  Quantum gravity (QG) theories over the past fifty years have sought to
understand the relationship between the four fundamental interactions. A major
insight gained in this area is that all interactions could possibly unify at
Planck-scale energies ~10$^{19}$ GeV. A potential consequence of the
unification of gravity with the other three interactions would be a breaking of
Lorentz symmetry at Planck-scale energies. The interpretation of Time-of-flight
(TOF) measurements from gamma-ray telescopes have been able to put constraints
on the energy scales of the Lorentz-invariance violations (LIV). The Crab
pulsar, the only pulsar detected at very high energies (VHE, E > 100 GeV)
presents a unique opportunity to put new constraints on LIV. Presented here are
the results of observations of the Crab pulsar with VERITAS and statistical
methods to determine limits of LIV effects from energy-dependent timing
differences.
