popper-logic-scientific-discovery

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some structural components of a theory of experience
by interposing, for instance, an electrical field or a filter in front of the
Geiger-counter, before we measure the position. But in consequence of
this (as will be shown more fully in appendix vii) we can make predictions
with any degree of precision about the B-particle travelling in the
PY direction.
This imaginary experiment allows us to see not only that precise
single predictions can be made, but also under what conditions they
can be made, or better, under what conditions they are compatible
with the quantum theory. They can be made only if we can obtain
knowledge about the state of the particle without being able to create
this state at will. Thus we really obtain our knowledge after the event,
as it were, since at the time when we obtain it the particle will already
have assumed its state of motion. Yet we can still make use of this
knowledge to deduce from it testable predictions. (If the B-particle in
question is a photon, for instance, we might be able to calculate the
time of its arrival on Sirius.) The impacts of particles arriving at X will
succeed each other at irregular time-intervals; which means that the
particles of the partial ray B about which we are making predictions
will also succeed each other after irregular time-intervals. It would
contradict the quantum theory if we could alter this state of things by,
for example, making these time-intervals equal. Thus we are able, as it
were, to take aim and to predetermine the force of the bullet; we can
also (and this before the bullet hits the target Y) calculate the exact time
at which the shot was fired at P. Yet we cannot freely choose the
moment of firing, but have to wait till the gun goes off. Nor can we
prevent uncontrolled shots being fired in the direction of our target
(from the neighbourhood of P).
It is clear that our experiment and Heisenberg’s interpretation are
incompatible. But since the possibility of carrying out this experiment
can be deduced from the statistical interpretation of quantum physics
(with the addition of the laws of energy and momentum), it appears
that Heisenberg’s interpretation, in contradicting it, must also contradict
the statistical interpretation of quantum theory. In view of the
experiments of Compton-Simon and Bothe-Geiger, it would seem that
it is possible to carry out our experiment. It can be regarded as a kind
of experiment crucis to decide between Heisenberg’s conception and a
consistently statistical interpretation of quantum theory.