  To explain both the OPERA experiment and all the known phenomenological
constraints/observations on Lorentz violation, the Background Dependent Lorentz
Violation (BDLV) has been proposed. We study the BDLV in a model independent
way, and conjecture that there may exist a "Dream Special Relativity Theory",
where all the Standard Model (SM) particles can be subluminal due to the
background effects. Assuming that the Lorentz violation on the Earth is much
larger than those on the interstellar scale, we automatically escape all the
astrophysical constraints on Lorentz violation. For the BDLV from the effective
field theory, we present a simple model and discuss the possible solutions to
the theoretical challenges of the OPERA experiment such as the Bremsstrahlung
effects for muon neutrinos and the pion decays. Also, we address the Lorentz
violation constraints from the LEP and KamLAMD experiments. For the BDLV from
the Type IIB string theory with D3-branes and D7-branes, we point out that the
D3-branes are flavour blind, and all the SM particles are the conventional
particles as in the traditional SM when they do not interact with the
D3-branes. Thus, we not only can naturally avoid all the known phenomenological
constraints on Lorentz violation, but also can naturally explain all the
theoretical challenges. Interestingly, the energy dependent photon velocities
may be tested at the experiments.
