**Authors:** Golden Gadzirayi Nyambuya

The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the Principle of Relativity. It is bonafide knowledge, known even to Einstein the founder, that the GTR violates the very principle upon which it is founded i.e., it violates the Principle of Relativity; because a central equation i.e., the geodesic law which emerges from the GTR, is well known to be in conflict with the Principle of Relativity because the geodesic law, must in complete violation of the Principle of Relativity, be formulated in special (or privileged) coordinate systems i.e., Gaussian coordinate systems. The Principle of Relativity clearly and strictly forbids the existence/use of special (or privileged) coordinate systems in the same way the Special Theory of Relativity forbids the existence of privileged and or special reference systems. In the pursuit of a more Generalized Theory of Relativity i.e., an all-encampusing unified field theory to include the Electromagnetic, Weak & the Strong force, Einstein and many other researchers, have successfully failed to resolve this problem. In this reading, we propose a solution to this dilemma faced by Einstein and many other researchers i.e., the dilemma of obtaining a more Generalized Theory of Relativity. Our solution brings together the Gravitational, Electromagnetic, Weak & the Strong force under a single roof via an extension of Riemann geometry to a new hybrid geometry that we have coined the Riemann-Hilbert Space (RHS). This geometry is a fusion of Riemann geometry and the Hilbert space. Unlike Riemann geometry, the RHS preserves both the length and the angle of a vector under parallel transport because the affine connection of this new geometry, is a tensor. This tensorial affine leads us to a geodesic law that truly upholds the Principle of Relativity. It is seen that the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the non-Abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac equation.

**Comments:** 40 pages

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[v1] 7 Oct 2010

[v2] 20 Dec 2010

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