popper-logic-scientific-discovery

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some structural components of a theory of experience
physical reality Heisenberg is obliged to leave in doubt, while others,
such as Schlick, deny it outright. But the experiments in question, (a),
(b), and (c)—see section 73—can all be interpreted in statistical terms.
For example, combination (c), i.e. a measurement of position followed
by a measurement of momentum, may be realized by an experiment
such as the following. We select a ray according to position with the
help of a diaphragm with a narrow slit (position-measurement). We
then measure the momentum of those particles which were travelling
from the slit in a definite direction. (This second measurement will of
course produce a new scatter of positions.) The two experiments
together will then determine precisely the path of all those particles
which belong to the second selection, in so far as this path lies between
the two measurements: both position and momentum between the
two measurements can be precisely calculated.
Now these measurements and calculations, which correspond precisely
to the elements regarded as superfluous in Heisenberg’s interpretation,
are on my interpretation of the theory anything but
superfluous. Admittedly, they do not serve as initial conditions or as a
basis for the derivation of predictions; but they are indispensable nevertheless:
they are needed for testing our predictions, which are statistical predictions.
For what our statistical scatter relations assert is that the momenta must
scatter when positions are more exactly determined, and vice versa. This
is a prediction which would not be testable, or falsifiable, if we were
not in a position to measure and calculate, with the help of experiments
of the kind described, the various scattered momenta which
occur immediately after any selection according to position has been
made.* 1
* 1 I consider this paragraph (and also the first sentence of the next paragraph) as one of
the most important in this discussion, and as one with which I can still agree completely.
Since misunderstandings continue, I will explain the matter more fully. The scatter relations
assert that, if we arrange for a sharp selection of the position (by a slit in a screen, say),
the momenta will scatter as a consequence. (Rather than becoming ‘indeterminate’, the
single momenta become ‘unpredictable’ in a sense which allows us to predict that they
will scatter.) This is a prediction which we must test by measuring the single momenta, so as to
determine their statistical distribution. These measurements of the single momenta
(which will lead to a new scatter—but this we need not discuss) will give in each single
case results as precise as we like, and at any rate very much more precise than ∆p, i.e. the
mean width of the region of the scatter. Now these measurements of the various single