Unification of Gravity and Electromagnetism II A Geometric Theory

TL;DR

This paper proposes a geometric framework using a non-symmetric affine connection to unify gravity and electromagnetism, where the electromagnetic field arises from the connection's trace, based on projective invariance broken by matter.

Contribution

It introduces a novel geometric approach to unify gravity and electromagnetism through an affine non-symmetric connection and projective invariance principles.

Findings

Electromagnetic field originates from the connection's trace.

Unification achieved via projective invariance breaking by matter.

Gravity emerges as a classical field in this framework.

Abstract

It is shown that unification of gravity and electromagnetism can be achieved using an affine non-symmetric connection $\Gamma^\lambda_{\mu\nu} \neq \Gamma^\lambda_{\nu\mu}$ and $\Gamma_\mu = \Gamma^\lambda_{[\mu\lambda]}\neq 0$. $\Gamma_\mu$ is shown to be the source of the electromagnetic field. This unification is based on {\em projective invariance} which is broken by matter fields, opening up the possibility of a unified theory of all forces in which gravity emerges as a classical field.