Effects of a scalar scaling field on quantum mechanics

TL;DR

This paper explores how a complex scalar scaling field, extending gauge freedom, influences quantum mechanics, affecting states and properties, with potential implications for understanding nonlocality and gauge structures.

Contribution

It introduces a complex scalar scaling field into quantum mechanics, extending gauge freedom to include scalar fields and analyzing its effects on quantum states and properties.

Findings

The scalar field affects quantum states via a nonunitary connection.

No current experimental evidence for the field due to small coupling.

Field gradients are constrained to be small locally but unrestricted cosmologically.

Abstract

This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces, both as structures, at different space time locations. Complex number structures and vector spaces at each location, are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. The lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region there are no restrictions on the field gradient.