Quaternions, Torsion and the Physical Vacuum: Theories of M. Sachs and G. Shipov Compared
Of several developments of unified field theories in the spirit of Einstein’s original objective of a fully geometric description of all classical fields as well as quantum mechanics, two are particularly noteworthy. The works of Mendel Sachs and Gennady Shipov stand apart as major life works comprising tens of papers, several monographs and decades of effort. Direct comparison of these theories is hampered however by differences in notation and conceptual view-point. Despite these differences, there are many parallels between the fundamental mathematical structures appearing in each. In this paper we discuss the main tenets of the two approaches and demonstrate that they both give rise to a factorization of the invariant interval of general relativity.
KeywordsCovariant Derivative Quaternion Algebra Affine Connection Physical Vacuum Tetrad Field
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- General Relativity and Matter; A Spinor Field Theory from Fermis to Light-Years, Mendel Sachs, D. Reidel Publishing Co., 1982.Google Scholar
- Quantum Mechanics from General Relativity; An Approximation for a Theory of Inertia, Mendel Saclis, Reidel Publishing Co., 1986.Google Scholar
- A Theory of Physical Vacuum, G. I. Shipov, English edition, Russian Academy of Natural Sciences, 1998.Google Scholar
- Mathematical Papers, by William Clifford, London, 1882. Lectures and Essays, Vol.1, London, 1879.Google Scholar
- I. Infield, B.L. Van Der Waerden, Sitzber. preuss. Akad. Wiss., Physik-math. Ki, 380, (1933).Google Scholar
- Two-Component Spinors in General Relativity, Peter G. Bergmann, Physical Review, Vol. 107,No.2, p.624.Google Scholar
- Tensor Analysis for Physicists, J. A. Schouten, 2nd edition, Dover Publications Inc., 1989.Google Scholar