The impact of quantum theory

Till quantum mechanics came along, it would not have occurred to many that the structure of a physical theory itself may be constrained by limitations on the precision of measurements. In classical mechanics, dynamical variables were implicitly assumed to be precisely measurable at all times, from which it followed that any mathematically well-defined function of the dynamical variables was precisely measurable at any time. Quantum mechanics severed the ‘natural’ link between the two concepts. Two observables, well-defined at all times, would be simultaneously measurable only if they commuted with each other. However, a single observable could always be measured precisely. Although the details are well known, it may be worth recalling that while it was the uncertainty principle that unsettled the theorists, what the experimentalists were unearthing were effects of the superposition principle, with measurement errors that far exceeded the uncertainty principle constraints.

What may be less well known (except to quantum field theorists) is that relativistic quantum field theory demands a severance of the link between being well defined and being measurable at yet another level. The classical electromagnetic field is well defined – and therefore measurable – at every point of space-time. However, no component of the quantized electric or magnetic field is precisely measurable at any point. The last fact was discovered by Landau and Peierls, but it remained for Bohr to point the way to the correct conclusion to be drawn.