Prequantum classical statistical model with infinite dimensional phase-space

Abstract

We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to statistical mechanics of classical particles. Notions of a system and causality can be reestablished on the prequantum level, but the price is sufficiently high -- the infinite dimension of the phase space. In our approach quantum observables, symmetric operators in the Hilbert space, are obtained as derivatives of the second order of functionals of classical fields. Statistical states are given by Gaussian ensembles of classical fields with zero mean value (so these are vacuum fluctuations) and dispersion $\alpha$ which plays the role of a small parameter of the model (so these are small vacuum fluctuations). Our approach might be called {\it Prequantum Classical Statistical Field Theory} - PCSFT. Our model is well established on the mathematical level. However, to obtain concrete experimental predictions -- deviations of real experimental averages from averages given by the von Neumann trace formula - we should find the energy scale $\alpha$ of prequantum classical fields.

We present a more general viewpoint to a small parameter in the representation of QM as an asymptotic projection of Prequantum Classical Statistical Field Theory - PCSFT

Cited by in corpus (18)

• Nonlinear Schrödinger equations from prequantum classical statistical field theory
• Reality without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics
• Classical Signal Model for Quantum Channels
• Quantum epistemology from subquantum ontology: quantum mechanics from theory of classical random fields
• Dirac-type equations in a gravitational field, with vector wave function
• Quantum Non-Objectivity from Performativity of Quantum Phenomena
• Quantum-like representation algorithm for trichotomous observables
• Quantum postulate vs. quantum nonlocality: Is Devil in h?
• An analog of Heisenberg uncertainty relation in prequantum classical field theory
• Born's rule from statistical mechanics of classical fields: from hitting times to quantum probabilities
• Born's rule from measurements of classical signals by threshold detectors which are properly calibrated
• The present situation in quantum theory and its merging with general relativity
• Detection model based on representation of quantum particles by classical random fields: Born's rule and beyond
• Classical signal model reproducing quantum probabilities for single and coincidence detections
• Quantum-like representation of neuronal networks' activity: modeling "mental entanglement"
• To quantum mechanics through random fluctuations at the Planck time scale
• Derive the Born's rule from environment-induced stochastic dynamics of wave-functions in an open system
• Measurement problem: from de Broglie to theory of classical random fields interacting with threshold detectors