Quantum Theory and External Reality

As we have seen, quantum theory deals with a wavefunction, which
it states is causally determined from some initial conditions. The
passage from this wavefunction to experimental observation uses
the assumption that the wavefunction gives probabilities for
measurements to yield particular values. In order to test the predictions
of the theory it is necessary to prepare a large number of
identical systems and perform the same measurement on each. We
recall that we used this procedure to define the probabilities of
transmission and reflection in $1.3. Of course, the word identical
now must refer to the wavefunction, i.e. ‘identical systems’ are
defined to be systems with the same initial wavefunction (and
therefore the same wavefunction for all future times).
The large number of identical systems is referred to as an
ensemble. For any such ensemble the predictions of quantum
theory are precise and deterministic. For example, quantum theory
tells us what percentage of a given (large) number of particles will
pass through a potential barrier. What it cannot tell us, of course,
is whether any particular one of the particles will pass through.
Some writers on this topic have therefore adopted the view that
quantum theory is a theory of ensembles and as such tells us
anything about individual systems. This is a perfectly reasonable
view and it may be the correct one to take. There are then no
further difficulties in the ‘interpretation of quantum theory’, and
the subject does not cause any philosophical problems. We must
not, however, go on from this to claim that we have solved the
problems met in the first chapter. We have merely ignored them.
We do not only have experimental results for ensembles. Individual
systems exist and the problems arise when we observe them. It is
possible to argue that quantum theory says nothing about such individual systems but, even if this is true, the problems do not go
away.
We shall, in this chapter, adopt a more positive view and
continue to hope that the theory which predicts our results might
also help to explain them.