Casimir effect

2007 Schools Wikipedia Selection. Related subjects: General Physics

In physics, the Casimir effect is a physical force exerted between separate objects, which is due to neither charge, gravity, nor the exchange of particles, but instead is due to resonance of all-pervasive energy fields in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, due to the mathematical form of one possible way of calculating the strength of the effect. Since the strength of the force falls off rapidly with distance it is only measurable when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors.

Dutch physicist Hendrik B. G. Casimir first proposed the existence of the force, and he formulated an experiment to detect it in 1948 while participating in research at Philips Research Labs. The classic form of his experiment used a pair of uncharged parallel metal plates in a vacuum, and successfully demonstrated the force to within 15% of the value he had predicted according to his theory.

The van der Waals force between a pair of neutral atoms is a similar effect. In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon, and in applied physics, it is becoming of increasing importance in development of the ever-smaller, miniaturised components of emerging micro- and nano- technologies.


The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alter the vacuum expectation value of the energy of the electromagnetic field. Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects.

Vacuum energy

The Casimir effect is an outcome of quantum field theory, which states that all of the various fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. In a naïve sense, a field in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field can be visualized as the displacement of a ball from its rest position. Vibrations in this field propagate, and are governed by the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. Canonically, the field at each point in space is a simple harmonic oscillator, and its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. However, as this picture shows, even the vacuum has a vastly complex structure. All calculations of quantum field theory must be made in relation to this model of the vacuum.




The Casimir effect

Casimir forces on parallel plates.
Casimir forces on parallel plates.







This value is finite in many practical calculations.

Casimir's calculation




k_n = \frac{n\pi}{a}









where polar coordinates q^2 = k_x^2+k_y^2 were introduced to turn the double integral into a single integral. The q in front in the Jacobian, and the comes from the angular integration. The integral is easily performed, resulting in









c is the speed of light,
a is the distance between the two plates.

The force is negative, indicating that the force is attractive: by moving the two plates closer together, the energy is lowered. The presence of \hbar shows that the Casimir force per unit area Fc / A is very small, and that furthermore, the force is inherently of quantum-mechanical origin.


One of the first experimental tests was conducted by Marcus Spaarnay at Philips in Eindhoven, in 1958, in a delicate and difficult experiment with parallel plates, obtaining results not in contradiction with the Casimir theory, but with large experimental errors.

The Casimir effect was measured more accurately in 1997 by Steve K. Lamoreaux of Los Alamos National Laboratory and by Umar Mohideen of the University of California at Riverside and his colleague Anushree Roy. In practice, rather than using two parallel plates, which would require phenomenally accurate alignment to ensure they were parallel, the experiments use one plate that is flat and another plate that is a part of a sphere with a large radius of curvature. In 2001, a group at the University of Padua finally succeeded in measuring the Casimir force between parallel plates using microresonators.

Further research has shown that, with materials of certain permittivity and permeability, or with a certain configuration, the Casimir effect could be made repulsive instead of attractive, although there are no experimental demonstrations of these predictions.



The heat kernel or exponentially regulated sum is















A similar analysis can be used to explain Hawking radiation that causes the slow " evaporation" of black holes (although this is generally explained as the escape of one particle from a virtual particle-antiparticle pair, the other particle having been captured by the black hole).

A more practical analogy is to look at two ships in the open ocean, sailing alongside each other. As they come closer together, their hulls shield the space in between from more and more wave energy, both from the sides as well as from front and back, which increasingly cancel out waves of longer wavelengths than the distance between the hulls. This causes the hulls to be increasingly pushed by this difference in wave activity toward each other, as they get closer to each other, such that if both ships do not actively steer away from each other under power, they will eventually collide. It is for this reason that naval vessels, when resupplying or transferring personnel at sea, must use lines and maintain a minimum distance from each other, based on vessel length and wave height.

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