Thermal Effects of Rotation in Random Classical Zero-Point Radiation

Abstract

The rotating reference system {µ τ }, along with the two-point correlation functions (CFs) and energy density, is defined and used as the basis for investigating thermal effects observed by a detector rotating through random classical zero-point radiation. The reference system consists of Frenet -Serret orthogonal tetrads µ τ . At each proper time τ the rotating detector is at rest and has a constant acceleration vector at the µ τ .The two-point CFs and the energy density at the rotating reference system should be periodic with the period T = 2π Ω , where Ω is an angular detector velocity, because CF and energy density measurements is one of the tools the detector can use to justify the periodicity of its motion. The CFs have been calculated for both electromagnetic and massless scalar fields in two cases, with and without taking this periodicity into consideration. It turned out that only periodic CFs have some thermal features and particularly the Planck's factor with the temperature T rot = hΩ 2πkB (k B is the Boltzman constant).Regarding to the energy density of both electromagnetic and massless scalar field it is shown that the detector rotating in the zero-point radiation observes not only this original zero-point radiation but , above that, also the radiation which would have been observed by an inertial detector in the thermal bath with the Plank's spectrum at the temperature T rot . This effect is masked by factor 2 3 (4γ 2 − 1) for the electromagnetic field and 2 9 (4γ 2 − 1) for the massless scalar field, where γ = (1−( Ωr c ) 2 ) −1/2 . Appearance of these masking factors is connected with the fact that rotation is defined by two parameters, angular velocity and the radius of rotation, in contrast with a uniformly accelerated linear motion which is defined by only one parameter, acceleration a.Our calculations involve classical point of view only and to the best of our knowledge the results have not been reported in quantum theory yet.