Abstract
In the Einstein field equations, the geometry or the curvature of space-time defined as depended on the distribution of mass and energy principally resides on the left-hand side is set identical to a non-geometrical tensorial representation of matter on the right-hand side. In one or another form, general relativity accords a direct geometrical significance only to the gravitational field while the other physical fields are not of space time. They reside only in space time. Less well known, though of comparable importance is Einstein’s dissatisfaction with the fundamental asymmetry between gravitational and non-gravitational fields and his contributions to develop a completely relativistic geometrical field theory of all fundamental interactions, a unified field theory. Of special note in this context and equally significant is Einstein’s demand to replace the symmetrical tensor field by a non-symmetrical one and to drop the condition gik = gki for the field components. Historically, many other attempts were made too, to extend the general theory of relativity’s geometrization of gravitation to non-gravitational interactions, in particular, to electromagnetism. Still, progress has been very slow. It is the purpose of this publication to provide a unified field theory in which the gravitational field, the electromagnetic field and other fields are only different components or manifestations of the same unified field by mathematizing the relationship between cause and effect under conditions of general theory of relativity.
Highlights
The historical development of physics as such shows that formerly unrelated and separated parts of physics can be fused into one single conceptual formalism
Despite of the many and different approaches of theorists worldwide spanning so many of years taken to develop a unified field theory, to describe and to understand the nature at the most fundamental level progress has been very slow
The point of departure for a unified field theory will be in accordance with general relativity theory from the beginning
Summary
The historical development of physics as such shows that formerly unrelated and separated parts of physics can be fused into one single conceptual formalism. Even Einstein himself spent years of his life on the unification [2] of the electromagnetic fields with the gravitational fields In this context, Einstein’s position concerning the unified field theory is strict and clear (Figure 1). Despite of the many and different approaches of theorists worldwide spanning so many of years taken to develop a unified field theory, to describe and to understand the nature at the most fundamental (quantum) level progress has been very slow. With regard to unified field theories, formerly unrelated parts of physics will be fused into one single conceptual formalism while following a deductive-hypothetical approach. We briefly define and describe the basic mathematical objects and tensor calculus rules needed to achieve unification In this context, the point of departure for a unified field theory will be in accordance with general relativity theory from the beginning. The section discussion examines some conditions and consequences of the theorems proved
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