Conservation, The Sum Rule and Confirmation

Extract

In 1924, Bohr, Kramers and Slater tried to introduce into microphysics conservation principles that hold only on the average. This attempt was abandoned in the light of the Compton-Simon experiment (and its later refinements). Since that time, except for a moment of doubt in 1936, it has been thought that the classical conservation laws (for energy and momentum) hold in quantum theory for each individual interaction, in a way that yields the classical exchange-and-balance of momentum (or energy) familiar from the laws of elastic collisions. It has been thought, that is, that in each individual “collision” what one part of the total system loses in linear momentum (say) another part gains, so as to maintain the same total amount afterwards as before. To those familiar with discussions of the interpretation of quantum theory, however, it will be apparent that the very concepts needed to express this idea of an elastic collision are generally not admitted in the theory. For one needs the idea that both before and after collision the total system has a well-defined value for the conserved quantity and, moreover, that the various component parts of the system have well-defined values for those quantities out of which the conserved one is composed. But in the case of spin, for example, it is customary to say that although total spin may be conserved in certain interactions one cannot attribute values to the separate components of spin (in various directions) because the associated operators do not commute. (Thus the whole sum is not even the sum of its parts.) Moreover, one does not generally refer to the values of quantities except in eigenstates. Hence, in general, one would not refer to the value of the conserved quantity before and after interaction, except for interactions initiated in eigenstates.