  According to general relativity, trapping surfaces and horizons are classical
causal structures that arise in systems with sharply defined energy and
corresponding gravitational radius. The latter concept can be extended to a
quantum mechanical state simply by means of the spectral decomposition, which
allows one to define an associated "horizon wave-function". Since this
auxiliary wave-function contains crucial information about the causal structure
of space-time, a new proposal is formulated for the time-evolution of quantum
states in order to account for the fundamental classical property that outer
observers cannot receive signals from inside a horizon. The simple case of a
single massive free particle at rest is used throughout the paper as a toy
model to illustrate the main ideas.
