  We develop a new method to predict the density associated with weak lensing
maps of (un)relaxed clusters in a range of theories interpolating between GR
and MOND (General Relativity and Modified Newtonian Dynamics). We apply it to
fit the lensing map of the bullet merging cluster 1E0657-56, in order to
constrain more robustly the nature and amount of collisionless matter in
clusters {\it beyond} the usual assumption of spherical equilibrium
(Pointecouteau & Silk 2005) and the validity of GR on cluster scales (Clowe et
al. 2006). Strengthening the proposal of previous authors we show that the
bullet cluster is dominated by a collisionless -- most probably non-baryonic --
component in GR as well as in MOND, a result consistent with the dynamics of
many X-ray clusters. Our findings add to the number of known pathologies for a
purely baryonic MOND, including its inability to fit the latest data from the
Wilkinson Microwave Anisotropy Probe. A plausible resolution of all these
issues and standard issues of Cold Dark Matter with galaxy rotation curves is
the "marriage" of MOND with ordinary hot neutrinos of 2eV. This prediction is
just within the GR-independent maximum of neutrino mass from current
$\beta$-decay experiments, and is falsifiable by the Karlsruhe Tritium Neutrino
(KATRIN) experiment by 2009. Issues of consistency with strong lensing arcs and
the large relative velocity of the two clusters comprising the bullet cluster
are also addressed.
