“How in the world can you make any money out of a theory like this?” asked Steven Weinberg. But quantum electrodynamics has proven a robust theory, and researchers are still pushing at its frontiers as a workshop in Bulgaria revealed.

Weinberg’s irreverent remark about quantum electrodynamics (made in his 1986 Dirac Memorial Lecture) is just one among many made by such luminaries as Dirac, who suggested that the remarkable agreement between QED calculations and experiment was a “fluke”, and Feynman, who described such calculations as a mathematical “hocus-pocus” (and who suspected that the renormalization technique that produces the agreement is not mathematically self-consistent).

In spite of this bad press, QED has not only survived but prospered after more than 50 years it has become the prototype against which every other quantum field theory is measured, and its status as the most successful theory we have ever had in physics remains unchallenged.

To some particle physicists, this very success seems to have excluded the notion that there might still be a QED scientific frontier. In fact, at least three of them could be discerned at a workshop held in June in Sandansky, Bulgaria, entitled “Frontier tests of QED and physics of the vacuum”.

The first concerns such exotic atomic systems as metastable antiprotonic helium (a helium atom with an antiproton substituted for one electron), singly-charged heavy ions such as uranium-91^{+}, muonium (a bound state of a muon and an electron), and antihydrogen (an antiproton with an orbital positron). Beyond a certain level of experimental precision, each of these hydrogen- and helium-like systems is a testbench atom for one QED aspect or another.

The second frontier is the study of macroscopic consequences of QED, with effects like vacuum polarization (spontaneous transient particles) and zero-point energy (the “dressing” surrounding a bare particle); hence the weak birefringence acquired by a vacuum under a magnetic field (a consequence of vacuum polarization) and the Casimir force between objects in the vacuum, this being related to the change of zero-point energy when the vacuum’s domain of quantization is restricted by boundaries. (The Casimir force between two parallel plates is proportional to the inverse fourth power of their separation and has magnitude of about 0.2×10^{5} newtons for 1 cm^{2} plates separated by 0.5 microns equivalent to a mosquito standing on one of the plates.)

Finally there is what might be called the Popperian frontier the line beyond which QED might yet be found lacking. The holy grail of researchers in this latter domain is to discover some effect that does not agree with the predictions of Feynman’s hocus-pocus.

As with geographical frontiers, there is some mystery and not a little argument about where QED frontiers begin, end, and overlap. The first of them is perhaps of most interest to particle physicists, much of the research having been done at CERN and other accelerator laboratories. Thus, several Sandansky talks dealt with experimental and theoretical aspects of the antiprotonic helium atom, which has been investigated spectroscopically by experiment PS205 at CERN’s LEAR low-energy antiproton ring. The steady advance in the measurement precision of spectral lines reported by H A Torii and E Widmann (Tokyo) has led this work into the parts-per million domain where QED and spin effects must be taken into account in calculating expected transition frequencies. These calculations were discussed by D Bakalov (Sofia) and V I Korobov (Dubna). The experiments will be taken yet further by the ASACUSA experiment at CERN’s AD Antiproton Decelerator. Its first results, expected in summer 1999, should inspire theorists to make still more refined QED calculations.

Also coming into sight at the AD are spectroscopic experiments on antihydrogen. As the underlying concepts of local field theory assert that there is no difference between the QED of hydrogen and antihydrogen atoms, laser spectroscopy can provide extremely precise tests by comparing identical spectral features in the two atoms.

The status of ATRAP, which is one of the two AD antihydrogen experiments, was discussed by G Gabrielse (Harvard), who also announced the latest results of his group’s ever-more precise determination of the antiproton charge/mass ratio. Other topics were improved measurements of the the muon magnetic moment (V Hughes, Yale) and of the hyperfine structure of the muonium atom (K Jungmann, Heidelberg). Muonium, containing no strongly interacting particles, is free of complications arising from hadron charge and magnetic form factors.