The Equivalence Principle Revisited

TL;DR

This paper revisits the strong Equivalence Principle, clarifying its precise mathematical formulation within General Relativity and torsion-inclusive theories, emphasizing the distinction between gravitation and other fundamental forces.

Contribution

It offers a concise, mathematically precise statement of the strong Equivalence Principle applicable to ideal observers, expanding understanding in contexts including torsion and gauge fields.

Findings

The principle holds for ideal observers but not for real, extended observers.

A clear mathematical formulation of the principle is provided.

Differences between gravitation and other interactions are highlighted.

Abstract

A precise formulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity, but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: "An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed". This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.