Abstract
Two parallel dielectric plates separated by vacuum interact through zero-point charge fluctuations and experience friction when the plates are in relative motion and the vacuum is sheared. Even at the absolute zero of temperature, residual quantum fluctuations remain because the zero-point energy gives rise to 'quantum friction'. In a recent paper, the reality of these fluctuations is questioned and the existence of quantum friction is called into question. Here we refute this assertion.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Even at absolute zero two surfaces in relative motion experience resistance from the drag created by quantum charge fluctuations. This model had been widely accepted as a correct physical description until a recent paper (T G Philbin et al 2009 New J. Phys. 11 033035) not only called the model into question, but categorically asserted that quantum friction does not exist.
Main results. We take a simple model dielectric function for each of the two surfaces and solve for the quantum friction, first in a full quantum mechanical treatment, exact in the limiting case, and then using the accepted formula derived in earlier papers from a semi-classical treatment. We show that the two results agree, and contend that the disagreement between this work and that of T Philbin and U Leonhardt results from their neglect of a subtle Doppler shift of frequency between the two surfaces, which in our opinion leads to an error in counting contributions to friction.
Wider implications. The most elemental frictional force is created by quantum charge fluctuations on two surfaces separated by vacuum. Relative motion of the two surfaces creates sparks of electromagnetic energy in the form of qbits: two correlated excitations, one on each surface. In contrast to most mechanisms of friction, the simplicity of this process gives a valuable insight at the quantum level into conversion of mechanical energy into heat. The entropy created is contained in the information content of the qbits.
Figure. Relative motion of two dielectric surfaces creates sparks of electromagnetic energy in the form of qbits. Conservation of momentum parallel to the surface requires that photons are created in pairs of equal and opposite momentum. The information content of the qbit represents the entropy of heat created in this frictional process.