Geometrization of Classical Wave Fields

Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations for these fields can be considered as relations describing the space topological defects. These defects, being closed topological manifolds, are embedded in the outer five-dimensional space, and observable objects appear to be intersections of above defects with the physical space. This interpretation explains irrational properties of quantum objects such as wave-corpuscular duality, stochastic behavior, instantaneous nonlocal correlation in EPR-paradox, the light velocity invariance and so on. Wave-corpuscular properties arise as a result of the defect periodical movement in the outer space relative to its intersection with the physical space, and just this periodical movement attributes phase to the propagating object. Appearance of probabilities within the formalism is a consequence of uncertainty of the closed topological manifold shape, and ensemble of all possible shapes for the same object can be considered as an ensemble of hidden variables that leads to probabilistic description. Embedded in the outer space topological defects provide channels for nonlocal correlations between their intersections-- noninteracting particles in EPR-experiments, and this means that the proposed approach can be considered as a nonlocal model with hidden variables.Comment: 7 pages, Int.Conf.,Quantum Theory: Reconsideration of Foundations-4, Vaxjo, Sweden. 11-16 June 200

Is Bell's theorem relevant to quantum mechanics? On locality and non-commuting observables

Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective of the issue of locality. Then, we try to disentangle the locality issue from the existence of joint distributions by introducing two models accounting for the EPR correlations but denying the existence of joint distributions. We will see that these models do not need to resort explicitly to non-locality: the first model relies on conservation laws for ensembles, and the second model on an equivalence class by which different configurations lead to the same physical predictions.Comment: Extended with new materia

Priors in quantum Bayesian inference

In quantum Bayesian inference problems, any conclusions drawn from a finite number of measurements depend not only on the outcomes of the measurements but also on a prior. Here we show that, in general, the prior remains important even in the limit of an infinite number of measurements. We illustrate this point with several examples where two priors lead to very different conclusions given the same measurement data.Comment: 7 pages; published in AIP Conference Proceedings 1101: Foundations of Probability and Physics 5, edited by L. Accardi et al, p. 255 (2009

Bohm's quantum potential and quantum force in superconductor

The Bohm's quantum potential, introduced in 1952, and the quantum force in superconductor, introduced in 2001, allow to describe non-local force-free momentum transfer observed in the Ahronov-Bohm effects. Comparison of the Ahronov-Bohm effects in the two-slit interference experiment and in superconductor ring reveals fundamental difference between the Schrodinger wave function and the wave function describing macroscopic quantum phenomena. The Ginzburg-Landau wave function describing the superconductivity phenomenon can not collapse and an additional postulate, which was implied first by L.D. Landau, must be used for the description of macroscopic quantum phenomena. It is note that quantum principles and postulates should not be universal till the quantum formalism is only phenomenological theory but no description of an unique reality. A simple Gedankenexperiment is considered which challenges the universality of the Heisenberg uncertainty relation and the Bohr's complementarity principle.Comment: 9 pages, 1 figure, the Invited talk was presented at the conference "Foundations of Probability and Physics-5" Vaxjo University, Sweden, August 24-27, 200

An analog of Heisenberg uncertainty relation in prequantum classical field theory

Prequantum classical statistical field theory (PCSFT) is a model which provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of the wave type. For example, "electron" is described by electronic field. In contrast to QM, this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of e.g. electron contains the irreducible contribution of the background field, vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper we derive a classical analog of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM. The quantum dispersion corresponds to the difference between e.g. the electron field dispersion and the dispersion of vacuum fluctuations. Classical Robertson-like inequality contains these differences. Hence, it does not imply such a rigid estimate from below for dispersions as it was done in QM

What's wrong with this rebuttal?

A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites.Comment: 2 page

About Essence of the Wave Function on Atomic Level and in Superconductors

The wave function was proposed for description of quantum phenomena on the atomic level. But now it is well known that quantum phenomena are observed not only on atomic level and the wave function is used for description of macroscopic quantum phenomena, such as superconductivity. The essence of the wave function on level elementary particles was and is the subject of heated argument among founders of quantum mechanics and other physicists. This essence seems more clear in superconductor. But impossibility of probabilistic interpretation of wave function in this case results to obvious contradiction of quantum principles with some fundamental principles of physics.Comment: 5 page

Understanding quantization: a hidden variable model

We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by stochastically-parameterized c-numbers. Unlike canonical quantization, the method is free from operator ordering ambiguity and the resulting quantum system has a straightforward interpretation as statistical modification of ensemble of classical trajectories. We then develop measurement without wave function collapse \`a la pilot-wave theory and point out new testable predictions.Comment: 16 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz von Foerster Conference 2011)", see http://iopscience.iop.org/1742-6596/361/

Classical signal model reproducing quantum probabilities for single and coincidence detections

We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 \cite{Grangier} played a crucial role in rejection of (semi-)classical field models in favor of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favor of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient $g^{(2)}(0),$ is zero (for one photon states), but in (semi-)classical models $g^{(2)}(0)\geq 1.$ In TSD the coefficient $g^{(2)}(0)$ decreases as $1/{\cal E}_d^2,$ where ${\cal E}_d>0$ is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient $g^{(2)}(0)$ essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient $g^{(2)}(0)$ on the detection threshold

Embedding Quantum Mechanics Into a Broader Noncontextual Theory: A Conciliatory Result

The extended semantic realism (ESR) model embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here an improved version of this model and show that it predicts that, whenever idealized measurements are performed, a modified Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality holds if one takes into account all individual systems that are prepared, standard quantum predictions hold if one considers only the individual systems that are detected, and a standard BCHSH inequality holds at a microscopic (purely theoretical) level. These results admit an intuitive explanation in terms of an unconventional kind of unfair sampling and constitute a first example of the unified perspective that can be attained by adopting the ESR model.Comment: 24 pages, standard Latex, Extensively revised versio