NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION

Abstract

The original approach for the self-consistent inclusion of gravity into quantum mechanics of a particle is developed. (There are no connections with second quantization.) The nonstandard action principle is constructed for the stationary situation: the quantum particle in a stationary state creating some nonclassical stationary gravitational field and interacting with it, The accompanying problem of covariantization of quantum operators is considered. The general theory is illustrated by the Newtonian-Schrödingerian and quasi classical limiting cases. The levels of applicability of ordinary quantum mechanics and the problems of measurements and interpretation of nonclassical gravity are discussed. The “uncertainty relations” connecting uncertainties of some “local” parts of curvature and those of the particle’s position and momentum are derived. The superposition principle is generalized on the base of some approximate action.