Minimum measurement uncertainty in quantum systems subject to high energy fluctuations

The stochastic generalization of the Madelung quantum hydrodynamics incorporates the fluctuations of the mass density into quantum equations induced by the gravitational background noise, a form of dark energy,. This model successfully addresses key aspects of quantum to classical transition through the definition of quantum potential length of interaction in addition to the De Broglie length, beyond which coherent quantum behavior and wavefunction evolution is perturbed or even deeply modified. The stochastic quantum hydrodynamic model emphasizes that an external environment is unnecessary, asserting that the stochastic behavior leading to wave-function collapse and macroscopic classical behavior with the Einstein realism can be an inherent property of physics in a spacetime with fluctuating metrics. The theory establishes a coherent link between the uncertainty principle and the constancy of light speed, aligning seamlessly with finite information transmission speed. Within quantum mechanics submitted to fluctuations, the stochastic quantum hydrodynamic model derives the indeterminacy relation between energy and time, offering insights into measurement processes impossible within a finite time interval in a truly quantum global system. The model offers also how the uncertainty relations modify themselves in an open quantum system submitted to fluctuations offering the possibility of describing how quantum mechanics can modify itself in nuclear and elementary particle physics up to the behavior of high energy black hole states. The self-consistency of the model lies in its ability to describe the dynamics of wavefunction collapse and the measure process within its mathematical structure. Additionally, the theory resolves the Einstein determinism and the pre-existing reality problem by showing that large-scale systems naturally self-decay into decoherent classical states stable in time without observer or measuring apparatus.