Linear physics: From classical mechanics to quantum electrodynamics

Yehonatan Knoll

Jaroslav Zamastil, Jakub Benda

Luis de la Peña, Ana Marı́a Cetto

During the last decades there has been a relatively extensive attempt to develop the theory of stochastic electrodynamics (SED) with a view to establishing it as the foundation for quantum mechanics. The theory had several important successes, but failed when applied to the study of particles subject to nonlinear forces. An analysis of the failure showed that its reasons are not to be ascribed to the principles of SED, but to the methods used to construct the theory, particularly the use of a Fokker-Planck approximation and perturbation theory. A new, non perturbative approach has been developed, called linear stochastic electrodynamics (LSED), of which a clean form is presented here. After introducing the fundamentals of SED, we discuss in detail the principles on which LSED is constructed. We pay attention to the fundamental issue of the mechanism that leads to the quantum behaviour of field and matter, and demonstrate that indeed LSED is a natural way to the quantum formalism by demanding its solutions to comply with a limited number of principles, each one with a clear physical meaning. As a further application of the principles of LSED we derive also the Planck distribution. In a final section we revisit some of the most tantalizing quandaries of quantum mechanics from the point of view offered by the present theory, and show that it offers a clear physical answer to them.

George Adolphus Schott

Daniel C. Cole

Stochastic electrodynamics (SED) is a classical theory of nature advanced significantly in the 1960s by Trevor Marshall and Timothy Boyer. Since then, SED has continued to be investigated by a very small group of physicists. Early investigations seemed promising, as SED was shown to agree with quantum mechanics (QM) and quantum electrodynamics (QED) for a few linear systems. In particular, agreement was found for the simple harmonic electric dipole oscillator, physical systems composed of such oscillators and interacting electromagnetically, and free electromagnetic fields with boundary conditions imposed such as would enter into Casimir‐type force calculations. These results were found to hold for both zero‐point and non‐zero temperature conditions. However, by the late 1970s and then into the early 1980s, researchers found that when investigating nonlinear systems, SED did not appear to provide agreement with the predictions of QM and QED. A proposed reason for this disagreement was advocated by Boyer and Cole that such nonlinear systems are not sufficiently realistic for describing atomic and molecular physical systems, which should be fundamentally based on the Coulombic binding potential. Analytic attempts on these systems have proven to be most difficult. Consequently, in recent years more attention has been placed on numerically simulating the interaction of a classical electron in a Coulombic binding potential, with classical electromagnetic radiation acting on the classical electron. Good agreement was found for this numerical simulation work as compared with predictions from QM. Here this worked is reviewed and possible directions are discussed. Recent simulation work involving subharmonic resonances for the classical hydrogen atom is also discussed; some of the properties of these subharmonic resonances seem quite interesting and unusual.

N. Rosen