popper-logic-scientific-discovery

some observations on quantum theory 221
measurement; I have referred only to physical selection. 3 It is now necessary
to clarify the relation between these two concepts.
I speak of physical selection or physical separation if, for example,
we screen off, from a stream of particles, all except those which pass
through a narrow aperture ∆x, that is, through a range ∆x allowed
to their position. And I shall say of the particles belonging to the ray
thus isolated that they have been selected physically, or technically,
according to their property ∆x. It is only this process, or its result, the
physically or technically isolated ray of particles, which I describe as
a ‘physical selection’—in contradistinction to a merely ‘mental’ or
‘imagined’ selection, such as we make when speaking of the class of
all those particles which have passed, or will pass, through the range
∆p; that is, of a class within a wider class of particles from which it
has not been physically screened off.
Now every physical selection can of course be regarded as a measurement,
and can actually be used as such. 4 If, say, a ray of particles is
selected by screening off or shutting out all those which do not pass
through a certain positional range (‘place-selection’) and if later the
momentum of one of these particles is measured, then we can regard
the place-selection as a measurement of position, because we learn
from it that the particle has passed through a certain position (though
when it was there we may sometimes not know, or may only learn from
another measurement). On the other hand, we must not regard every
measurement as a physical selection. Imagine, for example, a monochromatic
ray of electrons flying in the direction x. By using a Geiger
counter, we can then record those electrons that arrive at a certain
position. By the time-intervals between the impacts upon the counter,
we may also measure spatial intervals; that is to say, we measure their
positions in the x direction up to the moment of impact. But in taking
these measurements we do not make a physical selection of the particles
according to their positions in the x direction. (And indeed, these
3 Weyl too, among others, writes of ‘selections’; see Gruppentheorie und Quantenmechanik,
p. 67 ff., English translation p. 76 ff.; but unlike me he does not contrast measurement
and selection.
4 By a ‘measurement’ I mean, in conformity with linguistic usage accepted by physicists,
not only direct measuring operations but also measurements obtained indirectly by
calculation (in physics these are practically the only measurements that occur).