Geometrization of Classical Wave Fields

Abstract

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

New Approach to Geometrization of Electromagnetic Field

“…In this work the geometrization of electromagnetic field is achieved via 5-dimensional approach that is free from abovementioned disadvantages. The principally new idea here is that we use as the starting point the geometrization of quantum objects, suggested earlier by the author [4][5][6][7][8][9]. This geometrization assumes that quantum particles can be considered as projections of the spatial topological defects moving in the space with dimensionality more than three.…”

“…This geometrization of electromagnetic field is the geometrization of the bose-field. Geometrization of the Dirac equation, suggested earlier by the author, can be considered as geometrization of the fermi-field, and we start with presentation of the main points of this geometrization [4][5][6][7][8][9].…”

Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

“…It can be shown that due to pseudo-Euclidean metrics of the physical space-time such four-dimensional object represents moving topological defect of three-dimensional space and that this defect has wave-corpuscular and stochastic properties. And this gives an opportunity to identify such geometrical object with the quantum object, described by (1) [2,3] …”

“…Let us remind at first main points of the suggested geometrical interpretation of quantum mechanics [2,3]. The starting moment was the topological interpretation of Dirac's relativistic equation for free particle with spin ½. Symmetric form of this equation is [4] …”

Geometrical Interpretation of Time and New Models of the Space-Time

“…This space looks, intuitively, as understandable one because its standards have dimensionality of length. On the other hand, time does not look understandable on the basis of This work is a соntinuation of author's investigations of possibility to explain physical phenomena by geometrical properties of the space-time [4] [5] [6] [7] [8]. In these investigations the idea was used about increasing dimensionality of our Euclidean space from three to four-the idea firstly used by Kaluza and then by Bergmann and Einstein in their attempts to geometrize electromagnetic field [9] [10].…”