popper-logic-scientific-discovery

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some structural components of a theory of experience
principle; that is, as statements about ranges of uncertainty due to the
limits of precision which we may attain in our measurements. These
formulae, as I shall try to show, are to be interpreted as formally singular
probability statements (cf. section 71); which means that they in
their turn must be interpreted statistically. So interpreted the formulae
in question assert that certain relations hold between certain ranges of statistical
‘dispersion’ or ‘variance’ or ‘scatter’. (They will be here called ‘statistical
scatter relations’.)
(2) Measurements of a higher degree of precision than is permitted
by the uncertainty principle are not, I shall try to show, incompatible
with the system of formulae of quantum theory, or with its statistical
interpretation. Thus quantum theory would not necessarily be refuted
if measurements of such a degree of precision should ever become
possible.
(3) The existence of limits of attainable precision which was
asserted by Heisenberg would therefore not be a logical consequence
deducible from the formulae of the theory. It would be, rather, a
separate or an additional assumption.
(4) Moreover this additional assumption of Heisenberg’s actually
contradicts, as I shall try to show, the formulae of quantum theory if they
are statistically interpreted. For not only are more precise measurements
compatible with the quantum theory, but it is even possible to
describe imaginary experiments which show the possibility of more
exact measurements. In my view it is this contradiction which creates
all those difficulties by which the admirable structure of modern quantum
physics is beset; so much so that Thirring could say of quantum
theory that it ‘has remained an impenetrable mystery to its creators, on
their own admission’. 1
What follows here might be described, perhaps, as an inquiry into
the foundations of quantum theory. 2 In this, I shall avoid all mathematical
arguments and, with one single exception, all mathematical
1 H. Thirring, Die Wandlung des Begriffssystems der Physik (essay in Krise und Neuaufbau in den exakten
Wissenschaften, Fünf Wiener Vorträge, by Mark, Thirring, Hahn, Nobeling, Menger; Verlag
Deuticke, Wien und Leipzig, 1933, p. 30).
2 In what follows I confine myself to discussing the interpretation of quantum physics,
but I omit problems concerning wave-fields (Dirac’s theory of emission and absorption;
‘second quantization’ of the Maxwell-Dirac field-equations). I mention this restriction