Quantum physics

Casimir force changes sign

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This quantum attractive force induces measurable effects between ultrasmall mechanical components. New calculations indicate that systems could be engineered in which Casimir forces are repulsive.

In 1948, Hendrik Casimir calculated that the quantum fluctuations of an electromagnetic field, so-called zero-point fluctuations, give rise to an attractive force between objects1. This force is a particularly striking consequence of the quantum theory of electrodynamics (for a review, see ref. 2). Casimir's calculations were idealized — he considered two perfectly conducting parallel plates at absolute-zero temperature — but there are implications for more realistic objects. In Physical Review Letters, Kenneth et al.3 have extended these considerations to real-world materials.

Their work follows that of Boyer in 1974, who also studied the case of parallel plates but with one plate perfectly conducting and the other having infinite magnetic permeability (permeability is a measure of the material's response to an applied magnetic field). For this special case Boyer found that quantum fluctuations induce a force with the opposite sign, causing the plates to repel each other4. Kenneth et al. now extend understanding of the Casimir force phenomenon to the more general situation of realistic 'dielectric' materials that are characterized by both their electrical permittivity (a measure of the material's response to an applied electric field) and their magnetic permeability. Their numerical results show that repulsive forces can arise in the general class of materials with high magnetic permeability.

Although the Casimir effect is deeply rooted in the quantum theory of electrodynamics, there are analogous effects in classical physics. A striking example was discussed in 1836, in P. C. Caussée's L'Album du Marin (The Album of the Mariner)5. Caussée reported a mysteriously strong attractive force that can arise between two ships floating side by side — a force that can lead to disastrous consequences (Fig. 1). A physical explanation for this force was, however, offered only recently, by Boersma6, who suggested that it originates in the radiation pressure of water waves acting differently on the opposite sides of the ships.

Figure 1: A Casimir-like effect at sea.
figure1

In the days of square-riggers, sailors noticed that, under certain conditions, ships lying close to one another would be mysteriously drawn together, with various unhappy outcomes. Only in the 1990s was the phenomenon explained as a maritime analogy of the Casimir force. (Illustration from ref. 5.)

His argument goes as follows: the spectrum of possible wave modes around the two ships forms a continuum (any arbitrary wave-vector is allowed); but between the vessels their opposing sides impose boundary conditions on the wave modes, restricting the allowed values of the component of the wave-vector that is normal to the ships' surfaces. This discreteness created in the spectrum of wave modes results in a local redistribution of modes in the region between the ships, with the consequence that there is a smaller radiation pressure between the ships than outside them.

Analogous arguments had previously been employed by Milonni et al.7 to explain the origin of the Casimir effect itself. In this case, the radiation pressure is due to electromagnetic waves rather than water waves. Casimir had considered a system at zero temperature in which, classically, no radiation pressure is expected. But the quantum theory of electrodynamics states that the electromagnetic field exhibits quantum fluctuations even at zero temperature, and these are the source of Casimir forces acting on macroscopic bodies. Another outcome of these quantum fluctuations is the van der Waals force8, which, in essence, can be considered as the Casimir force at especially small separations.

Historically, the Casimir effect has been considered to be an exotic quantum phenomenon, but now it is starting to take on technological importance. Because of its relatively short range, it has only a very small effect on the dynamics of macroscopic mechanical systems. But the Casimir force has a major role in modern micro- and nanoelectromechanical systems (MEMS and NEMS), where the distances between neighbouring surfaces are typically far less than 1 μm (ref. 9). This new branch of microelectronics uses the methodology of integrated-circuits manufacturing for the fabrication of on-chip, fully integrated, miniature sensors and actuators, with a rapidly growing range of applications.

In tiny devices such as these, the Casimir force can cause mechanical elements to collapse onto nearby surfaces, resulting in permanent adhesion — an effect called 'stiction', which often proves to be an important factor in the malfunction of NEMS. Follow-up theoretical and experimental studies to the work of Kenneth et al.3 might uncover ways to engineer NEMS in which the Casimir forces are repulsive. They may even open the way for new applications of NEMS that are, in effect, immune to stiction.

Kenneth et al. also emphasize that the Casimir force is non-additive. For additive forces, the total force acting on a body is simply the sum of the pairwise contributions between bodies — for example, the total electrostatic force on an element A, interacting with elements B and C, is found by adding the force between elements B and A and the force between elements C and A. For the Casimir force, however, the additive approach can break down completely. For the case they considered, Kenneth et al. show that the additive pairwise approach can even erroneously predict attractive forces, although the exact calculation proves that the forces are repulsive.

The development of vital tools, such as scanning probe microscopy and MEMS and NEMS technology, has made possible a new generation of experiments2, and the importance of the Casimir phenomenon for both fundamental physics and practical applications is now becoming more widely appreciated. The interplay between basic science and technology is certain to motivate the study of Casimir forces in the years to come.

References

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Correspondence to Eyal Buks or Michael L. Roukes.

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Buks, E., Roukes, M. Casimir force changes sign. Nature 419, 119–120 (2002) doi:10.1038/419119a

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