Abstract
The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed). Important commonalities and complementarities between the two theories are identified, notwithstanding their dissimilar origins and approaches. Further, the dynamical equation of sqm is completed with the radiation terms that are an integral element in sed. The central problem of the transition to the quantum dynamics is addressed, pointing to the key role of diffusion in the emergence of quantization.
Highlights
A whole and diverse series of stochastic theories have been developed with the aim to throw some light on the nature of the quantum phenomenon [for some representative work see Fényes [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]
A common feature of these two theories is the explicit introduction of stochasticity as an ontological element missing in the quantum theory, with the aim to address many of the historical—and still current—conceptual difficulties associated with quantum mechanics
These expressions coincide precisely with those obtained for the two velocities of stochastic quantum mechanics (SQM), namely Equation (16), if the diffusion coefficient appearing in these equations is assigned the value
Summary
A whole and diverse series of stochastic theories have been developed with the aim to throw some light on the nature of the quantum phenomenon [for some representative work see Fényes [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]. Connecting Two Stochastic Quantum Theories statistical evolution equation (a generalized Fokker-Planck-type equation, GFPE) in phase space, to arrive at a description in x-space, in which the dissipative and diffusive terms are seen to bring about a definitive departure from the classical Hamiltonian dynamics The interplay between these two terms is what allows the system to eventually reach equilibrium and attain the quantum regime; the dynamics is described by the Schrödinger equation, and the operators become a natural tool for its description. The purpose of the present work is to establish the connection between SQM and SED and, by so doing, to identify the strengths and limitations of the two theories, as well as certain commonalities and complementarities between them With this aim, we first present the basic elements of SQM leading to the dynamical law that governs both classical and quantum stochastic processes in the Markov approximation. It is concluded that this more complete ontology which includes the ZPF as the source of stochasticity, leads in a natural process to the quantum description
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