  We showed before that self-dual electromagnetism in noncommutative (NC)
spacetime is equivalent to self-dual Einstein gravity. This result implies a
striking picture about gravity: Gravity can emerge from electromagnetism in NC
spacetime. Gravity is then a collective phenomenon emerging from gauge fields
living in fuzzy spacetime. We elucidate in some detail why electromagnetism in
NC spacetime should be a theory of gravity. In particular, we show that NC
electromagnetism is realized through the Darboux theorem as a diffeomorphism
symmetry G which is spontaneously broken to symplectomorphism H due to a
background symplectic two-form $B_{\mu\nu}=(1/\theta)_{\mu\nu}$, giving rise to
NC spacetime. This leads to a natural speculation that the emergent gravity
from NC electromagnetism corresponds to a nonlinear realization G/H of the
diffeomorphism group, more generally its NC deformation. We also find some
evidences that the emergent gravity contains the structure of generalized
complex geometry and NC gravity. To illuminate the emergent gravity, we
illustrate how self-dual NC electromagnetism nicely fits with the twistor space
describing curved self-dual spacetime. We also discuss derivative corrections
of Seiberg-Witten map which give rise to higher order gravity.
