popper-logic-scientific-discovery

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photographic plate which records the light that passes the two slits; and
on the other hand, that some experimental arrangement would make it
possible to find out, of a single photon, which of the two slits it has
passed through.’ 17
Jordan asserts ‘that these two assumptions contain a contradiction’. 18
I am not going to contest this, although the contradiction would not
be a logical or mathematical absurdity (as he suggests in one of the
previous quotations); rather, the two assumptions would, together,
merely contradict the formalism of the quantum theory. Yet I wish to
contest a different point. Jordan uses this experiment to illustrate his
formulation of the contents of the principle of complementarity. But
the very experiment by which he illustrates this principle may be
shown to refute it.
For consider Jordan’s description of the two-slit experiment, omitting
at first his last assumption (the one introduced by the words ‘on the
other hand’). Here we obtain interference fringes on the photographic
plate. Thus this is an experiment which ‘brings forth the wave properties
of the light’. Now let us assume that the intensity of the light is
sufficiently low to obtain on the plate distinct hits of the photons; or in
other words, so low that the fringes are analysable as due to the density
distribution of the single photon hits. Then we have here ‘one experiment’
that ‘brings forth, at the same time, both the wave properties and
the particle properties of light’—at least some of them. That is to say, it
does precisely what according to Jordan must be ‘absurd in a logical
and mathematical sense’.
Admittedly, were we able, in addition, to find out through which of
the slits a certain photon has passed, then we should be able to determine
its path; and we might then say that this (presumably impossible)
experiment would bring forth the particle properties of the photon
even more strongly. I grant all this; but it is quite irrelevant. For what
Jordan’s principle asserted was not that some experiments which might
seem at first sight possible turn out to be impossible—which is
trivial—but that there are no experiments whatever which ‘bring forth,
at the same time, both the wave properties and the corpuscle properties of
17 Op. cit., pp. 115 f. (The italics are Jordan’s.)
18 Op. cit., p. 116.