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A fluctuation-induced force depends on how boundaries restrict fluctuating fields. Changing the boundary conditions changes the permitted normal modes, their frequencies and the separation-dependent free energy. The resulting force is $-\partial \mathcal{F}/\partial L$ at the stated control conditions; confinement alone does not determine its sign.

For a concrete ideal example, take a massless scalar field of wave speed $c$ on a one-dimensional interval of length $L$ at zero temperature. Two Dirichlet boundary conditions give mode wavenumbers $n\pi /L$, $n\ge 1$. Replacing one end by a Neumann boundary condition gives $(n+1/2)\pi /L$, $n\ge 0$. With the same bulk subtraction, their finite zero-point energies are respectivelyDifferentiation gives attraction in the first case and repulsion in the second. These scalar examples are distinct from the three-dimensional electromagnetic Casimir force. The comparison illustrates why the boundary prescription must accompany any reported fluctuation-force law.

Fluctuation-induced forces arise because separation changes the fluctuations available to a system and therefore changes its free energy. The force is $F=-\partial \mathcal{F}/\partial d$ at fixed relevant control variables, not necessarily a force from a permanent charge or dipole.

For two neutral polarizable particles, correlated electromagnetic fluctuations give a short-distance dispersion attraction of the form $-C_6/r^6$. Retardation changes the asymptotic distance dependence. Boundaries produce a related Casimir force; for parallel ideal conducting plates at zero temperature,The negative pressure denotes attraction. Material response, nonplanar geometry and finite temperature alter the ideal result. The effect can be described through the separation-dependent electromagnetic mode spectrum rather than by treating a divergent absolute vacuum energy as observable.^[ref]

In a classical depletion force, smaller particles or polymer coils are excluded from a region near larger surfaces. Overlap of excluded regions increases their available volume. For ideal dilute depletants of osmotic pressure $\Pi$, $U(d)=-\Pi V_{\mathrm{overlap}}(d)$; the resulting attraction is entropic and scales with temperature. Confined interface fluctuations can instead generate repulsion when close approach removes entropy. Near a continuous phase transition, a large correlation length makes boundary-conditioned order-parameter fluctuations produce a critical Casimir force. Its sign depends on the boundary preferences, so fluctuation forces are not universally attractive.

The useful common idea is a free-energy difference with explicit boundary conditions; quantum vacuum, thermal field and excluded-volume mechanisms have different physical fluctuations and different ranges.

An experimental atomic physicist who measured the Casimir force between conducting surfaces in 1997. His electromechanical apparatus used a torsion pendulum to detect the weak attraction over separations of roughly 0.6–6 micrometres. The experiment tested a consequence of changing the allowed electromagnetic field fluctuations by changing boundaries, connecting quantum electrodynamics to a directly measured mechanical force.^[ref]