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

Abstract

We show that for a detector rotating in a random classical zero-point electromagnetic or massless scalar field at T=0 thermal effects exist. The rotating reference system is constructed as an infinite set of Frenet-Seret tetrads defined so that the detector is at rest in a tetrad at each proper time. Correlation functions, more exactly their frequency spectrum, contain the Planck thermal factor, and the energy density the rotating detector observes is proportional to the sum of energy densities of Planck's spectrum at the temperature T_rot = \hbar \Omega / (2 \pi k_B) and zero-point radiation. The proportionality factor is (2/3)(4\gamma^2 - 1) for an electromagnetic field and (2/9)(4\gamma^2 - 1) for a massless scalar field, where \gamma = (1 - (\Omega r/c)^2)^(-1/2), and r is a detector 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, f_vac, applied to the rotating detector from the vacuum field. The f_vac 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, it is directed to the center of the circular orbit. The f_vac infinitely grows by magnitude when r \to r_0 = c/\Omega, with a fixed \Omega. The orbits with a radius greater than r_0 do not exist simply because the returning vacuum force becomes infinite. On the uttermost orbit with the radius r_0, a linear velocity of the rotating particle would have become c. The f_vac becomes very small and proportional to r when r is small, r << c/\aOmega. Such vacuum force dependence on radius, at large and small r, can be associated respectively with so called confinement and asymptotic freedom, known in QCD, and provide a new explanation for them.