Casimir effect

Calculation of the Casimir effect

The intensity of the strength of the casimir effect drops rapidly with distance, and it is only measurable when the distance between the objects is extremely small, in a scale below the micrometer.

In the original calculation, was considered the clearance between a pair of conductive plates a distance . In this case, standing waves are easy to calculate, since the transverse component of the electric field and the normal component of the magnetic field must be overridden on the surface of a conductor.

Where is the electrical component of the electromagnetic field, and are the components of the vector wave in directions parallel to the plates, and It is the vector of perpendicular wave to them.

The frequency for this wave would be:

And the sum over the possible excitation modes:

Being the area of metal plates, and introducing a factor 2 due to the two possible polarizations of the wave.

And the Casimir force per unit area for ideal plates with vacuum between them, would be:

Where is the reduced Planck constant and the distance between the two plates.

The Casimir effect referred to in some structures or machines of the time.