Principles of maximally classical and maximally realistic quantum mechanics
S M ROY
Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
Abstract. Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than N+1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative definition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie--Bohm realistic theory gives highly nonclassical trajectories.
Keywords. Maximally realistic quantum theory; phase space Bell inequalities; maximally classical trajectories in realistic quantum theory.
PACS No. 03.65.Ta