popper-logic-scientific-discovery

some observations on quantum theory 241
there must correspond a second particle, of [B], which was deflected at
P with the momentum b 2, in the calculable direction PY. We now place
an apparatus at X—for instance a Geiger-counter or a moving film
strip—which records the impacts of particles arriving from P at the
arbitrarily restricted region X. Then we can say: as we note any such
recording of a particle, we learn at the same time that a second particle
must be travelling from P with the momentum b 2 towards Y. And we
also learn from the recording where this second particle was at any
given moment; for we can calculate from the time of the impact of the
first particle at X, and from its known velocity, the moment of its
collision at P. By using another Geiger-counter at Y (or the moving film
band), we can test our predictions for the second particle.* 4
The precision of these predictions as well as that of the measurements
undertaken to test them is in principle not subject to any of the limitations
due to the uncertainty principle, as regards both the position co-ordinate and
the component of the momentum in the direction PY. For my imaginary
experiment reduces the question of the precision with which predictions
can be made about a B-particle deflected in P to the question of
the precision attainable in taking measurements at X. These, at first,
seemed to be non-predictive measurements of the time, position and
momentum of the corresponding first particle [A]. The momentum of
this particle in the PX direction as well as the time of its impact at X, i.e.
of its position in the PS direction, can be measured with any desirable
degree of precision (cf. appendix vi) if we make a momentum selection
* 4 Einstein, Podolsky, and Rosen use a weaker but valid argument: let Heisenberg’s interpretation
be correct, so that we can only measure at will either the position or the
momentum of the first particle at X. Then if we measure the position of the first particle, we
can calculate the position of the second particle; and if we measure the momentum of the
first particle, we can calculate the momentum of the second particle. But since we can make
our choice—as to whether we measure position or momentum—at any time, even after
the collision of the two particles has taken place, it is unreasonable to assume that the
second particle was in any way affected, or interfered with, by the change in the experimental
arrangements resulting from our choice. Accordingly, we can calculate, with any
precision we like, either the position or the momentum of the second particle without
interfering with it; a fact which may be expressed by saying that the second particle ‘has’ both
a precise position and a precise momentum. (Einstein said that both position and
momentum are ‘real’; whereupon he was attacked as ‘reactionary’.) See also the note on
p. 232 and appendices *xi and *xii.