popper-logic-scientific-discovery

some observations on quantum theory 235
hypothesis. For the statement (which corresponds to Heisenberg’s view)
that exact single predictions are impossible, turns out to be equivalent
to the hypothesis that predictive measurements and physical selections are inseparably
linked. With this new theoretical system—the conjunction of the
quantum theory with this auxiliary ‘hypothesis of linkage’—my conception
must indeed clash. 1
With this, point (3) of my programme has been carried out. But
point (4) has still to be established; that is, we have still to show that
the system which combines the statistically interpreted quantum theory
(including, we assume, the conservation laws for momentum and
energy) with the ‘hypothesis of linkage’, is self-contradictory. There is,
I suppose, a deep-seated presumption that predictive measurement and
physical selection are always linked. The prevalence of this presumption
may explain why the simple arguments which would establish the
opposite have never been worked out.
I wish to stress that the mainly physical considerations now to be
presented do not form part of the assumptions or premises of my
logical analysis of the uncertainty relations although they might be
described as its fruit. In fact, the analysis so far carried out is quite
independent of what follows; especially of the imaginary physical experiment
described below,* 2 which is intended to establish the possibility
of arbitrarily precise predictions of the path of single particles.
By way of introduction to this imaginary experiment I will first
discuss a few simpler experiments. These are intended to show that we
can without difficulty make arbitrarily precise path predictions, and
also test them. At this stage I only consider predictions which do not
refer to definite single particles, but refer to (all) particles within a
definite small space-time region (∆x.∆y.∆z.∆t). In each case there is
only a certain probability that particles are present in that region.
We again imagine a beam (an electron or light beam) of particles
1 The auxiliary hypothesis here discussed can of course appear in a different form. My
reason for choosing this particular form for critical analysis and discussion is that the
objection which asserts the linkage of measurement and physical selection was actually
(in conversations as well as in letters) raised against the view here advanced.
* 2 Those of my critics who rightly rejected the idea of this imaginary experiment appear
to have believed that they had thereby also refuted the preceding analysis, in spite of the
warning here given.