  Does there exist a limit for the applicability of quantum theory for objects
of large mass or size, or objects whose states are of large complexity or
dimension of the Hilbert space? The possible answers range from practical
limitations due to decoherence within quantum theory to fundamental limits due
to collapse models that modify quantum theory. Here, we suggest the viewpoint
that there might be also fundamental limits without altering the quantum laws.
We first demonstrate that for two quantum spins systems of a given spin length,
no violation of local realism can be observed, if the measurements are
sufficiently coarse-grained. Then we show that there exists a fundamental limit
for the precision of measurements due to (i) the Heisenberg uncertainty
relation which has to be applied to the measuring apparatus, (ii) relativistic
causality, and (iii) the finiteness of resources in any laboratory including
the whole universe. This suggests that there might exist a limit for the size
of the systems (dimension of the Hilbert space) above which no violation of
local realism can be seen anymore.
