  We consider a theory with isotropic nonbirefringent Lorentz violation in the
photon sector and explore the effects on the development of the electromagnetic
component of extensive air showers in the Earth atmosphere. Specifically, we
consider the case of a "fast" photon with a phase velocity larger than the
maximum attainable velocity of a massive Dirac fermion (this case corresponds
to a negative Lorentz-violating parameter $\kappa$ in the action). Shower
photons with above-threshold energies decay promptly into electron-positron
pairs, instead of decaying by the conventional production of electron-positron
pairs in the background fields of atomic nuclei. This rapid production of
charged leptons accelerates the shower development, decreasing the atmospheric
depth of the shower maximum ($X_\text{max}$) by an amount which could be
measured by cosmic-ray observatories. Precise measurements of $X_\text{max}$
could then improve existing limits on the negative Lorentz-violating parameter
$\kappa$ by several orders of magnitude.
