popper-logic-scientific-discovery

some observations on quantum theory 229
scatter of position-cum-momentum, and therefore statements about
paths.
Now that we have shown that the uncertainty relations are formally
singular probability statements, we can also unravel the tangled web of
their objective and subjective interpretations. We learned in section 71
that every formally singular probability statement can also be interpreted
subjectively, as an indefinite prediction, a statement concerning
the uncertainty of our knowledge. We have also seen under what
assumptions the justified and necessary attempt to interpret a statement
of this kind objectively is bound to fail. It is bound to fail if one tries to
substitute for the statistical objective interpretation a singular objective
interpretation, by attributing the uncertainty directly to the single
event.* 3 Yet if one interprets the Heisenberg formulae (directly) in a
subjective sense, then the position of physics as an objective science is
imperilled; for to be consistent one would also have to interpret
Schrödinger’s probability waves subjectively. This conclusion is drawn
by Jeans 5 who says: ‘In brief, the particle picture tells us that our
knowledge of an electron is indeterminate; the wave picture that the
electron itself is indeterminate, regardless of whether experiments are
performed upon it or not. Yet the content of the uncertainty principle
must be exactly the same in the two cases. There is only one way of
making it so: we must suppose that the wave picture provides a representation
not of objective nature, but only of our knowledge of
nature. . . .’ Schrödinger’s waves are thus for Jeans subjective probability
waves, waves of our knowledge. And with this, the whole subjectivist
probability theory invades the realm of physics. The arguments I have
rejected—the use of Bernoulli’s theorem as a ‘bridge’ from nescience
to statistical knowledge, and similar arguments (cf. section 62)—
become inescapable. Jeans formulates the subjectivist attitude of
* 3 This is one of the points on which I have since changed my mind. Cf. my Postscript,
chapter *v. But my main argument in favour of an objective interpretation remains
unaffected. According to my present view, Schrödinger’s theory may and should be
interpreted not only as objective and singular but, at the same time, as probabilistic.
5 Jeans, The New Background of Science (1933, p. 236; 2nd edition 1934, p. 240). In Jeans’s
text, a new paragraph begins with the second sentence, i.e. with the words, ‘Yet the
content’. For the quotation that follows at the end of this paragraph, see op. cit., p. 237
(2nd edition, p. 241).