The validity of classical electromagnetism

In this course we shall investigate the classical theory of electromagnetism in Euclidian space-time. This theory is valid over a huge range of different conditions, but, nevertheless, breaks down under certain circumstances. On very large length-scales (or close to collapsed objects such as black holes) the theory must be modified to take general relativistic effects into account. On the other hand, the theory breaks down completely on very small length-scales because of quantum effects. It is legitimate to treat a gas of photons as a classical electromagnetic field provided that we only attempt to resolve space-time into elements that contain a great many photons. In conventional applications of electromagnetic theory (e.g., the generation and propagation of radio waves) this is not a particularly onerous constraint.