Demonstration of the Casimir Force in the 0.6 to 6 mm Range

where a is the plate separation; in principle, a QED effect can directly influence a macroscopic, classical, apparatus. In spite of the extensive theoretical attention this effect has received over the years (see [2,3] for recent reviews), there has been only one attempt at its measurement. This measurement, as reported by Sparnaay in 1958, showed an attractive force “not inconsistent with” the prediction given by Eq. (1), but with effectively 100% uncertainty [4]. A closely related effect, the attraction of a neutral atom to a conducting plate, has been recently measured [5]; good agreement with theory was found. The Casimir force is closely related to the van der Waals attraction between dielectric bodies. Formally, Eq. (1) is obtained by letting the dielectric constant e in the Lifshitz theory [6] approach infinity, which is an appropriate description for a conducting material. However, in practical terms, the Casimir and van der Waals forces are quite different; the van der Waals force is always attractive, whereas the sign of the Casimir force is geometry dependent. For example, if a thin spherical conducting shell is cut in half, the two hemispheres will experience a mutual repulsive force [7]. These points are discussed in Refs. [2,3]. A number of experimental measurements of short-range forces between dielectric bodies of various forms have been performed; see Ref. [2] for a review. For our measurement of the Casimir force, the conductors were in the form of a flat plate and a sphere. Our first attempts at measurements using parallel plates were unsuccessful; this is because it is very difficult to maintain parallelism at the requisite accuracy (1025 rad for 1 cm diameter plates). There is no issue of parallelism when one plate has a spherical surface; geometrically, the system is described by the separation at the point of closest approach. However, when one plate is spherical, Eq. (1)