  In quantum gravity there is no notion of absolute time. Like all other
quantities in the theory, the notion of time has to be introduced
"relationally", by studying the behavior of some physical quantities in terms
of others chosen as a "clock". We have recently introduced a consistent way of
defining time relationally in general relativity. When quantum mechanics is
formulated in terms of this new notion of time the resolution of the
measurement problem can be implemented via decoherence without the usual
pitfalls. The resulting theory has the same experimental results of ordinary
quantum mechanics, but every time an event is produced or a measurement happens
two alternatives are possible: a) the state collapses; b) the system evolves
without changing the state. One therefore has two possible behaviors of the
quantum mechanical system and physical observations cannot decide between them,
not just as a matter of experimental limitations but as an issue of principle.
This first-ever example of fundamental undecidability in physics suggests that
nature may behave sometimes as described by one alternative and sometimes as
described by another. This in particular may give new vistas on the issue of
free will.
