Prospects for Large Relativity Violations in Matter-Gravity Couplings

Deviations from relativity are tightly constrained by numerous experiments. A class of unmeasured and potentially large violations is presented that can be tested in the laboratory only via weak-gravity couplings. Specialized highly sensitive experiments could achieve measurements of the corresponding effects. A single constraint of $1\times {10}^{-11}\mathrm{GeV}$ is extracted on one combination of the 12 possible effects in ordinary matter. Estimates are provided for attainable sensitivities in existing and future experiments.