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51.1 Introduction 51.1 Introduction
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51.2 Stochastic Mechanics 51.2 Stochastic Mechanics
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51.2.1 Hydrodynamical Interpretation of Schrödinger equation 51.2.1 Hydrodynamical Interpretation of Schrödinger equation
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51.2.2 Stochastic Interpretation of Schrödinger Equation 51.2.2 Stochastic Interpretation of Schrödinger Equation
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51.2.3 Does Stochastic Mechanics Provide a Realistic Interpretation of Quantum Mechanics? 51.2.3 Does Stochastic Mechanics Provide a Realistic Interpretation of Quantum Mechanics?
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51.3 Stochastic Electrodynamics 51.3 Stochastic Electrodynamics
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51.3.1 The Harmonic Oscillator 51.3.1 The Harmonic Oscillator
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51.3.2 Comparison between the Stationary State in SED and the Ground State in QM 51.3.2 Comparison between the Stationary State in SED and the Ground State in QM
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51.3.3 Other Applications to Linear Systems 51.3.3 Other Applications to Linear Systems
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51.3.3.1 A Model for Quantum Entanglement in the London–Van Der Waals Forces 51.3.3.1 A Model for Quantum Entanglement in the London–Van Der Waals Forces
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51.3.3.2 Specific Heats of Solids 51.3.3.2 Specific Heats of Solids
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51.3.3.3 The Particle in a Homogeneous Magnetic Field 51.3.3.3 The Particle in a Homogeneous Magnetic Field
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51.3.4 Failure in Nonlinear Systems 51.3.4 Failure in Nonlinear Systems
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51.3.5 The Equilibrium between Radiation and Matter 51.3.5 The Equilibrium between Radiation and Matter
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51.4 Stochastic Optics 51.4 Stochastic Optics
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51.4.1 Vacuum Radiation Field in Confined Space 51.4.1 Vacuum Radiation Field in Confined Space
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51.4.2 Wave–Particle Behaviour of Light 51.4.2 Wave–Particle Behaviour of Light
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51.4.3 Spontaneous Parametric Down-Conversion (SPDC) 51.4.3 Spontaneous Parametric Down-Conversion (SPDC)
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References References
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51 Stochastic Interpretations of Quantum Mechanics
Get accessEmeritus Professor of Physics, Universidad de Cantabria
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Published:19 May 2022
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Abstract
It is argued that if quantum mechanical description is incomplete a plausible interpretation is stochastic. Two theories are briefly revisited: stochastic mechanics and stochastic (or random) electrodynamics. The former assumes that the paths of quantum particles are Markov processes having some similarity with Brownian motion. The latter rest on the assumption that vacuum fields are real stochastic fields, in particular the electromagnetic radiation. The motion of particles immersed in the field, treated with classical electrodynamics, leads to stationary states where emission and absorption of radiation are balanced. Agreement with the quantum ground state is achieved for linear systems, but not in general. An extension to a stochastic interpretation of quantum optics provides agreement with quantum optics in some cases, but difficulties appear that are pointed out.
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