popper-logic-scientific-discovery

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some structural components of a theory of experience
the group before disturbing it (so long, of course, as this would not
enable us to use our knowledge so as to effect a forbidden selection).
But there is no way of obtaining any such knowledge concerning the
single electrons without disturbing them. To conclude, it remains true
that precise single predictions are impossible.’
To this objection I should first reply that it would not be surprising if
it were correct. It is after all obvious that from a statistical theory exact
singular predictions can never be derived, but only ‘indefinite’ (i.e.
formally singular) single predictions. But what I assert at this stage is
that although the theory does not supply any such predictions, it does not
rule them out either. One could speak of the impossibility of singular
predictions only if it could be asserted that disturbing the system or
interfering with it must prevent every kind of predictive measurement.
‘But that is just what I assert’, my opponent will say. ‘I assert, precisely,
the impossibility of any such measurement. You assume that it is
possible to measure the energy of one of these moving electrons without
forcing it out of its path and out of the electron group. This is the
assumption which I regard as untenable. For assuming that I possessed
any apparatus with which I could make such measurements, then I
should with this or some similar apparatus be able to produce aggregates
of electrons which all (a) were limited as to their position, and (b) had
the same momentum. That the existence of such aggregates would
contradict the quantum theory is, of course, your view too, since it is
ruled out by your own ‘scatter relations’, as you call them. Thus you
could only reply that it is possible to conceive of an apparatus which
would allow us to take measurements but not to make selections. I
admit that this answer is logically permissible; but as a physicist I can
only say that my instincts revolt against the idea that we could measure
the momenta of electrons while being unable to eliminate, for instance,
all those whose momentum exceeds (or falls short of) some given
amount.’
My first answer to this would be that it all sounds quite convincing.
But a strict proof of the contention that, if a predictive measurement is
possible, the corresponding physical selection or separation would also
be possible, has not been given (and it cannot be given, as will be seen
soon). None of these arguments prove that the precise predictions
would contradict the quantum theory. They all introduce an additional