The Casimir effect: recent controversies and progress
Kimball A. Milton
Abstract and summary · read the original at the source
In one page
Kimball Milton wrote the field’s status report at the moment the Casimir effect stopped being a curiosity and became a measurement. His review takes stock of four fast years: the force between two surfaces in empty space, predicted by Casimir in 1948 from the modes the gap excludes, now confirmed by torsion pendulum, by atomic force microscope and by micromachined silicon devices — the best of them agreeing with theory to better than half a percent. Milton is candid about what is not settled. How temperature enters the force between real metals is genuinely disputed, and he lays out both camps. The energy a single body exerts on itself is harder still, and he reports his own unfinished calculation for a dielectric cylinder. He closes on the largest question: the zero-point energy of the vacuum, taken to the Planck scale, exceeds what cosmology allows by 123 orders of magnitude, and he proposes the dark energy we do see is Casimir energy in compact extra dimensions — a scenario that a Cavendish experiment could rule out this decade.
Why it matters hereChapter 2 rests on the vacuum being a real, structured medium, and this is the review that shows how thoroughly the laboratory has confirmed it: several independent techniques, different laboratories, agreement at the percent level and better. Chapter 6 needs to know where the frontier actually lies, and Milton names it precisely — self-energy, the temperature correction, and the enormous gap between the vacuum energy the theory carries and the dark energy the sky shows. The microwave dynamical-Casimir experiment he calls for at the end of section 6 was performed seven years later, and it is on this site at /library/stm-b8989fce8d.
What it claims
01The Casimir force is measured, by several independent techniques and in several laboratories. Lifshitz theory was confirmed in Sabisky and Anderson’s 1973 experiment; Lamoreaux’s 1997 torsion pendulum agreed at the 5 percent level; Mohideen and Roy’s 1998 atomic force microscope reached agreement at the 1 percent level with conductivity, roughness and temperature corrections included; and a Bell Labs micro-electromechanical torsional device agreed with theory to better than 0.5 percent at separations of about 75 nanometres.Section 3.6, Status of the Experimental Measurements on Casimir Forces
Settled physics02The force draws on a very wide band of frequencies, including wavelengths far larger than the gap itself. The Harvard group measured the force between a gold plate and a sphere coated with a hydrogen-switchable mirror; switching the mirror between reflecting and transparent in the visible changed the Casimir force not at all, exactly as the Lifshitz formula and the general dispersion relation for the permittivity require.Section 3.6, the paragraph on the hydrogen-switchable mirror
Published and peer-reviewed03How temperature enters the force between real metal surfaces is an open dispute in the literature, turning on how the zero-frequency term of the Matsubara sum is treated and on which model of the permittivity is used. The measurements available in 2004 cannot separate the competing prescriptions, and Milton names the experiment designed to do it: Mohideen and collaborators propose measuring the difference in force between a lens and a plate before and after a laser pulse heats both surfaces by 50 kelvin.Section 3.4, Thermal Corrections; Section 3.6, the difference-force proposal
What to watch04Integrating the zero-point energy of the electromagnetic field up to the Planck scale gives a vacuum energy density of order ten to the 118th GeV per cubic centimetre, about 123 orders of magnitude above the critical density that closes the universe, while the observations of distant type Ia supernovae, the microwave background anisotropy and large-scale structure put the cosmological constant near three quarters of the critical density with a pressure-to-energy ratio consistent with minus one.Section 7.1, Equations (7.1) to (7.6); the same estimate is made in Section 1 at Equation (1.6)
What to watch05Milton’s own proposal for dark energy makes it Casimir energy: quantum fluctuations of gravity and matter fields in compact extra dimensions of size a give a four-dimensional cosmological constant proportional to one over a to the fourth power. Keeping that below the observed value requires a larger than roughly 10 to 300 micrometres, while Cavendish-type tests of Newton’s law already require a smaller than 100 micrometres — so extra dimensions are either on the verge of discovery, or, if the Newtonian tests reach 10 micrometres cleanly, dark energy has another origin.Section 7.2, the five-point summary at the end
What to watch06Photon production from moving or time-varying boundaries is a real and calculable effect. A cavity mode driven parametrically — a wall oscillating at a multiple of the fundamental frequency, or a dielectric slab whose permittivity is modulated in time — produces photons whose number grows exponentially on resonance; the accelerated-mirror and Unruh results give a thermal spectrum at a temperature proportional to the acceleration. Milton’s verdict on the sonoluminescence proposal is that an actual calculation leaves the available energy short by ten orders of magnitude.Section 6, Dynamical Casimir Effects; Sections 6.1 and 6.2, Equations (6.4) and (6.5)
Published and peer-reviewed
Read it · abstract
Abstract
The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of δ-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measurements of the Casimir force between real materials is given, starting from a geometrical optics derivation of the Lifshitz formula, and including a rederivation of the Casimir-Polder forces. A great deal of attention is given to the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces. A summary of new improvements to the proximity force approximation is given, followed by a synopsis of the current experimental situation. New results on Casimir self-stress are reported, again based on δ-function potentials. Progress in understanding divergences in the self-stress of dielectric bodies is described, in particular the status of a continuing calculation of the self-stress of a dielectric cylinder. Casimir effects for solitons, and the status of the so-called dynamical Casimir effect, are summarized. The possibilities of understanding dark energy, strongly constrained by both cosmological and terrestrial experiments, in terms of quantum fluctuations are discussed. Throughout, the centrality of quantum vacuum energy in fundamental physics in emphasized.
PACS numbers: 11.10.Gh, 11.10.Wx, 42.50.Pq, 78.20.Ci
Kimball A. Milton, Oklahoma Center for High Energy Physics and Department of Physics and Astronomy, The University of Oklahoma, Norman. Review article, Journal of Physics A: Mathematical and General 37 (2004) R209.
(Abstract only — see the rights note above for why the full text is not reproduced here. The complete review, with its eight sections, seven figures and 383 references, is at the source. The microwave experiment Milton asks for at the close of section 6 was carried out in 2011 and is on this site at /library/stm-b8989fce8d, with the fifty-year account of that whole line of work at /library/stm-984130a356.)
The way in
https://doi.org/10.1088/0305-4470/37/38/R01LICENCE. Published as a review article in Journal of Physics A: Mathematical and General 37 (2004) R209; the Crossref record carries no licence at all. The author’s manuscript is public on arXiv as hep-th/0406024, submitted 2 June 2004, but that posting carries arXiv’s legacy assumed licence for 1991 to 2003 deposits rather than a Creative Commons statement, so this page holds the summary, the claims and the author’s own abstract and sends the reader to the source. The review runs to about eighty pages with seven figures and 383 references, from the Oklahoma Center for High Energy Physics and the Department of Physics and Astronomy at the University of Oklahoma, funded in part by the US Department of Energy. Registry note: the author’s name is given here as printed on the paper, Kimball A. Milton.
How to cite it
Kimball A. Milton (2004) The Casimir effect: recent controversies and progress. doi:10.1088/0305-4470/37/38/R01
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