Abstract

The present reading is part of our on-going attempt at the foremost endeavour of physics since man began to comprehend the heavens and the earth. We present a much more improved Unified Field Theory of all the forces of Nature i.e. the gravitational, the electromagnetic, the weak and the strong nuclear forces. The proposed theory is a radical improvement of Professor Hermann Weyl’s supposedly failed attempt at a unified theory of gravitation and electromagnetism. As is the case with Professor Weyl’s theory, unit vectors in the proposed theory vary from one point to the next, albeit, in a manner such that they are—for better or for worse; compelled to yield tensorial affinities. In a separate reading, the Dirac equation is shown to emerge as part of the description of the these variable unit vectors. The nuclear force fields—i.e., electromagnetic, weak and the strong— together with the gravitational force field are seen to be described by a four-vector field Aμ, which forms part of the body of the variable unit vectors and hence the metric of spacetime. The resulting theory very strongly appears to be a logically consistent and coherent unification of classical and quantum physics and at the same time a grand unity of all the forces of Nature. Unlike most unification theories, the present proposal is unique in that it achieves unification on a fourdimensional continuum of spacetime without the need for extra-dimensions.

Highlights

  • Much effort by a great many erudite, notable and foremost physicists and mathematicians has gone into the allnoble and all-esoteric search for an all-encompassing unified theory of all the forces of Nature; as for our own attempts, the present reading marks the third such effort

  • Our pedestrian feeling on the issue of the Mind of God, His thoughts and choices is that all the constraints— more so the gauge conditions that we find necessary for our theories; the constraints that we impose on fundamental physical theories, these are most certainly God’s subtle thoughts which He employed in making the Universe

  • Assuming—as already stated above; that mass is identified with the gravitational charge of the body in question—as is the case in physics; and as-well assuming the conservation of mass and momentum, which in-turn means the conservation of gravitational charge, there must exist two vector fields that satisfy a set of four Maxwell-type equations

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Summary

Introduction

Much effort by a great many erudite, notable and foremost physicists and mathematicians has gone into the allnoble and all-esoteric search for an all-encompassing unified theory of all the forces of Nature; as for our own attempts, the present reading marks the third such effort. No amount of logical reasoning in Newtonian gravitation would have led mankind into Professor Einstein’s brilliant geometric description of gravitation and spacetime, one had to “defy” logic and enter into much higher planes, terrains and farrows of logic and natural reality In this reading—given its length, we find no space to give a wide literature review or an overview of the history of unified field theories. In § (13), we demonstrate that the proposed unified theory does contain Yang-Mills Theory and in § (14), (15) and (16), we give a general discussion, the conclusion drawn thereof and the recommendations for future works

Motivation
New Weyl Geometry
Decomposition of the Metric Tensor
Riemann-Hilbert Space
Different Representations of the Metric
Unit Vector
Some Remarks
Tensorial Affinities
General Field Equations
Linear Riemann-Hilbert Space
First Bianchi Field Equations
Second Bianchi Field Equations
Resultant Field Equations
Modified Lorenz Gauge
Source Free Field Equations
Source Coupled Field Equations
Second Bianachi Identity Equations
10. Stocktaking
11. Gravitation and Gravitomagnetism
12. New Geodesic Equation
13. Global Symmetries and Yang-Mills Force Fields
13.1. Electromagnetism
13.2. Four Dimensional Yang-Mills Theory
14. Discussion
15. Conclusions
16. Recommendations
Full Text
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