Casimir energy

The Casimir energy is the configuration-dependent part of a quantum field's vacuum energy after a specified subtraction or renormalization. Only an energy difference or its derivative is physically meaningful in the idealized calculation; the separate zero-point sums are divergent.

For the electromagnetic field between two infinite perfectly conducting parallel plates at zero temperature and separation $a$, the renormalized energy per area is $E/A=-{\pi }^2\hslash c/(720a^3)$. Differentiation gives the attractive pressure $-\partial (E/A)/\partial a=-{\pi }^2\hslash c/(240a^4)$. Real materials, finite temperature and geometry alter this result. The Casimir effect therefore tests a response to changed boundaries, not a direct weighing of an unregularized infinite energy.