A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the $U_4$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the $U_4$ theory arises as a local gauge theory for the Poincaré group in space-time. The deviations of the $U_4$ theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

Stationary laboratories on Earth accelerate and rotate relative to the local inertial frames. Any experiment precise enough would detect and/or need to take into account the effects due to acceleration and rotation. We derive these inertial effects for a Dirac particle in a straightforward and unified way within the framework of special relativity. The effects found include the Bonse-Wroblewski phase shift due to acceleration, the Sagnac-type effect, the rotation-spin effect, and the redshift of the kinetic energy.

In order to take full account of spin in general relativity, it is necessary to consider space‐time as a metric space with torsion, as was shown elsewhere. We treat a Dirac particle in such a space. The generalized Dirac equation turns out to be of a Heisenberg‐Pauli type. The nonlinear terms induced by torsion express a universal spin‐spin interaction of range zero.

The field equations of general relativity with spin and torsion ($U_4$ theory) are considered to describe correctly the gravitational properties of matter on a microphysical level. By an averaging procedure one arrives at a macroscopic field equation, which under normal matter densities coincides with Einstein's equation of conventional general relativity. For very high matter densities, even if the spin are randomly distributed, Einstein's equation breaks down and $U_4$ theory must be applied. It is shown how the singularity theorems of Penrose and Hawking must be modified to apply in $U_4$ theory. All known cosmological models in $U_4$ theory which prevent singularities are shown to violate an energy condition of a singularity theorem.