Space-Time Structure and Electromagnetism

TL;DR

This paper explores geometric theories of gravity and electromagnetism using Lagrangians dependent on curvature and torsion within absolute parallelism geometry, highlighting the necessity of torsion for electromagnetic representation.

Contribution

It introduces a unified geometric framework with a W-tensor that incorporates both curvature and torsion, demonstrating electromagnetism arises from non-vanishing torsion.

Findings

Pure gravity arises from curvature-dependent Lagrangian.

Electromagnetism emerges when torsion is non-zero.

A single geometric object, the W-tensor, encapsulates curvature and torsion properties.

Abstract

Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first Lagrangian gives rise to pure gravity, while the theory constructed using the second Lagrangian gives rise to both gravity and electromagnetism. The two theories are constructed in a version of absolute parallelism geometry in which both curvature and torsion are, simultaneously, non-vanishing. One single geometric object, {\it W-tensor}, reflecting the properties of curvature and torsion, is defined in this version and is used to construct the second theory. The main conclusion is that a necessary condition for geometric representation of electromagnetism is the presence of a non-vanishing torsion in the geometry used.