On localisation in relativistic quantum mechanics

In nonrelativistic quantum mechanics causality is violated in an obvious way. The hope that this acausality would disappear in relativistic theories, in which the speed of propagation is finite, has turned out to be an idle hope. A localised state spreads over all space under a time translation or a boost. In this paper it is suggested that this strange behaviour is actually a semantic problem. The eigenstates of the Newton-Wigner position operator will be considered as single particle states, which are localised with an accuracy equal to their Compton wavelength. Correspondingly the nonlocality of a two-particle potential will not extend beyond the Compton wavelength of the particles and can therefore still be called local. These ideas will be elaborated in the framework of a previously formulated relativistic quantum theory. With this theory it will be shown that the sharp edge of a hard sphere interaction between two particles can still be determined with any accuracy by measuring the cross section in a high energy experiment.