popper-logic-scientific-discovery

238
some structural components of a theory of experience
‘non-predictive’ measurements, namely (a) measurement of two positions,
(b) measurement of position preceded or (c) succeeded by a
measurement of momentum. The above discussed measurement by
means of a filter in front of a film strip of a Geiger-counter exemplifies
(b), i.e. a selection according to momentum followed by a measurement
of position. This is presumably just that case which, according to
Heisenberg (cf. section 73), permits ‘a calculation about the past of the
electron’. For while in cases (a) and (c) only calculations for the time
between the two measurements are possible, it is possible in case (b) to
calculate the path prior to the first measurement, provided this measurements
was a selection according to a given momentum; for such a
selection does not disturb the position of the particle.* 3 Heisenberg, as
we know, questions the ‘physical reality’ of this measurement, because
it permits us to calculate the momentum of the particle only upon its
arrival at a precisely measured position and at a precisely measured
time: the measurement seems to lack predictive content because no
testable conclusion can be derived from it. Yet I shall base my imaginary
experiment, intended to establish the possibility of precisely predicting
the position and momentum of a definite particle, upon this
particular measuring arrangement which at first sight is apparently
non-predictive.
As I am about to derive such far-reaching consequences from the
assumption that precise ‘non-predictive’ measurements of this type
are possible, it seems proper to discuss the admissibility of this
assumption. This is done in appendix vi.
With the imaginary experiment that follows here, I directly challenge
the method of arguing which Bohr and Heisenberg have used
in order to justify the interpretation of the Heisenberg formulae as
* 3 This statement (which I tried to base upon my discussion in appendix vi) was
effectively criticized by Einstein (cf. appendix *xii), is false and so my imaginary experiment
collapses. The main point is that non-predictive measurements determine the path
of a particle only between two measurements, such as a measurement of momentum
followed by one of position (or vice versa); it is not possible, according to quantum theory,
to project the path further back, i.e. to the region of time before the first of these
measurements. Thus the last paragraph of appendix vi is mistaken; and we cannot know,
of the particle arriving at x (see below) whether it did come from P, or from somewhere
else. See also note **on p. 232.