Observations in Quantum Mechanics are subject to complex restrictions arising
from the principle of energy conservation. Determining such restrictions,
however, has been so far an elusive task, and only partial results are known.
In this paper we discuss how constraints on the energy spectrum of a
measurement device translate into limitations on the measurements which we can
effect on a target system with non-trivial energy operator. We provide
efficient algorithms to characterize such limitations and we quantify them
exactly when the target is a two-level quantum system. Our work thus identifies
the boundaries between what is possible or impossible to measure, i.e., between
what we can see or not, when energy conservation is at stake.Comment: Better read the 5-page published version firs
