  In it's usual presentation, classical mechanics appears to give time a very
special role. But it is well known that mechanics can be formulated so as to
treat the time variable on the same footing as the other variables in the
extended configuration space. Such covariant formulations are natural for
relativistic gravitational systems, where general covariance conflicts with the
notion of a preferred physical-time variable. The standard presentation of
quantum mechanics, in turns, gives again time a very special role, raising well
known difficulties for quantum gravity. Is there a covariant form of
(canonical) quantum mechanics? We observe that the preferred role of time in
quantum theory is the consequence of an idealization: that measurements are
instantaneous. Canonical quantum theory can be given a covariant form by
dropping this idealization. States prepared by non-instantaneous measurements
are described by "spacetime smeared states". The theory can be formulated in
terms of these states, without making any reference to a special time variable.
The quantum dynamics is expressed in terms of the propagator, an object
covariantly defined on the extended configuration space.
