We argue that it is fundamentally impossible to recover information about
quantum superpositions when a system has interacted with a sufficiently large
number of degrees of freedom of the environment. This is due to the fact that
gravity imposes fundamental limitations on how accurate measurements can be.
This leads to the notion of undecidability: there is no way to tell, due to
fundamental limitations, if a quantum system evolved unitarily or suffered
wavefunction collapse. This in turn provides a solution to the problem of
outcomes in quantum measurement by providing a sharp criterion for defining
when an event has taken place. We analyze in detail in examples two situations
in which in principle one could recover information about quantum coherence: a)
"revivals" of coherence in the interaction of a system with the environment and
b) the measurement of global observables of the system plus apparatus plus
environment. We show in the examples that the fundamental limitations due to
gravity and quantum mechanics in measurement prevent both revivals from
occurring and the measurement of global observables. It can therefore be argued
that the emerging picture provides a complete resolution to the measurement
problem in quantum mechanics.Comment: 14 pages, Latex, one figure, version to appear in Foundations of
Physic