On the one hand, it is a truism that quantum physics describes an indeterministic world. On the other, the quantum theory of an isolated system describes its state as evolving deterministically. How can the two be reconciled?
The question can be posed more generally: how could any theory be like that? In this form I discussed it already in Chapter 5 . We found three alternatives; I shall list these here, and mention the interpretations of quantum mechanics which they cover. The first is that, in certain isolated systems, the state does after all not develop deterministically. We examined this alternative, in von Neumann's version, in the preceding chapter. The second denies not the determinism but the apparent indeterminism. It says that a measurement is not a process characterizable as the evolution of an isolated system, ever: a measurement is an interaction incompletely described, by leaving out something or other. There are various interpretations along this line. Perhaps the most radical is the idea that quantum theory was devised to describe only situations in which an observer (or at least, the measuring environment) is involved, while leaving that part out of the description. John Wheeler noted this as a major alternative; it is certainly reminiscent of some early Copenhagen texts. 2 Equally radical, but in a different direction, is Everett's many-worlds interpretation: indeterminism is an illusion, and disappears if we also describe all the worlds there are besides our own. The third alternative is to deny neither the determinism of the total system evolution nor the indeterminism of outcomes, but to say that the two are different aspects of the total situation. Specifically, we can deny the identification of value-attributions to observables with attributions of states; the state can then develop deterministically, with only statistical constraints on changes in the values of the observables. The modal interpretation takes this third road. 3