  Spontaneous Lorentz violation is a viable mechanism to look for Planck scale
physics. In this work, we study spontaneous Lorentz violation models, in flat
spacetime, where a vector field produces such a violation and matter is modeled
by a complex scalar field. We show that it is possible to construct a Hamilton
density for which the evolution respects the dynamical constraints. However, we
also find that the initial data, as required by standard field theory, does not
determine the fields evolution in a unique way. In addition, we present some
examples where the physical effects of such ambiguities can be recognized. As a
consequence, the proposals in which the electromagnetic and gravitational
interactions emerge from spontaneous Lorentz violation are challenged.
