  The implications of the relativistic space-time structure for a physical
description by quantum mechanical wave-functions are investigated. On the basis
of a detailed analysis of Bell's concept of local causality, which is violated
in quantum theory, we argue that this is a subtle, as well as an important
effort. A central requirement appearing in relativistic quantum mechanics,
namely local commutativity, is analyzed in detail and possible justifications
are given and discussed. The complexity of the implications of wave function
reduction in connection with Minkowski space-time are illustrated by a quantum
mechanical measurement procedure which was proposed by Aharonov and Albert.
This procedure and its relativistic implications are explicitly analyzed and
discussed in terms of state evolution. This analysis shows that the usual
notion of state evolution fails in relativistic quantum theory. Two possible
solutions of this problem are given. In particular, it is shown that also a
theory with a distinguished foliation of space-time into space-like leafs -
accounting for nonlocality - makes the right predictions for the
Aharonov-Albert experiment. We will repeatedly encounter that an analysis of
the wave-function alone does not suffice to answer the question of relativistic
compatibility of the theory, but that the actual events in space time, which
are predicted and described by the theory, are crucial. Relativistic versions
of quantum mechanical theories which precisely describe actual processes in
space-time are briefly described and discussed in the appendix.
