Circular Motion of a Small Oscillator in a Zero-Point Field Without External Forces: Is It Possible?

Abstract

A small dipole oscillator moving along a circular trajectory in zero-point electromagnetic field ( ZPF ) and with a polarization normal to the rotation plane, is considered. Temporal periodicity conditions are imposed on ZPF, associated with the way the rotating oscillator observes ZPF. They are similar to spatial boundary conditions in Casimir phenomenon and therefore result in ZPF spectrum change from continuous one to a discrete one and, as a consequence, an effective temperature of the modified ZPF (Y. S. Levin ). The average centripetal average force on the oscillator, originating from this modified ZPF scattered by the oscillator in the near zone, is calculated in terms of the bilinear correlation functions of electromagnetic field. After renormalization of the correlation function, which physically means extraction of a pure effect of periodicity, the force has a finite value. All calculations are carried out using the methodology of stochastic electrodynamics. The radial component of the force is directed to the center of rotation. In non relativistic case and for oscillator frequency smaller than rotation frequency, the force turns out to be proportional to the rotation radius. Such result could mean a possibility that micro motion of the oscillator in ZPF sustains its average circular motion without any other external forces.Though the estimation done for the point-like electron shows that the effect is not observable because the radius of such circular electron motion would have been much smaller than the classical electron radius when our semi classical approach to the electromagnetic problem does not work. It is well expected result and considered as the first step in the application of the idea in the quark world governed by non abelian colored fields, subject of the next paper.