  I explain the geometric basis for the recently-discovered nonholonomic
mapping principle which permits deriving laws of nature in spacetimes with
curvature and torsion from those in flat spacetime, thus replacing and
extending Einstein's equivalence principle. As an important consequence, it
yields 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 makes trajectories autoparallel rather than geodesic. Its geometric
origin is the closure failure of parallelograms in the presence of torsion, A
simple generalization of the mapping principle transforms path integrals from
flat spacetimes to those with curvature and torsion, thus playing the role of a
quantum equivalence principle, applicable at present only to spaces with
gradient torsion.
