Geometrization of quantum mechanics

Olkhov, O. A.

doi:10.1088/1742-6596/67/1/012037

Cited by 7 publications

(7 citation statements)

References 3 publications

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“…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] …”

Section: Foundations Of the Hypothesismentioning

confidence: 99%

“…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] …”

Section: Foundations Of the Hypothesismentioning

confidence: 99%

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Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

Olkhov¹

2014

AJPA

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Abstract:The hypothesis was earlier suggested by the author where all micro-objects are considered as specific distortions of the physical space-time pseudo-Euclidean geometry, namely, as closed topological 4-manifolds. The foundation of the hypothesis is a geometrical interpretation of the basic equation of quantum mechanics for classical (not quantized) wave fields --the Dirac equation for free particle. Such hypothesis does not contradict to any physical laws and experimental facts and gives firstly an opportunity to explain qualitatively within classical notions (geometrical) the so called "paradoxical" properties of quantum particles such as wave-corpuscular duality, appearance of probabilities in the quantum mechanics formalism, spin, EPR-paradox.To demonstrate prospects for suggested geometrical approach the author early attempted to find new dynamic equations other than known quantum-mechanical ones for atomic spectra calculations. In this work above investigation is being continued on a more rigorous basis, representing a new geometrical interpretation of the equation for hydrogen atoms. Results of calculations of ionization potentials for helium atom are in agreement with experimental data.

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Section: Foundations Of the Hypothesismentioning

confidence: 99%

Section: Foundations Of the Hypothesismentioning

confidence: 99%

Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

Olkhov¹

2014

AJPA

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“…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].…”

Section: Introductionmentioning

confidence: 98%

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

Olkhov¹

2017

JHEPGC

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It is shown that two fundamental notions "space" and "time" can be reduced to the one notion-the "space", where time appears to be the length of geodesic lines of the space adjacent to the three-dimensional Euclidean space. The whole space is a topological product of the three-dimensional Euclidean space and some another space, that may have the screw structure. Within the framework of this model, the Galilei's inertia law and existence of limiting velocity of motions are consequences of the geometrical interpretation of time.

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“…This work is a continuation of author's investigations on geometrisation of quantum mechanics [1] [2] [3] [4] [5]. As "geometrisation" we understand the investigation of such models of physical phenomena when these phenomena are expressed through understandable geometrical patterns and notions.…”

Section: Introductionmentioning

confidence: 99%

Geometrical Meaning of Time and the Theory of Relativity

Olkhov¹

2020

JHEPGC

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New geometrical model of time is suggested where time of body's motion is defined as the length of its trajectories in four-dimension space-time. Within suggested approach periodical motions in clocks correspond to definite length of four-dimension trajectories that is clocks appear to be standards for measurements of length in four-dimension space analogously as hard sticks are standards for measurements of length in three-dimension space. This means that space and time are entities of the same geometrical nature. A suggested interpretation of time leads to necessity of changes in general theory of relativity. These changes are unessential for body's motion in weak gravitational field.

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Geometrization of quantum mechanics

Cited by 7 publications

References 3 publications

Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

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

Geometrical Meaning of Time and the Theory of Relativity

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