popper-logic-scientific-discovery

some observations on quantum theory 225
statistically—no precise singular predictions can be derived. (I do not count either
the law of conservation of energy nor the law of conservation of
momentum among the formulae peculiar to quantum theory.)
This is so because in view of the scatter relations, we must fail, more
especially, to produce precise initial conditions, by experimentally
manipulating the system (i.e. by what we have called physical selection).
Now it is indeed true that the normal technique of the experimenter
is to produce or to construct initial conditions; and this allows us to
derive from our statistical scatter relations the theorem—which, however,
only holds for this ‘constructive’ experimental technique—that from
quantum theory we cannot obtain any singular predictions, but only
frequency predictions. 1
This theorem sums up my attitude to all those imaginary experiments
discussed by Heisenberg (who here largely follows Bohr) with
the object of proving that it is impossible to make measurements of a
precision forbidden by his uncertainty principle. The point is in every
case the same: the statistical scatter makes it impossible to predict what
the path of the particle will be after the measuring operation.
It might well seem that not much has been gained by our reinterpretation
of the uncertainty principle. For even Heisenberg asserts in the
main (as I have tried to show) no more than that our predictions are
subject to this principle; and as in this matter I agree with him up to a
point, it might be thought that I am only quarrelling about words
rather than debating any substantial issue. But this would hardly do
justice to my argument. Indeed I think that Heisenberg’s view and
mine are diametrically opposed. This will be shown at length in my
next section. Meanwhile I shall attempt to resolve the typical difficulties
inherent in Heisenberg’s interpretation; and I shall try to make
clear how, and why, these difficulties arise.
First we must examine the difficulty over which, as we have seen,
Heisenberg’s programme comes to grief. It is the occurrence, in the
formalism, of precise statements of position-cum-momentum; or in
other words, of exact calculations of a path (cf. section 73) whose
1 The term ‘constructive experimental technique’ is used by Weyl, Gruppentheorie und
Quantenmechanik, p. 67; English translation p. 76.