popper-logic-scientific-discovery

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appendices
wave-packets (obtained by superimposition of waves of various frequencies)
give us only probabilities, to be interpreted statistically, of the
occurrence of particles in this group which have the given momentum.
For any given finite range of momenta ∆p x, this probability tends
towards to provided we make the length of the wavetrain infinitely
short, i.e. measure the position with arbitrary precision (by opening
the instantaneous shutter for an arbitrarily short time). In the same
way, the probability tends towards o for any finite period during which
the instantaneous shutter is open, i.e. for any value of the position
range ∆x, provided ∆p x tends towards 0. The more exactly we select the
position and the momentum, the more improbable it will be that we
shall find any particles at all behind the filter. But this means that only
among a very great number of experiments will there be some in
which any particles are found behind the filter—and this without our
being able to predict in advance in which of the experiments particles
will be found there. Thus we cannot by any means prevent these particles
from appearing only at intervals scattered at random; and consequently
we shall not be able to produce in this way an aggregate of
particles which is more homogeneous than a pure case.
There appears to be a comparatively simple crucial experiment for
deciding between the ‘theory of indeterminacy’ (described above) and
the quantum theory. According to the former theory, photons would
arrive on a screen behind a highly selective filter (or spectrograph)
even after the extinction of the source of light, for a period of time; and
further, this ‘after-glow’ produced by the filter would last the longer
the more highly selective the filter was.* 2
* 2 This is precisely what will happen, according to Einstein’s remarks printed here in
appendix *xii. See also C. F. von Weizsäcker’s criticism of my imaginary experiment in Die
Naturwissenschaften 22, 1934, p. 807.