Division algebras and the factorization of Einstein's field equations

Abstract

A division algebra of highest possible dimension is the eight-dimensional Cayley algebra. This remarkable property of mathematics suggests an intimate fundamental connection between Cayley algebras and descriptions of the physical universe. On this basis, it is suggested that Einstein's field equations with the huge A proposed by this author elsewhere be factored by use of such an algebra. This factorization promises to yield Diraclike spinor quantum wave equations.

Gravity, Particles, and Astrophysics

“…The theory of projective geometry in an n-dimensional space was studied in terms of homogeneous coordinates by Van Dantzig (1932), and was applied to physical field theory by Shouten and Van Dantzig (1932). These developments led to a new interest in studying the significance of conformal invariance {Shouten and Haantjes, 1936;Haantjes, 1940; see also Gross and Wess, 1970;Hoyle and Narlikar, 1974, and Chapters 8 and 9), and the role of changes of coordinate frame in classical and special relativistic mechanics (Hill, 1945a), classical electrodynamics (Hill, 1947;Motz, 1953) and general relativity (McVittie, 1942(McVittie, , 1945Walker, 1945;Infeld, 1945;Schild, 1945, 1946; see also Rosen, 1940a, b;Nariai and Ueno, 1960a;Dicke, 1962b;Synge, 1966;Nickerson, 1975;Browne, 1976a;Zel'manov, 1977;Kharbediya, 1977;Roxburgh and Tavakol, 1978;Altschul, 1978). These developments led to a new interest in studying the significance of conformal invariance {Shouten and Haantjes, 1936;Haantjes, 1940; see also Gross and Wess, 1970;Hoyle and Narlikar, 1974, and Chapters 8 and 9), and the role of changes of coordinate frame in classical and special relativistic mechanics (Hill, 1945a), classical electrodynamics (Hill, 1947;Motz, 1953) and general relativity (McVittie, 1942(McVittie, , 1945Walker, 1945;Infeld, 1945;Schild, 1945, 1946;...…”

Leibniz' principle, general relativity, and the observational dominance of euclidean geometry

“…spinor, factors and then to use nonlinear couplings to achieve derived masses and, hopefully, to derive the fundamental constants of physics. Actually, as indicated in another paper (Nickerson, 1975a), hopefully, quantum mechanics will be incorporated in this program at an early stage.…”