Introduction: the theory of local beables

This is a pretentious name for a theory which hardly exists otherwise, but which ought to exist. The name is deliberately modelled on ‘the algebra of local observables’. The terminology, be-able as against observ-able, is not designed to frighten with metaphysic those dedicated to realphysic. It is chosen rather to help in making explicit some notions already implicit in, and basic to, ordinary quantum theory. For, in the words of Bohr, ‘it is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms’. It is the ambition of the theory of local beables to bring these ‘classical terms’ into the equations, and not relegate them entirely to the surrounding talk.

The concept of ‘observable’ lends itself to very precise mathematics when identified with ‘self-adjoint operator’. But physically, it is a rather woolly concept. It is not easy to identify precisely which physical processes are to be given the status of ‘observations’ and which are to be relegated to the limbo between one observation and another. So it could be hoped that some increase in precision might be possible by concentration on the beables, which can be described in ‘classical terms’, because they are there. The beables must include the settings of switches and knobs on experimental equipment, the currents in coils, and the readings of instruments. ‘Observables’ must be made, somehow, out of beables.