Do the precise measurements of the Casimir force agree with the expectations?

An upper limit on the Casimir force is found using the dielectric functions of perfect crystalline materials which depend only on well defined material constants. The force measured with the atomic force microscope is larger than this limit at small separations between bodies and the discrepancy is significant. The simplest modification of the experiment is proposed allowing to make its results more reliable and answer the question if the discrepancy has any relation with the existence of a new force. The Casimir force [1] between closely spaced macroscopic bodies is the effect of quantum electrodynamics (QED) and for that reason could be predicted very accurately. In the rigorous Lifshitz theory [2, 3] the force is defined by the optical properties of used materials. Knowledge of these properties is the weakest element in the theory restricting the accuracy that can be achieved. Though the measurement of the Casimir force is not the best way to test QED, such experiments are of great importance because they are sensitive to the presence of new fundamental forces [4] predicted in many modern theories (see, for example, [5] and references therein). To distinguish a new force from the background, we should be able to calculate the Casimir force with a precision better than the experimental one. In the series of recent experiments this force has been measured with the torsion pendulum (TP) [6] in the range of distances 0.6−6 μm and with the atomic force microscope (AFM) [7, 8] in the range 0.1 − 0.9 μm. The corresponding precisions were 5% and 1%, respectively. The force per unit area between parallel plates arising as a result of electromagnetic fluctuations at nonzero temperature T is generalized by the Lifshitz theory [3], ∗To whom correspondence should be addressed. E-mail: [email protected]