  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].
