Abstract.This present paper connects to quantum mechanics our previous geometric construct of a combined space-time 4-manifold ``M3" published earlier in this journal. Here we resolve the (particle, wave) duality by establishing the proposition that 0.75 of a known particle is manifested as a point particle in the recognized space-time 4-manifold ``M1" of matter and light, and the remaining 0.25 is manifested as an electromagnetic wave of energy in a complex space-time (sub) 4-manifold ``M2" that is contained in a larger space-time 4-manifold ``M2+" comprising of electromagnetic waves only; i.e., we have identified the quantum wave function of a particle in ``M1" with the complex norm of the electric field in ``M2" as associated with the particle. In addition to settling the particle/wave energy ratio, we have also derived the other previously undetermined parameter, i.e., the gravitational constant of ``M2+," which turns out to be so astronomically large as to cause the Schwarzschild singularity ``M2," accounting for the quantum mechanics therein.

Received: April 24, 2009

AMS Subject Classification: 83C05, 53C55, 81T10, 53C80, 83C75

Key Words and Phrases: Einstein-Kähler metric, complex Riemannian, singularity dynamics, dual mass, dark matter, quantum EPR entanglement

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 2