popper-logic-scientific-discovery

some observations on quantum theory 227
The statistically interpreted theory, therefore, not only does not rule
out the possibility of exact single measurements, but would be untestable,
and thus ‘metaphysical’, if these were impossible. So the fulfilment
of Heisenberg’s programme, the elimination of metaphysical
elements, is here achieved, but by a method the very opposite of his.
For while he tried to exclude magnitudes which he regarded as
inadmissible (though without entirely succeeding), I invert the
attempt, so to speak, by showing that the formalism which contains
these magnitudes is correct just because the magnitudes are not metaphysical.
Once we have given up the dogma embodied in Heisenberg’s limitation
upon attainable precision, there is no longer any reason why we
should doubt the physical significance of these magnitudes. The scatter
relations are frequency predictions about paths; and therefore these
paths must be measurable—in precisely the same way as, say, throws of
five must be empirically ascertainable—if we are to be able to test our
frequency predictions about these paths, or about these throws.
Heisenberg’s rejection of the concept of path, and his talk of ‘nonobservable
magnitudes’, clearly show the influence of philosophical
and especially of positivistic ideas. Under the same influence, March
writes: ‘One may say perhaps without fear of being misunderstood . . .
that for the physicist a body has reality only in the instant in which he
observes it. Naturally nobody is so mad as to assert that a body ceases to
exist the moment we turn our backs to it; but it does cease, in that
moment, to be an object of inquiry for the physicist, because there
exists no possibility of saying anything about it which is based on
experiment.’ 2 In other words, the hypothesis that a body moves in this
or that path whilst it is not being observed is non-verifiable. This, of
momenta allow us to calculate their values back to the place where the position was
selected, and measured, by the slit. And this ‘calculation of the past history’ of the
particle (cf. note 3 to section 73) is essential; without it, we could not assert that we were
measuring the momenta immediately after the positions were selected; and thus we
could not assert that we were testing the scatter relations—which we do in fact with any
experiment which shows an increase of scatter as a consequence of a decrease of the
width of a slit. So it is only the precision of the prediction which becomes ‘blurred’ or
‘smeared’ in consequence of the scatter relations, but never the precision of a measurement.
2 March, Die Grundlagen der Quantenmechanik, p. 1. *Reichenbach’s position is similar; it is
criticized in my Postscript, section *13.