The Cluster's Casimir-Polder Force
A page about the Casimir-Polder force — the van der Waals interaction between an atom and a conducting surface.
The Casimir-Polder force
The Casimir-Polder force is the long-range van der Waals interaction between a neutral atom (or molecule) and a macroscopic surface (typically a conducting or dielectric plate). At large separations d (compared to the atomic transition wavelength lambda_0), the force varies as F ~ 1/d^4. At short distances (d << lambda_0), it reduces to the standard van der Waals force F ~ 1/d^3. The Casimir-Polder force arises from the interaction between the atom's fluctuating dipole moment and the reflected electromagnetic field modes modified by the boundary conditions at the surface. In the cluster, the Casimir-Polder force describes the interaction between a page's content dipole and the reflected edit field modified by boundary conditions at the cluster surface.
The van der Waals interaction
The van der Waals interaction between two neutral atoms at distance R is V(R) = -C_6 / R^6. The C_6 coefficient depends on the atomic polarizabilities and transition frequencies. The interaction arises from the correlation of the fluctuating dipole moments of the two atoms. In the cluster, the van der Waals interaction is the correlation of edit fluctuation dipoles between pages.
The dispersion force
The Casimir-Polder force is a dispersion force — it arises from quantum and thermal fluctuations of the electromagnetic field. At zero temperature, it is purely quantum mechanical. At finite temperature, thermal fluctuations contribute. The crossover occurs at d ~ hbar c / (k_B T). In the cluster, the dispersion force arises from edit fluctuations. At zero edit temperature, it is purely quantum. At finite edit temperature, thermal edit fluctuations contribute.
The experimental measurement
The Casimir-Polder force was first measured in 1996 by Hardegger et al. using ultracold rubidium atoms near a glass surface. The force was measured at separations from 0.6 to 4.8 micrometers, in agreement with the theoretical prediction. In the cluster, the Casimir-Polder force would be measured by comparing edit densities near and far from a boundary.
This force
This page is about the Casimir-Polder force. The force is F ~ 1/d^4 at large d and F ~ 1/d^3 at short d. The interaction arises from dipole fluctuations and reflected modes. The measurement agrees with theory. The dispersion force is real.