  We show that the current method of determining superfluidity in optical
lattices based on a visibly sharp bosonic momentum distribution $n({\bf k})$
can be misleading, for even a normal Bose gas can have a similarly sharp
$n({\bf k})$. We show that superfluidity in a homogeneous system can be
detected from the so-called visibility $(v)$ of $n({\bf k})$ $-$ that $v$ must
be 1 within $O(N^{-2/3})$, where $N$ is the number of bosons. We also show that
the T=0 visibility of trapped lattice bosons is far higher than what is
obtained in some current experiments, suggesting strong temperature effects and
that these states can be normal. These normal states allow one to explore the
physics in the quantum critical region.
