  In this paper, we study implications of the geometrical nature of space- time
for some of the basic tenets of quantum mechanics. That is, we study two
different implications of the principle of general covariance; first we
quantize a reparametrization invariant theory, the free particle in Minkowski
spacetime and point out in detail where this theory fails (no- tably these
comments appear to be missing in the literature). Second we study the
covariance of quantum field theory and show how it connects to causality, the
outcome of this study is that QFT is what we shall call ultra weakly covariant
with respect to the background spacetime. Third, we treat the question of
whether evolution in quantum theory (apart from the measurement act) needs to
be unitary, it is easily shown that a per- fectly satisfying probabilistic
interpretation exists which does not require unitary evolution. Fourth, we
speculate on some modifications quantum theory should undergo in order for it
to be generally covariant. The results in this paper hint at a profound change
of the theory in which causality as a fundamental principle is abandonned.
