Particle Brownian motion due to random classical radiation: superfluid-like behavior in the presence of classical zero-point radiation

Abstract

Nonrelativistic classical mechanics allows no fundamental transition between low-velocity and high-velocity forms of behavior, nor between low-temperature and high-temperature forms. In contrast, classical electrodynamics, which is a relativistic theory, allows fundamental transitions in velocity. Furthermore, the inclusion within the classical theory of Lorentz-invariant classical zero-point radiation allows classical electrodynamics to distinguish high-temperature and low-temperature forms of behavior. Because electromagnetism is a relativistic theory, it may provide a thermal radiation bath which gives rise to phenomena in Brownian motion which are not included in a model with a thermal bath based upon nonrelativistic particles. Here we explore the Brownian motion of a classical electric-dipole particle in random classical radiation, making use of the calculations of Einstein and Hopf. The Brownian motion as a function of temperature is analyzed in terms of the mean-square velocity and the diffusion constant for four different classical radiation spectra: the Rayleigh–Jeans spectrum, the Planck spectrum without zero-point radiation, the zero-point radiation spectrum, and the Planck spectrum including zero-point radiation. We illustrate how the inclusion of classical electromagnetic zero-point radiation alters Brownian motion behavior between high-temperature and low-temperature forms. For the Planck spectrum with zero-point radiation, the high-temperature Brownian motion agrees with some aspects found from nonrelativistic mechanics, while the low-temperature behavior includes some aspects analogous to superfluid behavior. At sufficiently low temperatures, the Brownian particle has an increasing mean-square velocity and more rapid diffusion with decreasing temperature due to the increasing dominance of the classical electromagnetic zero-point radiation.