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.

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 micromechanical torsion oscillator has been used to strengthen the limits on new Yukawa forces by determining the Casimir pressure between two gold-coated plates. By significantly reducing the random errors and obtaining the electronic parameters of the gold coatings, we were able to conclusively exclude the predictions of large thermal effects below 1 µm and strengthen the constraints on Yukawa corrections to Newtonian gravity in the interaction range from 29.5 nm to 86 nm.

We present supplementary information on the recent indirect measurement of the Casimir pressure between two parallel plates using a micromachined oscillator. The equivalent pressure between the plates is obtained by means of the proximity force approximation after measuring the force gradient between a gold coated sphere and a gold coated plate. The data are compared with a new theoretical approach to the thermal Casimir force based on the use of the Lifshitz formula, combined with a generalized plasmalike dielectric permittivity which takes into account interband transitions of core electrons. The theoretical Casimir pressures calculated using the new approach are compared with those computed in the framework of the previously used impedance approach and also with the Drude model approach. The latter is shown to be excluded by the data at a 99.9% confidence level within a wide separation range from 210 to 620 nm. The level of agreement between the data and theoretical approaches based on the generalized plasma model, or the Leontovich surface impedance, is used to set stronger constraints on the Yukawa forces predicted from the exchange of light elementary particles and/or extra-dimensional physics. The resulting constraints are the strongest in the interaction region from 20 to 86 nm with a largest improvement by a factor of 4.4 at 26 nm.

We apply the proximity force approximation, which is widely used for the calculation of the Casimir force between bodies with nonplanar boundary surfaces, to gravitational and Yukawa-type interactions. It is shown that for the gravitational force in a sphere-plate configuration the general formulation of the proximity force approximation is well applicable. For a Yukawa-type interaction we demonstrate the validity of both the general formulation of the proximity force approximation, and a simple mapping between the sphere-plate and plate-plate configurations. The claims to the contrary in some recent literature are thus incorrect. Our results justify the constraints on the parameters of non-Newtonian gravity previously obtained from the indirect dynamic measurements of the Casimir pressure.