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Foundations of Physics

On the nonoccurrence of two paradoxes in the measurement scheme of stochastic quantum mechanics

Franklin E. Schroeck

Published Mar 1, 1985• 12 citations
Publisher
DOI
10.1007/bf00737318

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It is hypothesized that the Langevin time of stochastic quantum quantization is a physical time over which quantum fields at all values of space and coordinate time fluctuate. The average over paths becomes a time average as opposed to an ensemble average. It is further hypothesized that the Langevin time also paces the motion of particles through coordinate time and is equal to the coordinate time of the present hypersurface in the frame of the Hubble expansion. Despite having a preferred frame, special relativity continues to hold in this formulation as a dynamical symmetry due to the presumed Lorentz invariance of interactions. The measurement process becomes an integral part of the theory and is realized as a process of spontaneous symmetry breaking. The continuously fluctuating history of fields, characteristic of having two times, and the switch from ensemble averages to time averages allows for logical and straightforward explanations of many quantum measurement paradoxes. The fluctuating history also evades hidden-variable prohibitions allowing an essentially classical system to underlie quantum mechanics. These changes to the stochastic quantization paradigm makes this stochastic classical system differ somewhat from standard quantum mechanics, so, in principle, distinguishable from it.
This thesis investigates a novel proposal for quantum reality and measurement, based on phase-space representations and forward-backward stochastic differential equations, that is consistent with macroscopic realism: a Q-based objective-field model for quantum mechanics. We study the model through macroscopic quantum paradoxes, quantum measurement, and continuous-variable Bell tests. We investigate techniques for enhancing the coherence of two-mode cat states and analyze macroscopic versions of Wigner’s friend and the three-box paradox. The measurement problem is examined through the dynamics of the Q function, providing an account of wave-function collapse. This work contributes to understanding quantum reality and measurement and provides a foundation for developing quantum technologies.