Plane waves viewed from an accelerated frame: quantum physics in classical setting

Abstract

We report here an analogue for the vacuum state in classical field theory and its Planckian nature with respect to uniformly accelerated observers. We find that when a real, monochromatic mode of a classical field is Fourier transformed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum has three separate terms none of which have a simple classical meaning. But they bear a striking resemblance to the quantum mechanical description. Specifically, the three terms are (i) a factor (½) that is typical of the ground state energy of a quantum oscillator, (ii) a Planckian distribution N(Ω) and, most importantly, (iii) a term proportional to √N(N+1), which is the root mean square fluctuations about the Planckian distribution. The implications of this result are discussed.