Role of the Electromagnetic Vacuum in the Transition from Classical to Quantum Mechanics

• Published in: Foundations of physics Vol. 52; no. 4
• Main Authors: Cetto, Ana María, de la Peña, Luis
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer Nature B.V
• Subjects: Charged particles; Classical and Quantum Gravitation; Classical Mechanics; Commutators; Electrodynamics; Fokker-Planck equation; History and Philosophical Foundations of Physics; Initial conditions; Mathematical analysis; Matrix representation; Philosophy of Science; Physics; Physics and Astronomy; Quantum mechanics; Quantum phenomena; Quantum Physics; Radiation; Relativity Theory; Response functions; Statistical Physics and Dynamical Systems; Elucidation of the classical-to-quantum transition; Origin of quantum operators; Stochastic electrodynamics; Zero-point radiation field
• ISSN: 0015-9018; 1572-9516
• DOI: 10.1007/s10701-022-00605-6

We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field ( zpf ), with the purpose of revealing the mechanism that takes it from the initially classical description to the final quantum-mechanical one. The combined effect of the zpf and the radiation reaction force results, after a characteristic time lapse, in the loss of the initial conditions and the concomitant irreversible transition of the dynamics to a stationary regime controlled by the field. In this regime, the canonical variables x ,  p become expressed in terms of the dipolar response functions to a set of field modes. A proper ordering of the response coefficients leads to the matrix representation of quantum mechanics, as was proposed in the early days of the theory, and to the basic commutator x ^ , p ^ = i ħ . Further, the connection with the corresponding Fokker–Planck equation valid in the Markov approximation, allows one to obtain the (nonrelativistic) radiative corrections of qed . These results reaffirm the essentially electrodynamic and stochastic nature of the quantum phenomenon, as proposed by stochastic electrodynamics.