  The result of a physical measurement depends on the timescale of the
experimental probe. In solid-state systems, this simple quantum mechanical
principle has far-reaching consequences: the interplay of several degrees of
freedom close to charge, spin or orbital instabilities combined with the
disparity of the time scales associated to their fluctuations can lead to
seemingly contradictory experimental findings. A particularly striking example
is provided by systems of adatoms adsorbed on semiconductor surfaces where
different experiments -- angle-resolved photoemission, scanning tunneling
microscopy and core-level spectroscopy -- suggest different ordering phenomena.
Using most recent first principles many-body techniques, we resolve this puzzle
by invoking the time scales of fluctuations when approaching the different
instabilities. These findings suggest a re-interpretation of ordering phenomena
and their fluctuations in a wide class of solid-state systems ranging from
organic materials to high-temperature superconducting cuprates.
