Abstract
Interpretation of wave function for free particle is suggested as a description of microscopic distortion of the space-time geometry, namely, as some closed topological 4-manifold. Such geometrical object looks in three-dimensional Euclidean space as its topological defect having stochastic and wave-corpuscular properties of quantum particle. All possible deformations (homeomorphisms) of closed topological manifold play the role of “hidden variables”, responsible for statistical character of the theory.
Highlights
This investigation started long ago as an attempt to extend Einstein’s idea of the geometrization of the theory of gravity to a possible geometrization of quantum theory
In the Einstein’s general theory of relativity, gravitation is considered as a result of macroscopic distortion of the space-time geometry [1]; in this work, quantum particles are considered as a microscopic distortion of the space-time geometry
Why any interpretation is needed for mathematical formalism if it is in a good agreement with experiment? One of reasons is the fact that new physical models open new opportunities for development of theories
Summary
This investigation started long ago as an attempt to extend Einstein’s idea of the geometrization of the theory of gravity to a possible geometrization of quantum theory. Suggested geometrizatiom of quantum mechanics means new interpretation of its existing mathematical formalism commonly referred to as “copenhagen interpretation” This new interpretation gives possibility to explain known strange features of above mathematical formalism (statistical description, wave-corpuscular dualism) with the help of notions from everyday life (physical model). Preliminary results see [13] [14] [15] [16] [17]
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