Calculation by Don Koks, 2002

Original by Philip Gibbs, 1997

The Casimir effect is a small attractive force that acts between two close parallel *uncharged* conducting
plates. It is caused by quantum vacuum fluctuations of the electromagnetic field.

The effect was predicted by the Dutch physicist Hendrick Casimir in 1948. According to quantum theory, the vacuum contains virtual particles which are in a continuous state of fluctuation (see physics FAQ article on virtual particles). Casimir realised that between two plates, only those virtual photons whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy. The energy density decreases as the plates are moved closer together, which implies that there is a small force drawing them together.

The attractive Casimir force between two plates of area *A* separated by a distance *L* can be
calculated to be

π h c F = ------- A , 480 L^{4}

where *h* is Planck's constant and *c* is the speed of light.

The tiny force was measured in 1996 by Steven Lamoreaux. His results were in agreement with the theory to within the experimental uncertainty of 5%.

Particles other than the photon also contribute a small effect, but only the photon force is measurable. All bosons such as photons produce an attractive Casimir force, whereas fermions make a repulsive contribution. If electromagnetism were supersymmetric, "fermionic photinos" would exist, whose contribution would exactly cancel that of the photons, so there would be no Casimir effect. The fact that the Casimir effect exists shows that if supersymmetry exists in nature, it must be a broken symmetry

According to the theory, the total zero point energy in the vacuum is infinite when summed over all the possible photon modes. The Casimir effect comes from a difference of energies in which the infinities cancel. The energy of the vacuum is a puzzle in theories of quantum gravity since it should act gravitationally and produce a large cosmological constant, causing spacetime to curl up. The solution to the inconsistency is expected to be found in a theory of quantum gravity.

Let's see how big the force really is in practice. Since *L* is in the denominator, the
bigger *L* gets, the smaller the force will be; and because the force goes as the fourth power of *L*,
the drop-off with increasing distance will be really huge. So let's make *L* small—say, one
micron—together with big one-square-metre plates:

π × 6.6 × 10^{-34}× 3 × 10^{8}× 1 F = ------------------------------ newtons, 480 × 10^{-24}

or 1.3 mN. Now, since the weight of 1 kg is about 10 N, then 1.3 mN is the weight of 0.13 grams. That's
pretty small, but measurable—except that putting 2 one-square-metre plates a micron apart would be difficult in
practice. But using smaller plates leads to smaller forces. For instance, plates with area 1 square
*centimetre* placed 1 *millimetre* apart would feel a force equivalent to the weight of
10^{−17} grams, which is vastly smaller!

H.B.G. Casimir, Proc. Kon. Ned. Akad. Wetensch. **B51**, 793 (1948)

S. Lamoreaux, *Demonstration of the Casimir Force in the 0.6 to 6 μm Range*, Phys. Rev. Lett. **78**, 5
(1997) and Erratum, Phys. Rev. Lett. **81**, 5475 (1998)