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The work derives the quantum evolution in a fluctuating vacuum by introducingthe related (dark) mass density noise into the Madelung quantum hydrodynamicmodel. The paper shows that the classical dynamics can spontaneously emerge onthe cosmological scale allowing the realization of the classicalsystem-environment super system. The work shows that the dark matter-inducednoise is not spatially white and owns a well defined correlation function withthe intrinsic vacuum physical length given by the De Broglie one. The resultingmodel, in the case of microscopic systems, whose dimension is much smaller thanthe De Broglie length, leads to the Langevin-Schrodinger equation whosefriction coefficient is not constant. The derivation puts in evidence the rangeof application of the Langevin-Schrodinger equation and the approximationsinherent to its foundation. The work shows that the classical physics can beachieved in a description whose length scale is much bigger both than the DeBroglie length and the quantum potential range of interaction. The model showsthat the quantum-to-classical transition is not possible in linear systems, anddefines the long-distance characteristics as well as the range of interactionof the non-local quantum potential in order to have a coarse-grainedlarge-scale classical phase. The theory also shows that the process ofmeasurement (by a large-scale classical observer) satisfies the minimumuncertainty conditions if interactions and information do not travel fasterthan the light speed, reconciling the quantum entanglement with therelativistic macroscopic locality.

Stochastic quantum hydrodynamic model from the dark matter of vacuum  fluctuations: The Langevin-Schr\"odinger equation and the large-scale  classical limit