popper-logic-scientific-discovery

APPENDIX vii
Remarks Concerning an Imaginary
Experiment (cf. section 77)* 1
We may start from the assumption that a 1 and |b 1| are measured, or
selected, with an arbitrary degree of precision. In view of the result
obtained in appendix vi, we may assume that the absolute momentum
|a 2| of the particle arriving at X from the direction PX can be measured
with an arbitrary degree of precision. Accordingly, |b 2| may
also be determined as precisely as we choose (by using the principle of
conservation of energy). Moreover, the position of Sl and X, and the
instants of the arrival of the [A]-particles at X, can be measured with
arbitrary precision. Thus we need only investigate the situation with
respect to the indeterminacies ∆a 2 and ∆b 2, which arise in consequences
of indeterminacies of the corresponding directions, and the
vector ∆P connected with the indeterminacy of the position of P which
also arises in consequence of the indeterminacy of a direction, viz. the
direction PX.
If the beam PX passes through a slit at X, then a directional
indeterminacy φ will occur, in consequence of the diffraction at the
* 1 For a criticism of some of the assumptions underlying section 77 and this appendix,
see note *1 to appendix vi.