Quantum friction
Fifty years ago Evgeny Lifshitz calculated the vacuum force between two parallel dielectric plates. Casimir’s simple formula for the vacuum force between two perfectly conducting metal plates placed in a vacuum then emerges in the limit of infinite permittivity.
For more than three decades scientists have been trying to generalize this problem. They have tried to find out what happens to the Casimir force when one of the plates moves at a constant speed parallel to the other. So far the results obtained have been conflicting. With the result interest in this problem has grown. Researchers are particularly interested in the lateral component of the Casimir force because this lateral component would give information on the extent of a quantum vacuum contribution to friction between bodies.
Thomas Philbin and Ulf Leonhardt of the University of St Andrews use the Lifshitz theory to find the zero-temperature Casimir forces between the plates for arbitrary velocity. For a problem like this it is generally accepted by physicists that there should be a lateral force between the plates, a quantum-mechanical friction. But Philbin and Leonhardt show that the motion between the plates does not in fact induce a lateral Casimir force. They argue that almost all of the treatments of this problem by other physicists (who claim that the motion between the plates does induce a lateral Casimir force) have made use of various approximations, and there is disagreement on the magnitude of the Casimir forces.
(To know more about Casimir effect please refer to the following post: The negative Casimir effect)
In the paper entitied ‘The Quantum Vacuum’, P W Milonni states that Casimir forces are caused by the vacuum zero-point modes of the electromagnetic field. Philbin and Leonhardt argue that if the plates under consideration were perfect mirrors then the zero-point modes do not penetrate the materials and the motion of one plate can therefore have no effect on the vacuum forces i.e. there is an attractive force between the mirrors given by Casimir’s formula with no lateral component. Philbin and Leonhardt further explain that for realistic materials, however, the zeropoint modes will penetrate the moving plate and the motion should therefore affect the Casimir force. The question they try to answer is whether the vacuum modes are influenced in a way that produces a lateral force on the plates.
First utilizing the following physical reasoning they try to suggest the absence of a lateral force: a moving medium is equivalent to a particular non-moving bi-anisotropic medium; for the present argument the bianisotropy can be very small. It would be very strange if a bi-anisotropic medium could be used to induce a unidirectional lateral Casimir force as this would seem to allow the extraction of unlimited energy from the quantum vacuum. (A “bi-anisotropic medium” is a material in which electric fields or magnetic fields applied separately will induce both magnetic dipoles and electric dipoles in the material, and that such a medium at rest is the equivalent of a certain kind of non bi-anisotropic material in motion.)
Finally based on results obtained from rigorous exact calculations (as claimed by them) they draw the following conclusion: Shear motion at a constant speed of one infinite plate parallel to another modifies the Casimir force between them compared to the non-moving case, but it does not induce a lateral force. Citing work done by other physicists they further claim that their result implies the absence of “quantum friction” on a particle moving a constant speed parallel to an infinite plate. The researchers further conclude that the case of two finite bodies moving past each other with constant velocities is very different i.e. it is a complicated dynamical problem, even if the effect of the vaccum forces on the velocities of the bodies is neglected and calculating this modified Casimir force is extremely difficult. They feel that previous efforts to do so have not been satisfactory because they have used approximations.
April 1, 2009