popper-logic-scientific-discovery

appendix v 299
(c) In a similar way, the atom with exactly measured momentum
but blurred or smeared position will be replaced by a pure selection
according to a given momentum; or, in other words, by a monochromatic
beam of photons travelling along parallel lines from some
(non-point-like) source of light.
In each of the two cases we obtain the correct experimental result:
interference patterns in case (b), and no interference patterns in
case (c).
(d) How are we to interpret the third case, which is supposed to
lead to two mutually contradictory predictions? To discover this we
imagine that we have exactly observed the path of the atom A, which
means both its position and its momentum. We should then find that
the atom emits single photons, and recoils with each emission. Each
recoil shifts it to another position, and each time the shift is in a new
direction. Assuming that the atom radiates in this way for a period of
time (we do not raise the question whether it also absorbs energy
during this period), it will take up a number of different positions
during this period, ranging over a considerable volume of space. For
this reason we are not allowed to replace the atom by a point-like
cluster of atoms: we can only replace it by a cluster of atoms distributed
over a considerable volume of space. Furthermore, since the atom radiates
in all directions, we have to replace it by a cluster of atoms radiating
in all directions. Thus we do not obtain a pure case; nor do we get
coherent radiation. And we do not get interference patterns.
Objections similar to the one here examined may be re-interpreted
statistically along the lines of this example.
(e) In connection with our analysis of this imaginary experiment I
should like to say that argument (a), contrary to what might be supposed
at first, would be in any case quite insufficient to elucidate the
so-called problem of complementarity (or the dualism of wave and
particle). It tries to do so by showing that the atom is able to emit only
either coherent waves or incoherent photons, and that therefore no contradiction
arises, because the two experiments are mutually exclusive. But
it is simply not true that the two experiments are mutually exclusive,
for we can of course combine a not too exact measurement of position
with a not too exact measurement of momentum; and in this case the
atom neither emits completely coherent waves nor completely