Unsharp Localization and Causality in Relativistic Quantum Theory

Abstract

The conflict between relativistic causality and localizability is analyzed in the light of the existence of unsharp localization observables. A theorem due to S. Schlieder is generalized, showing that the assumption of local commutativity implies the localization observable in question to be unsharp in a strong sense. Furthermore, a recent generalization of a theorem of L\"uders is applied to demonstrate that local commutativity is a necessary consequence of Einstein causality even in the case of unsharp observables if they admit local measurements. These findings raise the question whether localization observables can be measured by means of local operations.