From Quantum To Classical Dynamics: A Landau Continuous Phase Transition With Spontaneous Superposition Breaking

Abstract

Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking (effective hiding), as a special case of the corresponding general formalism (Bernstein). Critical values of the order parameters for this transition are determined by Heisenberg's indeterminacy relations, change continuously, and are in excellent agreement with the recent and remarkable experiments with Bose condensation. It is also shown that such a phase transition can sucessfully model self-collapse (self-decoherence), as an effective classical phenomenon, on the measurement device. This then induces a relative collapse (relative decoherence) as an effective quantum phenomenon on the measured quantum object by measurement. We demonstrate this (including the case of Bose-Einstein condensation) in the well-known cases of the Stern-Gerlach spin measurement, Bell's inequality and the recently discussed quantum superposition on a mirror a la Marshall et al. These results provide for a proof that quantum mechanics, in distinction to all absolute collapse and hidden-variable theories, is local and objective. There now appear no insuperable obstacles to solving the open problems in quantum theory of measurement and foundation of quantum mechanics, and strictly within the standard quantum-mechanical formalism. Simply put, quantum mechanics is a field theory over the Hilbert space, the classical mechanics characteristics of which emerge through spontaneous superposition breaking.