The Casimir Force

Note that the Casimir force does not depend on any material constants, but is solely formulated in terms of fundamental constants, namely the velocity of... 

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, "Quantum mechanical actuation of microelectro mechanical systems by the Casimir force," Science, 291, 1941-4 (2001) "Nonlinear micromechanical Casimir oscillator," Phys. Rev. Lett., 87, 211801 (2001). 

PW Milonni, M.-L. Shih, Source theory of the Casimir force. Phys. Rev. A 45 (1992) 4241. R.R. McLone, E.A. Power, On the Interaction Between Two Identical Neutral Dipole Systems, One in an Excited State and the Other in the Ground State. Mathematika 11 (1964) 91. 

Various quantum effects arising due to the motion of dielectric boundaries, including the modification of the Casimir force and creation of photons, in both one and three dimensions, and for different orientations of the velocity vector with respect to the surface, have been studied in detail in the series of papers by Barton and his collaborators [142-148]. In one paper [142] the term mirror-induced radiation (MIR) was introduced. 

It is not heretical to consider the electromagnetic vacuum as a physical system. In fact, it manifests some physical properties and is responsible for a number of important effects. For example, the field amplitudes continue to oscillate in the vacuum state. These zero-point oscillations cause the spontaneous emission [1], the natural linebreadth [5], the Lamb shift [6], the Casimir force between conductors [7], and the quantum beats [8]. It is also possible to generate quantum states of electromagnetic field in which the amplitude fluctuations are reduced below the symmetric quantum limit of zero-point oscillations in one quadrature component [9]. 

Bressi, G., Carugno, G., Onofrio, R., Ruoso, G. Measurement of the Casimir force between parallel metallic surfaces. Phys. Rev. Lett. 88 Art. No. 041804 (2002). 

Derjaguin used this approach to calculate the interaction between two ellipsoids [84]. The same approximation was also introduced in 1977 by Blodd et al. [85] for calculating interaction forces between nuclei of atoms. They coined the term proximity forces in their publication. While the term Derjaguin approximation is stUl the standard term in surface science, the term proximity force approximation has become popular among physicists in the field of nuclear physics and the Casimir force (see Section 2.6). 

At this point we should darify that the Casimir force is not a really new type of force. It is simply another term for a special case of the van der Waals forces, namely, the retrarded van der Waals force between metallic surfaces. While the terms retarded van der Waals force or retarded London dispersion force are prevalent in the physical chemistry and colloid community, the term Casimir force or Casimir-Polder force has become popular in the physics community. This means that in principle the lifshitz theory is apphcable to describe the Casimir forces. The problem with using Lifshitz theory for ideal metals is the fact that for these the didectric constant diverges (e oo) and therefore the Lifshitz theory breaks down. However, for real metals, the use of the Lifshitz theory is possible with corresponding dielectric models of the metals. 

The influence of finite temperature on the Casimir force has been calculated [120-122] and some experiments have been carried out [123]. Consensus has, however, not been reached. This is partially due to the fact that an experimental verification is difficult since van der Waals forces at large distances are weak. For that reason, they are usually also insignificant, and our poor understanding is more an academic problem. 

Casimir Force for Nontriviai Geometries As in the case of the normal van der Waals forces, the Derjaguin approximation can be used to calculate the Casimir force for geometries other than that of parallel plates. Note that in many papers on the Casimir force, this approach is called "proximity force approximation due to historic reasons (see Section 2.3). It was shown that the error introduced by this approximation should be smaller than 0.4 D/R for D < 300 nm [129]. Full calculations without approximation have been done for some configurations, for example, sphere/plate [130], but these are usually cumbersome. An alternative approach for approximate calculations was introduced by Jaffe and Scardicchio [131]. It is based... 

One year later Mohideen and coworkers [115] used the colloid probe AFM technique to probe the Casimir force between a metalcoated planar surface and a metal coated sphere. After several improvements [135], they could achieve a measurement over the range of distance starting from 62 to 400 nm with an experimental error ofless than 1% at the lowest distance (Figure 2.10). This level of precision allows a quantitative comparison with theory. In this case, the influences of surface roughness, finite temperature, and finite conductivity of the metal have been taken into account. 

Figure 2.10 Measurement of the Casimir force between a gold-coated sphere and gold-coated plate. (From Ref [135] with permission from U. Mohideen.)...

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