Does Euclidean geometry imply quantum physics?

Abstract

In a previous paper, it was proposed that the cosmological term in Einstein's field equations be huge. This proposal heuristically followed from the combination of Leibniz' principle, Einstein's general relativity, and the observational dominance of Euclidean geometry. This paper presents preliminary results of a treatment of the large A field equations which holds promise of yielding quantum wave mechanics with no additional assumptions.

Division algebras and the factorization of Einstein's field equations

“…To apply the factorization to the "big A" field equations proposed by this author elsewhere (Nickerson, 1975b, c) would straight away seem a very interesting thing to do. One would guess, based on how quantum wave equations seem to come from the "big A" theory (Nickerson, 1975c), that such an application might yield the Dirac-type quantum equations for elementary "particles" as well as Sachs' results, but now quantized, with no assumptions other than the three classical principles of the "big A" theory.…”

“…One would guess, based on how quantum wave equations seem to come from the "big A" theory (Nickerson, 1975c), that such an application might yield the Dirac-type quantum equations for elementary "particles" as well as Sachs' results, but now quantized, with no assumptions other than the three classical principles of the "big A" theory. This is the program proposed here, with a slight, but significant, modification to be discussed in Sec.…”

“…(See any special relativity text, e.g., Taylor & Wheeler, 1966). Mendel Sachs, in important recent work (Sachs, 1967-72), has carried out an analogous factorization program on the general quadratic (4a), more specifically on the Einstein field equation (1) in "preferred" form (Nickerson, 1975b), i.e., with A = 0. Note that, because of the intimate relationship between quadratic forms and symmetric matrices (Paige & Swift, 1961), factorization of the quadratic form leads to a factorization of the symmetric matrix.…”

“…The suggestion here is to apply a similar factorization procedure to the large A field equations proposed by this author (Nickerson, 1975b);…”

“…Since, as discussed elsewhere (Nickerson, 1975c), the large A theory leads to quantum wave equations, one expects that a quaternion factorization of the large A equations will yield quantum wave equations of the Dirac form for various elementary "particles". The preceding discussion deals with real quaternion factorization.…”