popper-logic-scientific-discovery

some observations on quantum theory 239
limitations upon attainable precision. For they tried to justify this
interpretation by showing that no imaginary experiment can be
devised which will produce more exact predictive measurements. But
this method of arguing can clearly not exclude the possibility that an
imaginary experiment might some day be devised which (using
known physical effects and laws) would show that such measurements
are possible after all. It was taken for granted that any such
experiment would contradict the formalism of the quantum theory
and it appears that this idea determined the direction of the search
for such experiments. My analysis—the carrying out of the points of
my programme (I) and (2)—has however cleared the way for an
imaginary experiment to be devised which shows, in full agreement
with quantum theory, that the precise measurements in question are
possible.
To carry out this experiment, I shall make use of ‘imaginary selection’,
as before; but shall choose an arrangement such that, if a particle
which is characterized by the selection really exists, we shall be able to
ascertain the fact.
My experiment, in a way, forms a kind of idealization of the
experiments of Compton-Simon and Bothe-Geiger. 2 Since we wish to
obtain singular predictions, we cannot operate with statistical assumptions
only. The non-statistical laws of the conservation of energy and
momentum will have to be used. We can exploit the fact that these
laws permit us to calculate what occurs when the particles collide,
provided we are given two of the four magnitudes which described
the collision (i.e. of the momenta a 1 and b 1 before, and a 2 and b 2 after
the collision) and one component 3 of a third one. (The method of
calculation is well known as part of the theory of the Comptoneffect.
4 )
Let us now imagine the following experimental arrangement. (See
figure 2.) We cross two particle beams (of which one at most may be a
2 Compton and Simon, Physical Review 25, 1924, p. 439; Bothe und Geiger, Zeitschrift für
Physik 32, 1925, p. 639; cf. also Compton, X-Rays and Electrons, 1927; Ergebnisse der exakten
Naturwissenschaft 5, 1926, p. 267 ff.; Haas, Atomtheorie, 1929, p. 229 ff.
3 ‘Component’ to be understood here in the widest sense (either as the direction or as
the absolute magnitude).
4 Cf. Haas, op. cit.