  While it has often been proposed that, fundamentally, Lorentz-invariance is
not respected in a quantum theory of gravity, it has been difficult to
reconcile deviations from Lorentz-invariance with quantum field theory. The
most commonly used mechanisms either break Lorentz-invariance explicitly or
deform it at high energies. However, the former option is very tightly
constrained by experiment already, the latter generically leads to problems
with locality. We show here that there exists a third way to integrate
deviations from Lorentz-invariance into quantum field theory that circumvents
the problems of the other approaches. The way this is achieved is an extension
of the standard model in which photons can have different speeds without
singling out a preferred restframe, but only as long as they are in a quantum
superposition. Once a measurement has been made, observables are subject to the
laws of special relativity, and the process of measurement introduces a
preferred frame. The speed of light can take on different values, both
superluminal and subluminal (with respect to the usual value of the speed of
light), without the need for Lorentz-invariance violating operators and without
tachyons. We briefly discuss the relation to deformations of special relativity
and phenomenological consequences.
