‘Thermal’ ambience and fluctuations in classical field theory

A plane monochromatic wave will not appear monochromatic to a noninertial observer. We show that this feature leads to a ‘thermal’ ambience in an accelerated frame even in classical field theory. When a real, monochromatic, mode of a scalar field is Fourier analyzed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum consists of three terms: (i) a factor (1/2) that is typical of the ground state energy of a quantum oscillator, (ii) a Planckian distribution N(Ω) and—most importantly—(iii) a term √ N(N + 1), which is the root mean square fluctuations about the Planckian distribution. It is the appearance of the root mean square fluctuations that motivates us to attribute a ‘thermal’ nature to the power spectrum. This result shows that some of the ‘purely’ quantum mechanical results might have a classical analogue. The ‘thermal’ ambience that we report here also proves to be a feature of observers stationed at a constant radius in the Schwarzschild and de-Sitter spacetimes. [email protected] [email protected] [email protected] 1