popper-logic-scientific-discovery

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some structural components of a theory of experience
modern physics as follows: ‘Heisenberg attacked the enigma of the
physical universe by giving up the main enigma—the nature of
the objective universe—as insoluble, and concentrating on the minor
puzzle of co-ordinating our observations of the universe. Thus it
is not surprising that the wave picture which finally emerged should
prove to be concerned solely with our knowledge of the universe as
obtained through our observations.’
Such conclusions will no doubt appear highly acceptable to the positivists.
Yet my own views concerning objectivity remain untouched.
The statistical statements of quantum theory must be inter-subjectively
testable in the same way as any other statements of physics. And my
simple analysis preserves not only the possibility of spatio-temporal
descriptions, but also the objective character of physics.
It is interesting that there exists a counterpart to this subjective
interpretation of the Schrödinger waves: a non-statistical and thus a
directly (i.e. singular) objective interpretation. Schrödinger himself in
his famous Collected Papers on Wave-Mechanics has proposed some such
interpretation of his wave equation (which as we have seen is a formally
singular probability statement). He tried to identify the particle
immediately with the wave-packet itself. But his attempt led straight to
those difficulties which are so characteristic of this kind of interpretation:
I mean the ascription of uncertainty to the physical objects
themselves (objectivized uncertainties). Schrödinger was forced to
assume that the charge of the electron was ‘blurred’ or ‘smeared’ in
space (with a charge density determined by the wave amplitude); an
assumption which turned out to be incompatible with the atomic
structure of electricity. 6 Born’s statistical interpretation solved the
problem; but the logical connection between the statistical and the
non-statistical interpretations remained obscure. Thus it happened that
the peculiar character of other formally singular probability
statements—such as the uncertainty relations—remained
unrecognized and that they could continue to undermine the physical
basis of the theory.
I may conclude perhaps with an application of what has been said in
6 Cf. for instance Weyl, Gruppentheorie und Quantenmechanik, p. 193; English translation
pp. 216 f.