Understanding the Casimir force: Although the Casimir force seems completely counterintuitive, it is actually well understood. In the old days of classical mechanics the idea of a vacuum was simple. The vacuum was what remained if you emptied a container of all its particles and lowered the temperature down to absolute zero. The arrival of quantum mechanics, however, completely changed our notion of a vacuum. All fields - in particular electromagnetic fields - have fluctuations. In other words at any given moment their actual value varies around a constant, mean value. Even a perfect vacuum at absolute zero has fluctuating fields known as "vacuum fluctuations", the mean energy of which corresponds to half the energy of a photon. However, vacuum fluctuations are not some abstraction of a physicist's mind. They have observable consequences that can be directly visualized in experiments on a microscopic scale. For example, an atom in an excited state will not remain there infinitely long, but will return to its ground state by spontaneously emitting a photon. This phenomenon is a consequence of vacuum fluctuations. Imagine trying to hold a pencil upright on the end of your finger. It will stay there if your hand is perfectly stable and nothing perturbs the equilibrium. But the slightest perturbation will make the pencil fall into a more stable equilibrium position. Similarly, vacuum fluctuations cause an excited atom to fall into its ground state.
The Casimir force is the most famous mechanical effect of zero-point-energy (ZPF) vacuum fluctuations. Consider the gap between two plane mirrors as a cavity. All electromagnetic fields have a characteristic "spectrum" containing many different frequencies. In a free vacuum all of the frequencies are of equal importance. But inside a cavity, where the field is reflected back and forth between the mirrors, the situation is different. The field is amplified if integer multiples of half a wavelength can fit exactly inside the cavity. This wavelength corresponds to a "cavity resonance". At other wavelengths, in contrast, the field is suppressed. Vacuum fluctuations are suppressed or enhanced depending on whether their frequency corresponds to a cavity resonance or not. The Casimir force is the most famous mechanical effect of vacuum fluctuations. Consider the gap between two plane mirrors as a cavity. All electromagnetic fields have a characteristic "spectrum" containing many different frequencies. In a free vacuum all of the frequencies are of equal importance. But inside a cavity, where the field is reflected back and forth between the mirrors, the situation is different. The field is amplified if integer multiples of half a wavelength can fit exactly inside the cavity. This wavelength corresponds to a "cavity resonance". At other wavelengths, in contrast, the field is suppressed. Vacuum fluctuations are suppressed or enhanced depending on whether their frequency corresponds to a cavity resonance or not. An important physical quantity when discussing the Casimir force is the "field radiation pressure". Every field - even the vacuum field - carries energy. As all electromagnetic fields can propagate in space they also exert pressure on surfaces, just as a flowing river pushes on a floodgate. This radiation pressure increases with the energy - and hence the frequency - of the electromagnetic field. At a cavity-resonance frequency the radiation pressure inside the cavity is stronger than outside and the mirrors are therefore pushed apart. Out of resonance, in contrast, the radiation pressure inside the cavity is smaller than outside and the mirrors are drawn towards each other. It turns out that, on balance, the attractive components have a slightly stronger impact than the repulsive ones. For two perfect, plane, parallel mirrors the Casimir force is therefore attractive and the mirrors are pulled together. While the Casimir force is too small to be observed for mirrors that are several metres apart, it can be measured if the mirrors are within microns of each other. For example, two mirrors with an area of 1 cm2 separated by a distance of 1 µm have an attractive Casimir force of about 10-7 N - roughly the weight of a water droplet that is half a millimetre in diameter. Although this force might appear small, at distances below a micrometre the Casimir force becomes the strongest force between two neutral objects.
New physics on the horizon? The Casimir effect could also play a role in accurate force measurements between the nanometre and micrometre scales. Newton's inverse-square law of gravitation has been tested many times at macroscopic distances by observing the motion of planets. But no-one has so far managed to verify the law at micron length scales with any great precision. Jens Gundlach and colleagues at Washington, for example, have used a torsion pendulum to determine the gravitational force between two test masses separated by distances from 10 mm down to 220 µm. Their measurements confirmed that Newtonian gravitation operates in this regime but that the Casimir force dominates at shorter distances. At any rate such tests are important because many theoretical models that attempt to unify the four fundamental forces of nature predict the existence of previously undiscovered forces that would act at such scales. Any deviation between experiment and theory could hint at the existence of new forces. But all is not lost even if both values agree: the measurements would then put new limits on existing theories.
Real materials: The problem with studying the Casimir effect is that real mirrors are not like the perfectly smooth plane mirrors. In particular, real mirrors do not reflect all frequencies perfectly. They reflect some frequencies well - or even nearly perfectly - while others are reflected badly. In addition, all mirrors become transparent at very high frequencies. When calculating the Casimir force the frequency-dependent reflection coefficients of the mirrors have to be taken into account - a problem first tackled by Evgeny Lifshitz in the mid-1950s, and then by Julian Schwinger and many others. It turns out that the measured Casimir force between real metallic mirrors that are 0.1 µm apart is only half the theoretical value predicted for perfect mirrors. If this discrepancy is not taken into account when comparing experimental data with theory, then an experimental measurement could erroneously be interpreted as a new force.