popper-logic-scientific-discovery

appendix *xi 475
electron’s position if we measure its momentum with Heisenberg’s
microscope, and that this ‘smearing’ effect has been established by
Heisenberg’s discussion of his imaginary experiment.
My own imaginary experiment of section 77 was largely based on
this asymmetry in Heisenberg’s experiment. (Cf. note *1 to appendix
vi.) Yet my experiment is invalid just because the asymmetry invalidates
Heisenberg’s whole discussion of measurement: only measurements
resulting from physical selection (as I call it) can be used to illustrate
Heisenberg’s formulae, and a physical selection, as I quite correctly
pointed out in the book, must always satisfy the ‘scatter relations’.
(Physical selection does disturb the system.)
Were Heisenberg’s ‘measurements’ possible we could even check
the momentum of an electron between two position measurements
without disturbing it, which would also allow us—contrary to point
(c), above—to check (part of) its spatio-temporal ‘path’ which is
calculable from these two position measurements.
That the inadequacy of Heisenberg’s argument has remained
unnoticed for so long is no doubt due to the fact that the
indeterminacy formulae clearly follow from the formalism of the
quantum theory (the wave equation), and that the symmetry
between position (q) and momentum (p) is also implicit in this
formalism. This may explain why many physicists have failed to
scrutinize Heisenberg’s imaginary experiment with sufficient care:
they did not take it seriously, I suppose, but merely as an illustration
of a derivable formula. My point is that it is a bad illustration—just
because it fails to account for the symmetry between position and
momentum. And being a bad illustration, it is quite inadequate as a
basis for interpreting these formulae—let alone the whole quantum
theory.
(10) The immense influence of Heisenberg’s imaginary experiment
is, I am convinced, due to the fact that he managed to convey
through it a new metaphysical picture of the physical world, whilst at
the same time disclaiming metaphysics. (He thus ministered to a curiously
ambivalent obsession of our post-rationalist age: its preoccupation
with killing the Father—that is, Metaphysics—while keeping Him
inviolate, in some other form, and beyond all criticism. With some
quantum physicists it sometimes looks almost as if the father was