The subject of this book is the Casimir effect, i.e., a manifestation of zero-point oscillations of the quantum vacuum in the form of forces acting between closely spaced bodies. It is a purely quantum effect. There is no force acting between neutral bodies in classical electrodynamics. The Casimir effect has become an interdisciplinary subject. It plays an important role in various fields of physics such as condensed matter physics, quantum field theory, atomic and molecular physics, gravitation and cosmology, and mathematical physics. Most recently, the Casimir effect has been applied to nanotechnology and for obtaining constraints on the predictions of unification theories beyond the Standard Model. The book assembles together the field-theoretical foundations of this phenomenon, the application of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force, including the comparison between experiment and theory. There is increasing interest in forces of vacuum origin. Numerous new results have been obtained during the last few years which are not reflected in the literature, but are very promising for fundamental science and nanotechnology. The book provides a source of information which presents a critical assessment of all of the main results and approaches contained in published journal papers. It also proposes new ideas which are not yet universally accepted but are finding increasing support from experiment.

We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

We have used an atomic force microscope to make precision measurements of the Casimir force between a metallized sphere of diameter 196 µm and flat plate. The force was measured for plate-sphere surface separations from 0.1 to 0.9 µm. The experimental results are consistent with present theoretical calculations including the finite conductivity, roughness and temperature corrections. The root mean square average deviation of 1.6 pN between theory and experiment corresponds to a 1% deviation at the smallest separation.

The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has been achieved in the last few years.

A precision measurement of the Casimir force using metallic gold surfaces is reported. The force is measured between a large gold-coated sphere and flat plate using an atomic force microscope. The use of gold surfaces removes some theoretical uncertainties in the interpretation of the measurement. The forces are also measured at smaller surface separations. The complete dielectric spectrum of the metal is used in the comparison of theory to the experiment. The average statistical precision remains at the same 1% of the forces measured at the closest separation. These results should lead to the development of stronger constraints on hypothetical forces. PACS number͑s͒: 12.20.Fv The Casimir force ͓1,2͔ has its origin in the zero-point electromagnetic vacuum fluctuations predicted by quantum electrodynamics. If two perfectly reflecting metal plates are held parallel, then the alteration of the zero-point energy by the metal boundaries leads to an attractive force between the plates called the Casimir force ͓1,2͔. Lifshitz ͓3͔ generalized the force to any two infinite dielectric half-spaces as the force between fluctuating dipoles induced by the zero-point electromagnetic fields and obtained the same result as Casimir for two perfectly reflecting ͑infinite conductivity͒ flat plates. The Casimir force has been demonstrated between two flat plates ͓4͔ and a large sphere and a flat plate ͓5,6͔ and its value shown to be in agreement with the theory to an average deviation of 1% ͓7-9͔. For dielectric bodies the resulting force has been measured with reasonable agreement to the theory ͓10͔. Theoretical treatments of the Casimir force have shown that it is a strong function of the boundary geometry and spectrum ͓11-13͔. Experiments with periodically corrugated boundaries have also demonstrated the nontrivial boundary dependence of the Casimir force ͓14͔. Here we report an improved precision measurement of the Casimir force between a metallized sphere of diameter 191.3 m and a flat plate using an atomic force microscope ͑AFM͒. The use of gold surfaces and the related experimental changes are the primary differences between the experiments reported here and the last version of the experiment ͓9͔. In the previous experiments ͓7,9͔, Al surfaces were used due to their high reflectivity and ease of fabrication. However, in order to prevent the effects of oxidation of the Al surfaces, a thin layer of sputtered Au/Pd was used on top of the Al surface. This thin Au/Pd coating was treated in a phenomenological manner in the earlier experiments ͓7-9͔. A more complete theoretical treatment is complicated as nonlocal effects such as spatial dispersion need to be taken into account in the calculation of the Casimir force ͓15͔. Thus it is necessary to use chemically inert materials such as gold for the measurement of the Casimir force that is reported here. The complete dielectric properties of Au is used in the theory. An important application of Casimir force measurements is to develop strong limits on hypothetical long-range forces ...