Evolutionary forms: Conservation laws and causality

TL;DR

This paper introduces a mathematical framework based on evolutionary differential forms to describe physical processes, conservation laws, and quantum jumps, revealing how material media generate physical fields and explaining evolutionary phenomena.

Contribution

It develops a novel mathematical apparatus using evolutionary forms to describe discrete transitions, quantum jumps, and the generation of physical fields from material media.

Findings

Material media generate physical fields.

Mathematical formalism describes quantum jumps.

Mechanism of evolutionary processes in media explained.

Abstract

Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific feature of evolutionary forms is the fact that from the evolutionary forms, which correspond to the conservation laws for material media, the closed exterior forms, which correspond to the conservation laws for physical fields, are obtained. This shows that material media generate physical fields. And by this the determinacy of physical processes and phenomena is revealed. In this paper we obtain the mathematic apparatus that allows to describe discrete transitions and quantum jumps. This relates to the fact that the mathematic apparatus of exterior and evolutionary forms, which basis involves nonidentical relations and degenerate transformations, can describe transitions from nonconjugate operators to conjugate ones. None of mathematic formalisms contains such possibilities. The physical results that disclose a mechanism of evolutionary processes in material media and a generation of physical fields are obtained. These results explain many actual processes.