We would like to offer a few comments in connection with the article “Science and technology of the Casimir effect” by Alex Stange, David Campbell, and David Bishop (Physics Today, January 2021, page 42). First, as Steve Lamoreaux mentioned in another excellent article on the Casimir effect (Physics Today, February 2007, page 40), Niels Bohr played a brief but seminal role in Hendrik Casimir’s thinking. With Dirk Polder, Casimir calculated the large-distance van der Waals interaction without reference to zero-point energy.
In a 1992 letter to one of us (Milonni), Casimir recalled mentioning his results to Bohr during a walk sometime around 1947. When Casimir said that he was “puzzled by the extremely simple form of the expressions for the interaction at very large distance,” Bohr mumbled something about zero-point energy. “That was all,” Casimir wrote, “but it put me on a new track.” That track led Casimir to use the zero-point electromagnetic energy of the modes of a resonant cavity to calculate the force between conducting plates. In his letter, Casimir said that he was “somewhat familiar with the theory of modes of resonant cavities and their perturbations” because of his position at the Philips Research Laboratories in the Netherlands.
Casimir remarked in a 1948 paper that the force between the plates “may be interpreted as a zero point pressure of electromagnetic waves,”1 an interpretation fully supported by a calculation of the vacuum stress tensor.2 That perspective might suggest, as do Stange and his coauthors, that the net inward pressure results from a “higher density of modes outside the plates” than inside. But such an argument is superficial in that the calculated inward and outward forces on the plates both diverge. In fact, the spectral mode density of the field between the plates can be greater at some frequencies than it is outside the plates. And it depends, of course, on the boundary conditions for the electric and magnetic fields.3
Stange and his coauthors highlight the major role Casimir forces play in microelectromechanical systems (MEMS) today. Interestingly, when one of us (Maclay) and two coauthors tried in 1994 to publish the first paper on the potential role of quantum forces in MEMS,4 the reviewers initially rejected it on the grounds that the dimensions of MEMS, typically in the tens or hundreds of microns, made the discussion irrelevant.
Stange and his coauthors describe how repulsive Casimir forces can result from different dielectric properties of the interacting objects. Repulsive Casimir forces can also arise from combinations of dielectric and permeable materials, as shown in 1974 by Timothy Boyer. When one of two parallel plates is a perfect conductor and the other is infinitely permeable, for example, the force between them is repulsive. And whether the Casimir force is attractive or repulsive generally depends on the geometrical configuration of the interacting bodies. The Casimir force on a perfectly conducting sphere, for example, is repulsive, in contrast to Casimir’s assumption that it should be attractive. More recently, researchers have focused on the possibility of realizing repulsive Casimir forces with metamaterials and chiral media. Qing-Dong Jiang and Frank Wilczek, for instance, have shown that chirality can be employed to obtain Casimir forces that are “repulsive,” “enhanced,” and “tunable.”5
