The author's research program over the past 50 years has dealt with a generalization of the expression of the theory of general relativity, within its own logical base, and its application to problems of cosmology, astrophysics and particle physics. One part of this program was to show that a generalized version of the theory yields the formal structure of quantum mechanics as a linear approximation for a generally covariant field theory of the inertia of matter (Sachs, 1986).The second part of this program was to demonstrate that the generalized version of general relativity yields a unified field theory of gravitation and electromagnetism, in terms of a single field (Sachs, 1982). This paper is devoted to the latter, demonstrating a unified field theory within the confines of the logical basis of the theory of general relativity.

A substantial part of the research of Albert Einstein in the first half of the 20^th century was devoted to a derivation of a unified field theory in the context of general relativity (Sachs, 1982). This theory incorporates the explanation of the physical phenomena of gravitation and electromagnetism under a single umbrella. It is well-known that he did not succeed in this pursuit, though he was aware that the logical basis of the theory of relativity implies such unification.

The unified field theory sought by Einstein (1955) and Schrödinger (1954) was meant to reformulate the variables of the field theory into a single field that incorporates the gravitational and the electromagnetic variables in a single (16-component) field. It is well-known that their attempts were not successful. Still, it was clear to Einstein and Schrodinger that the unified field theory is implied by the logical basis of the theory of general relativity. Then, how was it to be formulated?

The spacetime points (the `words' of this language) form a continuous set. The principle of relativity then implies that the transformations of the expression of the laws from one perspective in spacetime (i.e., one reference frame) to another `continuously connected' spacetime point preserves the forms of the laws of nature. Thus the laws of nature must be continuously distributed-they are `field equations' rather than equations of the motion of point particles (as in classical physics). The first discovered set of such field equations was Maxwell's equations for electromagnetism. Thus, the variables which are the solutions of the laws of nature, are `continuous fields'. It is further postulated, according to Noether's theorem, that the inclusion of the laws of conservation (of energy, momentum and angular momentum), in the flat space limit, is that the transformations of the laws of nature between reference frames must be analytic. This is a necessary and sufficient condition. Thus, the field solutions of the laws of nature are `regular'-continuous functions, without any singularities `anywhere'.

Physics Journal, Einstein's Unified Field Theory, General Relativity, Cosmology, Astrophysics, Particle Physics, Inertia of Matter, Gravitation and Electromagnetic Theory, Covariance, Metric Tensor, Curved Spacetime, Geodesic Equation, Maxwell Field Equations, Riemannian Spacetime.