Why zero-point quantum noise cannot be detected at thermal equilibrium: Casimir force and zero-point contribution in the fluctuation-dissipation theorem

Abstract

The role played by zero-point contribution, also called quantum noise or vacuum fluctuations, in the quantum expression of the fluctuation-dissipation theorem (FDT) is a long-standing open problem widely discussed by the physicist community since its announcement by Callen and Welton pioneer paper of 1951 [1]. From one hand, it has the drawbacks of: (i) the expectation value of its energy is infinite, (ii) it produces an ultraviolet catastrophe of the noise power spectral density and, (iii) it lacks of an experimental validation under thermal equilibrium conditions. From another hand, by imposing appropriate boundary conditions and eliminating divergences by regulation techniques, vacuum fluctuations are the source of an attractive force between opposite conducting plates, firstly predicted by Casimir in 1948 [2] and later validated experimentally with increasing accuracy. As a consequence, a quantum formulation of FDT should account for the presence of the Casimir force and of its consequences. In this letter we show that at thermal equilibrium the Casimir force should be balanced by the mechanical reaction of the physical system. As a consequence, no zero-point spectrum can be detected and the power spectrum emitted by the physical system is the same of that calculated by Planck in 1901 [3] for a black-body. Accordingly, the experimental validation of the standard expression of the quantum FDT [1] is prevented in favor of the Nyquist expression that includes the Planck factor [4].