  There is current interest in dynamical description of dif- ferent
decompositions of a quantum system into subsystems. We investi- gate usefulness
of the Nakajima-Zwanzig projection method in this context. Particularly, we are
interested in simultaneous description of dynamics of open systems pertaining
to dierent system-environment splits (decompo- sitions). We find that the
Nakajima-Zwanzig and related projection meth- ods are system-environment split
specific, that every system-environment split requires specific projector, and
that projector adapted to a split nei- ther provides information about nor
commute with a projector adapted to an alternative system-environment split.
Our findings refer to finite- and infinite-dimensional systems and to arbitrary
kinds of system-environment splitting. These findings are a direct consequence
of the recently established quantum correlations relativity. We emphasize the
subtlety and delicacy re- quired of the task of simultaneously describing the
dynamics of alternate system-environment splits.
