popper-logic-scientific-discovery

appendix *xi 471
significance only for the position of the one particle and the
momentum of the other. For as explained under point (4) above, we
may measure the position of B, and somebody far away may measure
the momentum of A accidentally at the same instant, or at any rate
before any smearing effect of our measurement of B could possibly
reach A. Yet this is all that is needed to show that Bohm’s attempt to
save Heisenberg’s idea of our interference with A is misplaced.
Bohm’s reply to this objection is implicit in his assertion that the
smearing effect proceeds with super-luminal velocity, or perhaps even
instantaneously (cf. Heisenberg’s super-luminal velocity commented
on in section 76), an assumption to be supported by the further
assumption that this effect cannot be used to transmit signals. But what
does happen if the two measurements are carried out simultaneously?
Does the particle you are supposed to observe in your Heisenberg
microscope begin to dance under your very eyes? And if it does, is this
not a signal? (This particular smearing effect of Bohm’s, like the
‘reduction of the wave packet’, is not part of his formalism, but of its
interpretation.)
(8) A similar example is a reply of Bohm’s to another critical
imaginary experiment proposed by Einstein (who thereby revived
Pauli’s criticism of de Broglie’s pilot wave theory). 12
Einstein proposes to consider a macroscopic ‘particle’ (it may be
quite a big thing, say a billiard ball) moving with a certain constant
velocity to and fro between two parallel walls by which it is elastically
reflected. Einstein shows that this system can be represented in
Schrödinger’s theory by a standing wave; and he shows further that the
pilot wave theory of de Broglie, or Bohm’s so-called ‘causal interpretation
of quantum theory’ leads to the paradoxial result (first pointed
out by Pauli) that the velocity of the particle (or billiard ball) vanishes;
or in other words, our original assumption that the particle moves with
some arbitrarily chosen velocity leads in this theory, for every chosen
velocity, to the conclusion that the velocity is zero, and that it does not
move.
Bohm accepts this conclusion, and replies on the following lines:
‘The example considered by Einstein’, he writes, ‘is that of a particle
12 See A. Einstein in Scientific Papers Presented to Max Born, 1953, pp. 33 ff; see especially p. 39.