Gravitation Is Torsion

TL;DR

This paper argues that gravitation should be understood as torsion rather than curvature, proposing a teleparallel interpretation that aligns with Einstein's original ideas and maintains the same field equations.

Contribution

It introduces a torsion-based formulation of gravitation that preserves Einstein's 1907 principle of equivalence and uses the same Riemannian metric and field equations.

Findings

Gravitational acceleration is related to torsion, not curvature.

The teleparallel approach aligns with Einstein's original concept of gravity.

The formulation uses the same metric and field equations as standard General Relativity.

Abstract

The mantra about gravitation as curvature is a misnomer. The curvature tensor for a standard of rest does not describe acceleration in a gravitational field but the \underline{gradient} of the acceleration (e.g. geodesic deviation). The gravitational field itself (Einstein 1907) is essentially an accelerated reference system. It is characterized by a field of orthonormal four-legs in a Riemann space with Lorentz metric. By viewing vectors at different events having identical leg-components as parallel (teleparallelism) the geometry in a gravitational field defines torsion. This formulation of Einstein's 1907 principle of equivalence uses the same Riemannian metric and the same 1916 field equations for his theory of gravitation and fulfills his vision of General Relativity.