  The assumption of Lorentz invariance is one of the founding principles of
Modern Physics and violation of it would have profound implications to our
understanding of the universe. For instance, certain theories attempting a
unified theory of quantum gravity predict there could be an effective
refractive index of the vacuum; the introduction of an energy dependent
dispersion to photons could in turn lead to an observable Lorentz invariance
violation signature. Whilst a very small effect on local scales the effect will
be cumulative, and so for very high energy particles that travel very large
distances the difference in arrival times could become sufficiently large to be
detectable. This proceedings will look at testing for such Lorentz invariance
violation (LIV) signatures in the astronomical lightcurves of gamma-ray
emitting objects, with particular notice being given to the prospects for LIV
testing with, the next generation observatory, the Cherenkov Telescope Array.
