reconstruct “abstract” quantum theory. “Abstract” means the general frame of quantum theory, without reference to a three-dimensional position space, to concepts like particle or field, or to special laws of dynamics. “Reconstruction” is the attempt to do this by formulating simple and plausible postulates on prediction in order to derive the basic concepts of quantum theory from them. Thereby no law of “classical” physics is presupposed which would then have to be “quantized.” We briefly discuss the relationship of “theory” and “interpretation” in physics and the fundamental role of time as a basic concept for physics. Then a number ofassertions are given, formulated as succinctly as possible in order to make them easily quotable and comparable. The assertions are arranged in four groups: heuristic principles, verbal definitions of some terms, three basic postulates, and consequences. The three postulates of separable alternatives, indeterminism, and kinematics are the central points of this work. These brief assertions are commented upon, and their relationship with the interpretation of quantum theory is discussed. Also given are an outlook on the further development into “concrete quantum theory” and some philosophical reflections.

On the logical foundations of the Jauch-Piron approach to quantum physics

Abstract: We make a critical analysis of the basic concepts of the Jauch-Piron (JP) approach to quantum physics Then, we exhibit a formalized presentation of the mathematical structure of the JP theory by introducing it as a completely formalized syntactic system, ie, we construct a formalized languageL e and formally state the logical-deductive structure of the JP theory by means ofL e Finally, we show that the JP syntactic system can be endowed with an intended interpretation, which yields a physical model of the system A mathematical model endowed with a physical interpretation is given which establishes (in the usual sense of the model theory) the coherence of the JP syntactic system

On a Recent Attempt to Define the Interpretation Basis in the Many Worlds Interpretation of Quantum Mechanics

Abstract: David Deutsch's 1985 algorithm to determine the preferred product structure and basis in the many worlds interpretation is examined. His heuristic argument for the conditions appearing in the algorithm is found wanting. The question of the existence and uniqueness of a final solution to his algorithm is discussed. The algorithm is shown to be inadequate to account for certain types of measurement which are, at least in principle, possible.

What do we learn about quantum mechanics from the theory of measurement

Abstract: It is argued that a quantum mechanical analysis of the measurement process permits one to adjudicate between an individual system interpretation of the state vector and an ensemble interpretation, in favor of the latter. Possible changes to quantum mechanics that would be necessary to enable it to describe individual systems are discussed.

A discrete geometry: Speculations on a new framework for classical electrodynamics

Abstract: An attempt is made to describe the basic principles of physics in terms of discrete partially ordered sets. Geometric ideas are introduced by means of an action at a distance formulation of classical electrodynamics. The speculations are in two main directions: (i) Gravity, one of the four elementary forces of nature, seems to be fundamentally different from the other three forces. Could it be that gravity can be explained as a natural consequence of the discrete structure? (ii) The problem of the observer in quantum mechanics continues to cause conceptual problems. Can quantum statistics be explained in terms of finite ensembles of possible partially ordered sets? The development is guided at all stages by reference to the simplest, and most well-established principles of physics.

Three- and five-dimensional considerations of the geometry of Einstein's * g-unified field theory

Abstract: We study the algebraic and differential geometric structures of three- and five-dimensional* g-unified field theory, with emphasis on the five-dimensional* g-unified field theory, in which we derive a new set of powerful recurrence relations which hold in a five-dimensional generalized Riemannian manifoldX 5 , prove a necessary and sufficient condition for the existence and uniqueness of the solution of the system of the Einstein equations in the first two classes, and find a precise tensorial representation of the Einstein connection Γ λ in terms of*gνν .

Canonical formalism and equations of motion for a spinning particle in general relativity

Abstract: A canonical formalism for spinning particles suitable for the formulations of a general relativistic covariant statistical mechanics of particles endowed with spin is developed. For that purpose the bracket for internal and external variables is given. In particular, limiting consideration to the spin tensor S/sup ..mu..v/, it has been possible to define momenta that are the true conjugates to the position variables. For the case considered the Hamiltonian function in addition to the invariant mass involves only one additional scalar. The equations of motion are then found by calculating the brackets of the dynamical variables with that Hamiltonian, and are compared to those obtained by other methods. The conjugate variables in the internal space that has to be adjoined to the (eight-dimensional) phase space for a complete covariant description of spinning particles are also given.

Conditional expectations, conditional distributions, and a posteriori ensembles in generalized probability theory

Abstract: A general probabilistic framework containing the essential mathematical structure of any statistical physical theory is reviewed and enlarged to enable the generalization of some concepts of classical probability theory. In particular, generalized conditional probabilities of effects and conditional distributions of observables are introduced and their interpretation is discussed in terms of successive measurements. The existence of generalized conditional distributions is proved, and the relation to M. Ozawa'sa posteriori states is investigated. Examples concerning classical as well as quantum probability are discussed.

Gleason's theorem and completeness of inner product spaces

Abstract: We generalize the result of Hamhalter and Ptak showing that an inner product space whose dimension is either a nonmeasurable cardinal or an arbitrary cardinal is complete iff its lattice of strongly closed subspaces possesses at least one state or one completely additive state, respectively. Moreover, we show that this lattice of any separable space possesses manyσ-finite measures, and we give the Gleason analogue for them.

Bayesian approach to thermostatistics

Abstract: Bayes' theorem is used to derive the dual of the Gibbs formulation of statistical thermodynamics. An asymptotic analysis is performed, akin to Khinchin's use of the central limit theorem, to determine approximate expressions for the moment-generating functions. The prior densities, which are determined by equating the maximum-likelihood estimates with the moment expressions in the asymptotic limit, satisfy Jeffreys' invariant properties of improper prior densities.

Derivation of quantum statistics from Gauss's principle and the second law

Abstract: Quantum statistical laws are derived from bona fide stationary probability distributions of physical stochastic processes. These distributions are shown to be the laws of error for which the average occupation numbers are the most probable values. They determine uniquely the statistical entropy functions and the second law gives the quantum statistical distributions.

Stability of the general exponent of nonlinear impulsive differential equations in a Banach space

Abstract: A theorem is proved which gurantees stability under small perturbations of the general exponent of impulsive nonlinear systems in a Banach space.

Stiff magnetofluid cosmological model

Abstract: We intestigate the behavior of the magnetic field in a cosmological model filled with a stiff perfect fluid in general relativity The magnetic field is due to an electric current along thex axis The behavior of the model when a magnetic field is absent is also discussed

State on splitting subspaces and completeness of inner product spaces

Abstract: We show that an inner produce space V is complete if the system of all splitting subspaces, i.e., of all subspaces M for which M + M/sup perpenficular/ = V, possesses at least one completely additive state.

Phase Transformations in Quaternionic Quantum Field Theory

Abstract: Phase transformations of a scalar quaternionic quantum field are examined as unitarily implemented symmetries. Under very general quantization conditions it is shown, in both global and local cases, that the only sensible phase invariance that has been suggested isφ →pφp−1, wherep is a quaternion andφ a quaternionic scalar field.