The Casimir force: background, experiments, and applications
Steven K. Lamoreaux
Abstract and summary · read the original at the source
In one page
Steven Lamoreaux, who made the 1997 torsion-pendulum measurement that restarted this field, wrote this thirty-six page review at Los Alamos. The Casimir force is the pull between two uncharged plates that comes from the change in the electromagnetic modes allowed in the gap between them, and Lamoreaux takes the reader through where it comes from, how it is now measured, and what it is used for. The force law is startlingly bare: only Planck’s constant and the speed of light appear in it, not the electron’s charge, so in the limit of perfect mirrors the materials do not matter. Real mirrors are not perfect, and most of the review is spent on the corrections — finite conductivity, surface roughness, thin films and temperature — that stand between a per-cent measurement and a per-cent test of the theory. He closes with the applications, from Hawking radiation and the Unruh effect to the best limits on new short-range forces.
Why it matters hereChapter 2 is the vacuum, and this is the review that shows the vacuum being weighed on a bench rather than argued about: a laboratory force, measured to the per cent, that exists because boundaries change what the electromagnetic field is allowed to do between them.
What it claims
01For perfectly conducting parallel flat plates a distance d apart, the Casimir force per unit area is pi squared times Planck’s reduced constant times the speed of light, divided by 240 times d to the fourth — about 0.013 dyne per square centimetre for a one micrometre gap; the only fundamental constants in it are Planck’s reduced constant and the speed of light, and the electron charge is absent, so in the perfect-conductivity limit the microscopic properties of the plates do not enter.Section 1, Equation 1
Settled physics02The force has been measured to per-cent-level accuracy only in recent years: a torsion pendulum reached better than 10 per cent, an atomic force microscope with a coated sphere reached a fractional error of about 1 per cent at 100 nanometres, microelectromechanical torsional oscillators running near 700 hertz with a sensitivity around 1.4 piconewtons per root hertz set the accuracy standard, and the force between flat plates was measured to 15 per cent precision over the 0.5 to 3.0 micrometre range.Section 6, Experiments, 6.1 to 6.3
Settled physics03Casimir’s derivation assigns an energy of half Planck’s reduced constant times the frequency to every mode, while Lifshitz’s derivation of the same force uses the fluctuation–dissipation theorem and does not require the electromagnetic field to be quantised at all, and Schwinger and colleagues and Milonni have each derived the force without reference to a vacuum radiation field; the two routes have been shown to be identical, so on Lamoreaux’s reading the Casimir force is not by itself sufficient proof of a zero-point electromagnetic vacuum field, and the discriminating cases are those phenomena that truly require field quantisation.Section 2.3, Identification of the source of the Casimir force
What to watch04The energy density in the zero-point excitations of the electromagnetic field exceeds ten to the sixtieth grams per cubic centimetre depending on where the integral is cut off, and it has to be carried into general relativity where it acts as a cosmological constant; astronomical data put the cosmological constant many orders of magnitude below that figure, and Lamoreaux records that this difficulty remains unresolved.Section 2.3, cosmological-constant paragraph
What to watch05Real materials require corrections that are large where the measurements are best: finite conductivity handled through a plasma-model expansion in the ratio of plasma wavelength to gap, surface roughness handled by geometrical averaging that has been carried out only for the leading term, and thin surface films that can dominate the force even when a few hundred angstroms thick — which is why Lamoreaux judges testing the theory much better than 10 per cent a daunting task, and names the finite-temperature contribution of the transverse-electric mode as the outstanding open problem in the theory.Section 4, Corrections; Section 5.1; Section 8, Conclusion
Published and peer-reviewed06Moving boundaries turn the same physics into radiation: the dynamical Casimir effect generates photons when the plates are accelerated, and it is closely related to the Unruh result that an accelerated frame appears bathed in a thermal field at a temperature of Planck’s reduced constant times the acceleration divided by two pi times Boltzmann’s constant times the speed of light — which, evaluated at a black hole’s Schwarzschild radius, returns Hawking’s temperature exactly; separately, the agreement between measured Casimir forces and theory gives the best current limits on new forces at sub-millimetre range.Section 7.1, Equations 62 and 63; Section 7.4
Published and peer-reviewed
The way in
https://doi.org/10.1088/0034-4885/68/1/R04Reports on Progress in Physics 68 (2005) 201–236, received 22 June 2004, in final form 14 September 2004, published online 30 November 2004; cited by its issue year, 2005. The article carries the line ‘© 2005 IOP Publishing Ltd’ and no Creative Commons statement, so only the author’s own abstract is reproduced here. The article is free to read at IOPscience; the copy read for this sheet was a PDF of the published article hosted on a University of California San Diego physics course page, and the section numbers in the locators are the published ones.
How to cite it
Steven K. Lamoreaux (2005) The Casimir force: background, experiments, and applications. doi:10.1088/0034-4885/68/1/R04
Where it sits in the curriculum