Quantum field theory offers physicists a tremendously wide range of application: it is a language with which a vast variety of physical processes can be discussed and also provides a model for fundamental physics, the so-called ‘standard model’, which thus far has passed every experimental test. No other framework exists in which one can calculate so many phenomena with such ease and accuracy. Nevertheless, today some physicists have doubts about quantum field theory, and here I want to examine these reservations. So let me first review the successes.

Field theory has been applied over a remarkably broad energy range and whenever detailed calculations are feasible and justified, numerical agreement with experiment extends to many significant figures. Arising from a mathematical account of the propagation of fluids (both ‘ponderable’ and ‘imponderable’), field theory emerged over a hundred years ago in the description within classical physics of electromagnetism and gravity. [1] Thus its first use was at macroscopic energies and distances, with notable successes in explaining pre-existing data (relationship between electricity and magnetism, planetary perihelion precession) and predicting new effects (electromagnetic waves, gravitational bending of light). Schrödinger's wave mechanics became a bridge between classical and quantum field theory: the quantum mechanical wave function is also a local field, which when ‘second’ quantized gives rise to a true quantum field theory, albeit a non-relativistic one. This theory for atomic and chemical processes works phenomenally well at electron-volt energy scales or at distances of O(10−5 cm).