  There has been much interest in possible violations of Lorentz invariance,
particularly motivated by quantum gravity theories. It has been suggested that
a small amount of Lorentz invariance violation (LIV) could turn off photomeson
interactions of ultrahigh energy cosmic rays (UHECRs) with photons of the
cosmic background radiation and thereby eliminate the resulting sharp
steepening in the spectrum of the highest energy CRs predicted by Greisen
Zatsepin and Kuzmin (GZK). Recent measurements of the UHECR spectrum reported
by the HiRes and Auger collaborations, however, indicate the presence of the
GZK effect. We present the results of a detailed calculation of the
modification of the UHECR spectrum caused by LIV using the formalism of Coleman
and Glashow. We then compare these results with the experimental UHECR data
from Auger and HiRes. Based on these data, we find a best fit amount of LIV of
$4.5^{+1.5}_{-4.5} \times 10^{-23}$,consistent with an upper limit of $6 \times
10^{-23}$. This possible amount of LIV can lead to a recovery of the cosmic ray
spectrum at higher energies than presently observed. Such an LIV recovery
effect can be tested observationally using future detectors.
