Periodicity, Thermal Effects, and Vacuum Force: Rotation in Random Classical Zero-Point Radiation

TL;DR

This paper demonstrates that a detector rotating in a classical zero-point field perceives thermal effects characterized by a temperature proportional to its angular velocity, with vacuum forces influencing its motion and potentially explaining confinement phenomena.

Contribution

It introduces a model showing thermal effects and vacuum forces for rotating detectors in classical zero-point fields, linking these effects to rotation-induced periodicity and spectrum discretization.

Findings

Rotating detectors perceive a thermal spectrum with temperature proportional to angular velocity.

Vacuum force on the detector is attractive, depends on orbit radius, and diverges at the maximum radius.

The vacuum force's radius dependence relates to confinement and asymptotic freedom in QCD.

Abstract

We show that, for a detector rotating in a random classical zero-point electromagnetic or massless scalar field at zero temperature, thermal effects exist. The rotating reference system is constructed as an infinite set of Frenet-Seret tetrads so that the detector is at rest in a tetrad at each proper time. Frequency spectrum of correlation functions contains the Planck thermal factor with temperature $T_{rot} = \frac{\hbar \Omega}{2 \pi k_B} $. The energy density the rotating detector observes is proportional to the sum of energy densities of Planck's spectrum at the temperature $T_{rot}$ and zero-point radiation. The proportionality factor is $2/3 (4 \gamma^2 -1)$ for an EMF and $2/9 (4 \gamma^2 -1)$ for a MSF, where $\gamma = (1 - (\frac{\Omega r}{c})^2)^{-1/2}$, and r is a rotation radius. The origin of these thermal effects is the periodicity of the correlation functions and their discrete spectrum, both following rotation with angular velocity $\Omega$. The thermal energy can also be interpreted as a source of a vacuum force (VF) applied to the rotating detector from the vacuum field. The VF depends on the size of neither the charge nor the mass, like the force in the Casimir model for a charged particle, but, contrary to the last one, VF is attractive and directed to the center of the circular orbit. VF infinitely grows in magnitude with orbit radius. The orbits with a radius greater than $c/ \Omega$ do not exist because the returning VF becomes infinite. On the uttermost orbit with the radius $c / \Omega$, a linear velocity of the rotating particle would have become c. The VF becomes very small and proportional to radius when r is very small. Such VF dependence on radius, at large and small radii, can be associated respectively with so called confinement and asymptotic freedom, known in quantum chromodynamics, and provide a new explanation for them.