Casimir

Casimir refers to several concepts in physics and mathematics, named after Dutch physicist Hendrik B. G. Casimir (1910–2000). In physics, the Casimir effect is a quantum phenomenon arising from vacuum fluctuations of the electromagnetic field. Predicted in 1948, it manifests as an attractive force between neutral conducting bodies placed in close proximity in vacuum, due to the restriction of allowed vacuum modes by boundary conditions. For ideal parallel plates of area A separated by distance d, the Casimir force is F = - (π^2 ħ c A) / (240 d^4), and the associated energy is E = - (π^2 ħ c A) / (720 d^3). The effect depends on geometry, boundary conditions, materials, and temperature; real metals require finite-conductivity corrections, and thermal effects become relevant at larger separations. The Casimir-Polder force extends the concept to atom-surface interactions and more complex geometries.

Experimental verification has progressed since the 1990s. Early measurements by Lamoreaux and later high-precision experiments by Mohideen and collaborators used torsion pendulums, atomic force microscopes, and microelectromechanical systems, achieving results consistent with theory within uncertainties.

Applications and implications include relevance to micro- and nano-scale devices, where Casimir forces can cause stiction and actuation issues in MEMS/NEMS. Ongoing research seeks to tailor or mitigate the interaction through geometry, material choice, and metamaterials, and to explore regimes where repulsive Casimir forces may arise.

In mathematics, Casimir also denotes a Casimir operator, a central element of the universal enveloping algebra of a Lie algebra. Such invariants commute with all generators and help label representations; for su(2), the quadratic Casimir has eigenvalue j(j+1) on spin-j representations.

The term thus captures both a fundamental quantum force manifestation and a key construct in representation theory.