Dpset beyond Quantum Determinacy: Dark Soliton Evidence for Kinematic Framework of Entanglement Histories

Abstract

The Dirac's Principle of Superposition of Evolution of Time (DPSET) postulates four temporal motions: forward from the past, backward to the past, forward to the future, and backward from the future. Together these are claimed to account for all possible quantum evolution outcomes, with a system's physical configuration determining which motion occurs and thereby restoring determinacy via kinematic time-reversal of otherwise irreversible processes. This paper tests that claim quantitatively, for the first time, in a nonlinear stochastic setting: dark soliton wavefunctions are evolved using the quantum-noise-extended nonlinear Schrödinger equation, and the corresponding transition timescales are obtained from the Bose–Hubbard model in the Mott insulator regime of an optical-lattice Bose–Einstein condensate. Under realistic, ultracold microsecond timescales, the forward and backward soliton branches display a real but uniformly small density asymmetry that proves to be strictly kinematic, not a signature of reversed-time dynamics derived from the underlying stochastic equation of motion. DPSET is thereby shown to lack two dynamical ingredients: the additional score-function drift term required by Anderson's reverse-time diffusion theorem for the reversed process to reproduce forward statistics, and an explicit coupling rule for temporal modes under stochastic noise. Rather than a dynamical theory of collapse, DPSET is better recommended as a candidate kinematic framework for probing entanglement histories within linear, unitary quantum systems.