[en] Measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state are modeled by systems of differential equations. The latter model is a local model with hidden variables of the EPR-Bohm gedanken experiment. Although there is no dynamical interaction between the pair of spin-1/2 objects, the model reproduces approximately the quantum-mechanical correlations by coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the apparent nonlocality in the EPR Bohm gedanken experiment

[en] 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 subjective 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

[en] The Dirac operator arises naturally on S¹ x S³ from the connection on the Lie group U(1) x SU(2) and maps spacetime rays into rays in the Lie algebra. The author constructs both simple harmonic and pulse solutions to the neutrino equations on S¹ x S³, classified by helicity and holonomy, using this map. Helicity is interpreted as the internal part of the Noether charge that arises from translation invariance; it is topologically quantized in integral multiples of a constant g that converts a Lie-algebra phase shift into an action. The fundamental unit of helicity is associated with a full twist in u(1) x su(2) phase per global lightlike cycle. If one passes to the projective space RP¹ x RP³, one gets half-integral helicity

[en] The physical motivations for the dynamical group are presented and it is shown how Barut's mathematical speculations were combined with the idea of an elementary length to provide group theoretical models of relativistic extended objects. Then the simplest nonrelativistic and relativistic models are described. 18 refs., 4 figs

[en] Asim Barut once, en passant, asked the question open-quotes For what transitions of the hydrogen atom do the spectral lines coincide?close quotes The answer is presented in this paper. In the spectrum of the hydrogen atom the coincidence of spectral lines is abundant and is governed by a four-parametric solution. The lowest energy for the first coincidence corresponds to n = 5, the Pfund series

[en] The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of contemporary orthodox physical theory, namely the notion that nature's response to the probing action of an observer is determined by pure chance, and hence on the basis of absolutely no reason at all. This appeal to pure chance can be deemed to have no rational fundamental place in reason-based Western science. It is argued here, on the basis of the other basic principles of quantum physics, that in a world that conforms to the principle of sufficient reason, the usual quantum statistical rules will naturally emerge at the pragmatic level, in cases where the reason behind nature's choice of response is unknown, but that the usual statistics can become biased in an empirically manifest way when the reason for the choice is empirically identifiable. It is shown here that if the statistical laws of quantum mechanics were to be biased in this way then the basically forward-in-time unfolding of empirical reality described by orthodox quantum mechanics would generate the appearances of backward-time-effects of the kind that have been reported in the scientific literature.

[en] Elementary particles, regarded as the constituents of quarks and leptons, are described classically in the framework of the general relativity theory. There are neutral particles and particles having charges ± 1/3e. They are taken to be spherically symmetric and to have mass density, pressure, and (if charged) charge density. They are characterized by an equation of state P = -ρ suggested by earlier work on cosmology. The neutral particle has a very simple structure. In the case of the charged particle there is one outstanding model described by a simple analytic solution of the field equations

[en] Klein's paradox - the prediction by Dirac's equation of the anomalous reflection of electrons from a large potential barrier - has attracted the attention of physicists for several decades. Assessments of its significance vary widely: Some say that it is unimportant, because the problem is resolved by second quantization, but for others it represents a real failure of quantum electrodynamics. Here, a 4-space formulation of Dirac's equation gives results formally identical to those of the usual Klein paradox. However, some extra physical detail can be inferred, and this suggests that the most extreme case involves pair production within the potential barrier

[en] For several examples of Hermitian operators, the issues involved in their possible self-adjoint extension are shown to conform with recognizable properties in the solutions to the associated classical equations of motion. This result confirms the assertion made in an earlier paper that there are sufficient classical open-quotes symptomsclose quotes to diagnose any quantum open-quotes illness.close quotes 3 refs

[en] In this paper the authors investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ⁴ and φ⁶ field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m ≠ 0) and massless (M = 0) cases are considered, as well as tachyonic solutions allowed (v>c). The authors first present a complete set of translationally invariant solutions for the φ⁴ model and demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both φ⁴ and φ⁶ cases since they provide the most realistic models of elementary particles. 52 refs., 7 figs., 2 tabs