by K A Milton, World Scientific, ISBN 9810243979 $87/£58.
In 1948 Hendrik Casimir showed that, according to quantum electrodynamics (QED), two parallel conducting plates should exert a force on each other – an effect that now bears his name. This force, according to one of several possible interpretations, is a direct result of the existence of zero-point vacuum fluctuations of the electromagnetic field. In simple terms, as the plates are placed closer and closer together, more and more modes of the electromagnetic field are excluded, with a corresponding reduction in the (admittedly infinite) amount of zero-point energy between them and an associated (and, amazingly, finite) attractive force. Similar effects occur whenever boundaries are placed in the vacuum, and all are collectively considered to be manifestations of the Casimir effect.
Milton’s book reviews this remarkable phenomenon from a theoretical viewpoint. Starting with parallel conducting plates, he goes on to extensions to different geometries; partially conductive and dielectric materials in place of conductors; the relation to van der Waals forces; dimensions more and less than the usual 3+1; contributions due to fermion fields; finite temperature effects; radiative corrections; and implications for hadronic physics and even cosmology.
With all these calculations and applications one might imagine that the Casimir effect would be well understood, but hardly anything could be further from the truth. For example, Casimir forces can be repulsive; they tend to expand a spherical shell, which is by no means intuitively obvious and in fact is a bit of a pity. Anticipating a force of the opposite sign, Casimir had hoped that they might supply the Poincaré stresses needed to stabilize a model of an electron as a tiny spherical shell of charge, and even lead to a calculation of the numerical value of the fine structure constant.
If the sign of the Casimir effect for a spherical shell is somewhat surprising, what happens in other cases can be even stranger. Change a spherical shell to a cubical box and it still tries to expand, but make it a long thin rectangular box and it tends to collapse. Go to an even number of space dimensions and the force on a hyperspherical shell becomes infinite. It’s all wonderfully bewildering.
Perhaps the most interesting recently recognized manifestation of the Casimir effect – if indeed that’s what it is – is the phenomenon of sonoluminescence, in which an acoustically tickled bubble of air in water releases visible light in 100 picosecond bursts. While the jury is still out on what exactly is going on, there are calculations suggesting that this could be due to a dynamical version of the Casimir effect in which vibrations of the bubble excite the QED vacuum. Here, however, the theory is much more difficult to work out, and different approximations lead to wildly differing estimates of how big the effect ought to be.
The Casimir effect is about a lot more than a force between two metal plates, and Milton’s book offers a great opportunity to read about it and learn the techniques by which it can be calculated. My one criticism of the book, which is probably not really fair given that the author is a theorist, is that it would be beneficial to have a discussion of the techniques by which the effect is observed in the laboratory. That said, the book is very comprehensive, clearly written and filled with wonderful physics.
