On the attraction between two perfectly conducting plates
H. B. G. Casimir
Summary and citation · read the original at the source
In one page
In three pages read to the Royal Netherlands Academy on 29 May 1948, Hendrik Casimir showed that two perfectly conducting plates facing each other across empty space must attract. The method is startlingly plain. Put a conducting plate inside a conducting box, and count the electromagnetic modes that fit in the gap when the plate sits close to one wall, then again when it is far away. Every mode carries a half-quantum of energy. Both totals are infinite and, as Casimir says, devoid of physical meaning on their own — but the difference between them is finite, and it depends on the size of the gap. Differentiate that difference and you have a force per unit area: F equals ħc π² over 240 a⁴, roughly 0.013 dyne per square centimetre at a gap of one micron. His own name for what he had found is a zero point pressure of electromagnetic waves.
Why it matters hereThis is the founding result of chapter 2 — the vacuum has structure, and a boundary placed in it changes the energy by an amount you can push on. Every device in chapter 6, from Sonny White's power cell to Garret Moddel's resonator, is engineering built on these three pages.
What it claims
01The sum of half-quanta over all the resonance frequencies of a cavity is divergent and devoid of physical meaning, but the difference between two such sums — the plate at a small distance from the wall, and the plate far away — has a well defined value, and that value is the interaction between the plate and the wall.pp. 793–794
Settled physics02Two perfectly conducting plates a distance a apart attract with a force per unit area F = ħc π²/240 a⁴, which comes to about 0.013 dyne per square centimetre when the separation is one micron.p. 795, final formula
Settled physics03The attractive force between two metal plates is independent of the material of the plates, so long as the separation is large enough that for wavelengths comparable with it the penetration depth is small compared with the distance.p. 795, conclusions
Settled physics04The force may be interpreted as a zero point pressure of electromagnetic waves — that is, the vacuum's own field energy pushing on a boundary.p. 795, conclusions
Settled physics05The retarded interactions Casimir and Polder derived for a plate and an atom, and for two polarisable particles, can be obtained a second way: by using classical electrodynamics to study the change in electromagnetic zero point energy — and the same method carries straight over to two conducting plates.p. 793, opening
Settled physics06Casimir names the test himself in his last line: although the effect is small, an experimental confirmation seems not unfeasible and might be of a certain interest.p. 795, closing paragraph
Settled physics
The way in
https://dwc.knaw.nl/DL/publications/PU00018547.pdfCommunicated at the Academy meeting of 29 May 1948 and printed in Proc. Kon. Ned. Akad. Wetensch. B51, 793–795. A free scan is served by the Royal Netherlands Academy digital library, which also reprinted the paper in its 1997 centenary issue.
How to cite it
H. B. G. Casimir (1948) On the attraction between two perfectly conducting plates. https://dwc.knaw.nl/DL/publications/PU00018547.pdf
Where it sits in the curriculum