The Influence of Retardation on the London-van der Waals Forces
H. B. G. Casimir · D. Polder
Abstract and summary · read the original at the source · none found
Em uma página
This is the paper that turned the van der Waals force into a vacuum effect, and it is the one Casimir wrote immediately before the parallel-plate result the whole Casimir programme is named for. London had already explained the weak attraction between two neutral atoms quantum-mechanically, with an energy falling as the inverse sixth power of the separation. Casimir and Polder ask what happens when the separation is large enough that the light carrying the interaction takes time to cross it. They work the problem in quantum electrodynamics, in two parts: first a single neutral atom facing a perfectly conducting plane, then the harder case of two atoms. Both give the same shape of answer. Retardation multiplies the unretarded energy by a correction factor that falls monotonically with distance — equal to one while the separation is short compared with the atomic wavelengths, and falling off as one over the separation once it is long. The force therefore weakens faster than London's law at long range, and the two limiting energies come out as clean closed formulas.
Por que importa aquiChapter 2 needs the step where a chemistry-scale attraction between molecules becomes a property of the electromagnetic field in the space between bodies. This is that step: once the interaction is carried by a field with a finite signal speed, the answer depends on the modes in the gap, and the parallel-plate force follows from the same reasoning within the year.
O que afirma
01The influence of retardation on the energy of interaction between two neutral atoms is investigated by means of quantum electrodynamics — that is, the problem is treated as a question about the electromagnetic field between the bodies, not as a question about the molecules alone.Abstract, first sentence
Settled physics02As a preliminary step, Part I treats the interaction between a neutral atom and a perfectly conducting plane, and finds that retardation reduces the interaction energy by a correction factor which decreases monotonically with increasing separation.Abstract, second sentence
Settled physics03That correction factor is equal to unity for separations small compared with the wavelengths corresponding to the atomic frequencies, and is proportional to the inverse of the separation for distances large compared with those wavelengths — so the short-range answer is the familiar unretarded one and the long-range answer is weaker.Abstract, third sentence
Settled physics04In the long-distance limit the atom-plane interaction energy is minus three h-bar c alpha divided by eight pi times the fourth power of the separation, where alpha is the static polarizability of the atom.Abstract, fourth sentence
Settled physics05The two-atom problem of Part II is much more difficult to handle mathematically, but the results are very similar: again a monotonically decreasing correction factor, unity at small distances and proportional to the inverse separation at large ones.Abstract, fifth and sixth sentences
Settled physics06In that limit the energy of interaction between two atoms is minus twenty-three h-bar c times the product of the two polarizabilities, divided by four pi times the seventh power of the separation — the inverse seventh power that replaces London's inverse sixth power once retardation is taken into account.Abstract, closing sentence
Settled physics
Leia · abstract
Abstract
The influence of retardation on the energy of interaction between two neutral atoms is investigated by means of quantum electrodynamics. As a preliminary step, Part I contains a discussion of the interaction between a neutral atom and a perfectly conducting plane, and it is found that the influence of retardation leads to a reduction of the interaction energy by a correction factor which decreases monotonically with increasing distance R. This factor is equal to unity for R small compared with the wave-lengths corresponding to the atomic frequencies, and is proportional to 1/R for distances large compared with these wave-lengths. In the latter case the total interaction energy is given by −3ħcα / (8πR⁴), where α is the static polarizability of the atom. Although the problem of the interaction of two atoms discussed in Part II is much more difficult to handle mathematically, the results are very similar. Again the influence of retardation can be described by a monotonically decreasing correction factor which is equal to unity for small distances and proportional to 1/R for large distances. In the latter case the energy of interaction is found to be −23ħcα₁α₂ / (4πR⁷).
H. B. G. Casimir and D. Polder, The Influence of Retardation on the London-van der Waals Forces, Physical Review 73, 360 (1948).
(Abstract only, and the full text was not reachable — see the rights note above. On this site, the derivation of this result and its parallel-plate successor, worked in the Green's function language, is in Milton's lectures at /library/stm-2cebf57857; the review that traces the whole measurement history is Lamoreaux's at /library/stm-4c6743a6b7.)
A porta de entrada
https://doi.org/10.1103/PhysRev.73.360SOURCE NOT REACHED IN FULL. The article is held by the American Physical Society and is closed: on 2026-09-11 OpenAlex reported open-access status closed with no repository location, and no preprint or repository copy was found — the paper predates every preprint server. What is reproduced below is the authors’ own complete abstract as OpenAlex carries it, and the summary and every claim are written from that abstract, which is why each locator says Abstract. FORMULAE. The bibliographic record stores the two closing results as TeX markup; they are set out below in plain reading order, with the same symbols the authors use — R for the separation, alpha for the static polarizability of an atom, h-bar for the reduced Planck constant and c for the speed of light. The numerical coefficients, 3 over 8 pi and 23 over 4 pi, are the record’s and are the ones the paper is known for. AUTHORS. Hendrik Brugt Gerhard Casimir and Dirk Polder, both then at the Philips Research Laboratories in Eindhoven.
Como citar
H. B. G. Casimir, D. Polder (1948) The Influence of Retardation on the London-van der Waals Forces. doi:10.1103/PhysRev.73.360
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