The theory of the fluctuations of the van der Waals (vdW) attractive force between macroscopic bodies is developed. A general equation for the spectral density of the fluctuating surface Maxwell stress (force per unit area) in vacuum near the surface of a body is derived under the assumption that, inside the bodies, the random Langevin sources of the electric and magnetic fields (charges, polarizations, currents) are Gaussian. This spectral density of stress is an integral over frequencies of a sum of terms each of which is a product of Fourier amplitudes of two field components' correlation functions. For metallic bodies, the contribution of free electrons to the vdW force (at frequencies up to the frequency of electron scattering) is calculated. This contribution to the force and its noise grows with temperature. Application of noiseless voltage to two interacting metals across the vacuum gap between them generates an additional force noise. This additional noise is proportional to the voltage squared and to the spectral density of the random electric field at the frequency of noise measurement. The theoretical qualitative conclusions are in good agreement with experiments.
A. Shulim Kogan,
"Fluctuations of Van Der Waals force between macroscopic bodies", Proc. SPIE 5112, Noise as a Tool for Studying Materials, (9 May 2003); doi: 10.1117/12.497417; https://doi.org/10.1117/12.497417