Is the principle of equivalence a principle?

TL;DR

This paper argues that the principle of equivalence should be viewed as a theorem rather than an axiom, providing a detailed analysis and proof within gravitational theories based on linear connections.

Contribution

It reclassifies the principle of equivalence as a theorem and explores its validity and potential generalizations in gravitational theories.

Findings

The equivalence principle is valid at every point and along every path in theories based on linear connections.

The paper provides a detailed analysis of normal and inertial frames.

Possible generalizations of the equivalence principle are discussed.

Abstract

The work argues the principle of equivalence to be a theorem and not a principle (in a sense of an axiom). It contains a detailed analysis of the concepts of normal and inertial frame of reference. The equivalence principle is proved to be valid (at every point and along every path) in any gravitational theory based on linear connections. Possible generalizations of the equivalence principle are pointed out.