Is a first order space-time theory possible?

Abstract

Einstein's general relativity relates the curvature of space time, a second order differential property, to the stress-energy-momentum tensor. In this paper we ask whether it is possible to develop a first order theory relating space-time angles to the energy-momentum vector. We suggest several concepts that would be relevant, including quantum mechanical concepts that are usually treated separately. Phenomenological Lorentz covariance arises from both field and coordinate transformation and the Dirac equation becomes a special case of the space-time field equation. We reinterpret Kaluza-Klein theory in this context by considering the compact fifth dimension as the quantum wavefunction phase. Further directions for development are suggested.