  If Nature allowed nonlocal correlations other than those predicted by quantum
mechanics, would that contradict some physical principle? Various approaches
have been put forward in the past two decades in an attempt to single out
quantum nonlocality. However, none of them can explain the set of quantum
correlations arising in the simplest scenarios. Here it is shown that
generalized uncertainty relations, as well as a specific notion of locality
give rise to both familiar and new characterizations of quantum correlations.
In particular, we identify a condition, relativistic independence, which states
that uncertainty relations are local in the sense that they cannot be
influenced by other experimenters' choices of measuring instruments. We prove
that theories with nonlocal correlations stronger than the quantum ones do not
satisfy this notion of locality and therefore they either violate the
underlying generalized uncertainty relations or allow experimenters to
nonlocally tamper with the uncertainty relations of their peers.
