Simulation Results Related to Stochastic Electrodynamics

Abstract

Abstract. Stochastic electrodynamics (SED) is a classical theory of nature advanced signi…cantly 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 …elds 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 su¢ ciently 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 di¢ cult. 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.

The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics

“…The simulations of Cole and Zou typically ran for about 10 −11 sec or roughly 100, 000 orbits and showed that as time increased, the radial distribution in r tended to look more like that predicted by quantum mechanics. In subsequent simulations using 30 PCs, Cole increased the span of wavelengths used for the applied zero-point field from 10 4 to 10 6 and found ionization occurred unless they increased the precision of the computation [8]. These preliminary results were only for about 10 −12 sec, about one tenth the time of the previous work and showed general agreement with the previous work.…”

“…Cole and Zou performed the first simulations of the hydrogen atom [3] [8]. They retained the effect of the magnetic field, approximated the radiative term as discussed above, and did not use a dipole approximation.…”

Review of Experimental Concepts for Studying the Quantum Vacuum Field

“…Speculatively, but quite possibly, the source of these difficulties lies in accurately dealing with the nonlinear stochastic differential equations in SED for these problems. However, even if this can be satisfied, it is most likely there will still be differences that should clearly be testable by experimental means (Cole, 2005).…”

“…According to the quantum vacuum inertia hypothesis (Haisch et al, 1994;Rueda and Haisch, 1998a;1998b;2005), as well as the connectivity approach of Nickisch and Mollere (2002), at least some component of inertial mass derives from charge interactions with the ZPF. It is possible to investigate the electromagnetic basis of inertial mass experimentally by using Casimir plates immersed in a plasma.…”

“Einstein's Dream”—Quantum Mechanics as Theory of Classical Random Fields

“…In 1907 in a letter to Einstein, he said: "I am not seeking the meaning of the quantum of action (light quantum) in the vacuum but rather in places where emission and absorption occur, and I assume that what happens in the vacuum is rigorously described by Maxwell's equations," see, for example, [222]. We also mention stochastic electrodynamics (SED) -a variant of classical electrodynamics which postulates the existence of a classical Lorentz-invariant radiation field (zero point field, Marshall and Brafford, Boyer, de la Pena and Cetto, Coli see, e.g., [41], [53]- [57], [46], see also [42], [224]). The presence of this field plays the crucial role in SED's description of quantum effects.…”