Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion: New Covariant Conservation Law for Energy-Momentum Tensor

摘要

I explain the geometric basis for the recently-discovered nonholonomic mapping principle which enables me to derive laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force which makes trajectories autoparallel rather than geodesic, as a manifestation of inertia. Its geometric origin is the closure failure of parallelograms in the presence of torsion. The torsion force changes the covariant conservation law of the energy-momentum tensor whose new form is derived.