Quantum Mechanics in the Geometry of Space-Time

Pavel Bóna

Fosco Ruzzene

The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.

James B. Hartle

Yuri A. Rylov

One uses the investigation strategy: ”Find a mistake in foundation of physics and correct it”. Two fundamental defects are corrected: (1) nonrelativistic concept of the particle state, (2) inadequacy of the differential geometry formalism at the metric approach to geometry. Usage of relativistic concept of the particle state admits one to create united formalism for description of deterministic and stochastic particles motion. The quantum mechanics is founded as a statistical description of the stochastic particles motion. Stochasticity of the quantum particles motion is explained by multivariance of the space-time geometry, which leads to the world lines wobbling of elementary particles. Relativistic concept of the particle state and the metric approach to the space-time geometry admit one to construct the skeleton conception of elementary particles. The skeleton conception admits one to investigate the arrangement of elementary particles (but not only to systamatize them, ascribing quantum numbers to them).

Ingemar Bengtsson, Carlos Herdeiro, Roger Picken

Gennaro Auletta