The Logic of Scientific Discovery

By Karl R. Popper | Go to book overview

CHAPTER IX
SOME OBSERVATIONS ON QUANTUM THEORY
OUR analysis of the problem of probability has placed instruments at our disposal which we may now put to the test, by applying them to one of the topical problems of modern science; and I will try, with their help, to analyse, and to clarify, some of the more obscure points of modern quantum theory.My somewhat audacious attempt to tackle, by philosophical or logical methods, one of the central problems of physics, is bound to arouse the suspicion of the physicist. I admit that his scepticism is healthy and his suspicions well-founded; yet I have some hope that I may be able to overcome them. Meanwhile it is worth remembering that in every branch of science, questions may crop up which are mainly logical. It is a fact that quantum physicists have been eagerly participating in epistemological discussions. This may suggest that they themselves feel that the solution of some of the still unsolved problems in quantum theory has to be sought in the no-man's-land that lies between logic and physics.I will begin by setting down in advance the main conclusions which will emerge from my analysis.
There are some mathematical formulae in quantum theory which have been interpreted by Heisenberg in terms of his uncertainty 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'.)

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