On the attraction between two perfectly conducting plates.

✨ Summary

Paper summary

H. B. G. Casimir derives the interaction between two parallel, perfectly conducting plates by calculating the change in the electromagnetic zero-point energy produced by the plates. He compares the spectrum of electromagnetic modes when a conducting plate is separated from another conducting wall by a distance (a) with the spectrum when the plate is moved far away.

Because the individual zero-point-energy sums are divergent, Casimir introduces a high-frequency cutoff function representing the fact that real metals do not perfectly reflect arbitrarily short wavelengths. He then applies the Euler–Maclaurin formula to compare the discrete mode sum with its continuum limit. In the limit where the plate separation is large compared with the relevant electromagnetic penetration depth, the cutoff-dependent terms do not affect the leading result.

The resulting interaction energy per unit area is

[ \frac{\delta E}{L^2}=-\frac{\pi^2\hbar c}{720a^3}, ]

which gives an attractive force per unit area of magnitude

[ \frac{F}{A}=\frac{\pi^2\hbar c}{240a^4}. ]

The paper interprets this attraction as a zero-point pressure of the electromagnetic field and argues that, under the ideal-conductor conditions used in the calculation, it is independent of the plates’ material. The paper does not contain a separately labeled abstract.

Influence

The result became the basis of what is now called the Casimir effect: an experimentally testable attraction between closely separated, electrically neutral conducting surfaces arising from altered electromagnetic mode structure. Later theoretical work generalized the calculation to finite conductivity, temperature, material response, and nonparallel geometries. Experimental measurements subsequently tested the predicted interaction using torsion pendulums, micromechanical oscillators, and atomic-force-microscope methods; the effect is also relevant to adhesion and stiction in microelectromechanical and nanoelectromechanical systems. (physicstoday.aip.org)

The paper’s bibliographic record shows that it has been cited extensively and remains the standard historical reference for the ideal parallel-plate Casimir force. (inspirehep.net)