Heisenberg's uncertainty relation of position and momentum in experiments without mutual disturbance

Abstract

Arranging target atoms in a plane monolayer, one may produce by atomic or nuclear reaction an ensemble of particles with small initial position spread without disturbing their momentum spread. This would either allow a violation of Heisenberg's uncertainty relation, by creating a situation not described by quantum mechanics hence rendering quantum mechanics incomplete, or, if the uncertainty relation should hold also in this non-disturbative situation, it would mean a permanent violation of energy conservation. Thus an uncertainty relation for position and momentum and energy conservation appear to be mutually exclusive.