  Many quantum theories of gravity propose Lorentz violating dispersion
relations of the form $\omega = |k|\, f(|k|/M)$, with recovery of approximate
Lorentz invariance at energy scales much below $M$. We show that a quantum
field with this dispersion predicts drastic low energy Lorentz violation in
atoms modelled as Unruh-DeWitt detectors, for any $f$ that dips below unity
somewhere. As an example, we show that polymer quantization motivated by loop
quantum gravity predicts such Lorentz violation below current ion collider
rapidities.
