  Ultrahigh energy cosmic rays that produce giant extensive showers of charged
particles and photons when they interact in the Earth's atmosphere provide a
unique tool to search for new physics. Of particular interest is the
possibility of detecting a very small violation of Lorentz invariance such as
may be related to the structure of space-time near the Planck scale of $\sim
10^{-35}$m. We discuss here the possible signature of Lorentz invariance
violation on the spectrum of ultrahigh energy cosmic rays as compared with
present observations of giant air showers. We also discuss the possibilities of
using more sensitive detection techniques to improve searches for Lorentz
invariance violation in the future. Using the latest data from the Pierre Auger
Observatory, we derive a best fit to the LIV parameter of $3.0^{+1.5}_{-3.0}
\times 10^{-23}$, corresponding to an upper limit of $4.5 \times 10^{-23}$ at a
proton Lorentz factor of $\sim 2 \times 10^{11}$. This result has fundamental
implications for quantum gravity models.
