## The Sachs Unified Field Extension of Einsteins Theory

Another notable extension of Einstein's theory, which does include electrodynamics and the results of quantum mechanics as well, is the theory by Sachs {510}. Starting with Einstein's general relativity view and the group symmetry of its underlying mathematics, Sachs extended Einstein's theory into a fundamental theory of matter in all domains. Einstein's group formalism and the spinor-quaternion calculus in a curved spacetime provide the genesis of matter fields. The theory encompasses globally covariant field equations for inertial features of matter including its force manifestations. Unification is provided by the generalized spinor formalism. Quoting a popularized summation {511}:

"Novelfeatures ofgeneral relativity are shown to emerge, in elementary particle physics as well as astrophysics. Especially noteworthy ...is a factorization ofEinstein's field equations to a quaternion field formalism which, by way of a single covariant field, includes both gravitation and electromagnetism coupled to matter field equations — whose linear(low energy) limit recovers quantum mechanics. The ...original approach also furnishes derivations, not previously available, of several observed properties of inertial mass and gravitational force.

For a more technical description of how the unification of electrodynamics with general relativity is derived, we quote directly from Sachs {512}:

"It was demonstrated earlier that the factorization of Einstein s second-rank, symmetric tensor field equations, by removing the space and time-reflection elements from the underlyingcovariancegroup, yields a 16-component quaternion metrical field equation. The 16 equations were then re-expressed in a second-rank tensor form, breaking up into 10 & 6 equations. The 10 equations are in one-to-one correspondence with Einstein s symmetric tensor equations for gravitation; they are even under reflections. The remaining 6 equations are in antisymmetric tensor form; they are odd under reflections. Taking the covariant divergence ofthe latter equations then puts them into one-to-one correspondence with the structure ofMaxwell's equationsfor electromagnetism. What was shown earlier was that the four ofMaxwell's equations with sources followed. What is shown in this paper is that the other four ofMaxwell's equations that are source-free also follow, thus indicating the absence ofmagnetic monopoles from this theory, as in the usual Maxwellformalism. This shows that the factorization ofEinstein's field equations to the quaternion form fully unifies the gravitational and electromagnetic manifestations ofinteracting charged matter."

To freely download several of Professor Sachs's important technical papers, one is referred to his website at http://www.compukol.com/mendel/articles/articles.html.

The O(3) electrodynamics of Evans and Vigier has been shown to be a special subset of Sachs's electrodynamics {513a}. Hence O(3) can be used to engineer much of the Sachs unified field theory phenomenology, including — in our view — both gravity and antigravity. The first theoretical indication of this has been published by the AIAS (Alpha Foundation's Institute for Advanced Study) {513b}. Shortly we discuss our own views on how to directly perform engineering of antigravity.

A great many excellent publications on general relativity and the background of scientific knowledge in gravity exist; e.g., the text by Wheeler et al. {514} is particularly good. Einstein himself wrote a book on his special and general theory for the nonspecialist {515}. A collection of English translations of some of the original papers on relativity is provided in a book by Einstein, Lorentz, Minkowski, and Weyl {516}. Many other gravitational theories or changes to major theories have also been proposed by other scientists, but are not discussed here. For our purposes, an abbreviated discussion will suffice to understand a fundamental approach to feasible antigravity.

Since we are interested in actual working systems, a short review of some of the efforts in asymmetric lifting and propulsion experiments is useful.

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