Historical research guide · 0660 · 2003
The Casimir Effect: Physical Manifestations of Zero-Point Energy
Peter W. Milonni
In one minute
Peter Milonni, himself a leading writer on the quantum vacuum, reviews Kimball Milton’s monograph on the Casimir effect for Physics Today. He opens with the history from the inside. Casimir and Polder calculated the long-range attraction between two atoms in 1946; Bohr, on a walk, mumbled something about zero-point energy, and Casimir — as he wrote to Milonni in 1992 — found that calculating changes in zero-point energy gave the same answer. That track led in 1948 to the famous prediction: two parallel conducting plates in empty space pull together. Milonni reports that after decades of quiet the field is busy again, driven by experiments that confirm Casimir’s prediction unambiguously and by a growing sense that the effect is fundamental. Milton’s book, he writes, is the rigorous guide through it — one unified Green’s function method, developed with Julian Schwinger, applied to plates, spheres, dielectrics, cylinders, higher dimensions, hadronic bag models and cosmology.
Connection
Chapter 1 asks how firmly each rung of the evidence ladder is fixed, and this is a working physicist’s verdict in a mainstream journal: the Casimir prediction is confirmed, unambiguously, and the effect is fundamental rather than a curiosity. For chapter 2 it supplies the definition the field uses — the stress on bounding surfaces when a quantum field is confined to a finite volume — and for chapter 6 it marks where the calculational frontier sat, including the sign of the force in curved geometries and the energy budget of the dynamical Casimir effect.
From the source
The Casimir force was found by following zero-point energy. Casimir and Polder computed the long-separation van der Waals interaction between two atoms, and between an atom and a conducting plate, in 1946; Bohr’s remark about zero-point energy put Casimir on a new track, and in his own words to Milonni, calculating changes of zero-point energy leads to the same results. Further thinking about zero-point field energy led him in 1948 to predict the attractive force between two parallel conducting plates.Page 49, opening paragraphs, quoting Casimir’s letter of 12 March 1992
After many years of relative dormancy the study of Casimir forces is an active field again, and Milonni credits the revival to recent experiments that unambiguously confirm Casimir’s predictions and to a growing recognition of the fundamental importance of the effect.Page 49, second column
Milton’s working definition, quoted in the review, is that the Casimir effect is the stress on the bounding surfaces when a quantum field is confined to a finite volume of space. The book treats it through one unified apparatus — the Green’s function methods Milton and others developed in collaboration with Julian Schwinger — applied to the electromagnetic force between parallel conducting and dielectric plates, the fermionic force between parallel surfaces, the electromagnetic and fermionic forces at spherical boundaries and the effect for dielectric balls, with finite temperature and conductivity corrections analysed in detail.Page 49, second and third columns
Two thirds of the book runs past flat plates: cylindrical geometries, spheres in D dimensions, applications to hadronic physics and the bag model, Chern-Simons electrodynamics, and cosmology including a brief treatment of the cosmological constant problem. The emphasis throughout is not on physical motivation but on how to calculate Casimir effects and how to handle the divergences that appear.Pages 49 to 50
Geometry decides the sign of the force and intuition does not. Because van der Waals forces are non-additive, the force between macroscopic bodies is not the sum of pairwise contributions, and it can come out repulsive or attractive with no simple rule as to which: Casimir expected a conducting spherical shell to be pulled inward, and Timothy Boyer found in 1968 that the force is outward instead. For dilute media the non-additive corrections are small and the pairwise approximation is accurate.Page 50, first column
On the dynamical Casimir effect, Milonni reports that Milton examines Schwinger’s proposal that the Casimir effect is the origin of sonoluminescence and argues that it cannot generate anything like the observed energies, without ruling the dynamical effect out entirely. What to watch: the energy budget of a moving-boundary Casimir process measured against the light a collapsing bubble actually emits — the quantity that would settle where the dynamical effect can and cannot supply the power.Page 50, on the chapter Sonoluminescence and the Dynamical Casimir Effect
The way in
https://doi.org/10.1063/1.1554139How to cite it
Peter W. Milonni (2003) The Casimir Effect: Physical Manifestations of Zero-Point Energy doi:10.1063/1.1554139