  We discuss the potential of neutrinoless double beta decay for testing
Lorentz invariance and the weak equivalence principle as well as contributions
from dilaton exchange gravity in the neutrino sector. While neutrino
oscillation bounds constrain the region of large mixing of the weak and
gravitational eigenstates, we obtain new constraints on violations of Lorentz
invariance and the equivalence principle from neutrinoless double beta decay,
applying even in the case of no mixing. Double beta decay thus probes a totally
unconstrained region in the parameter space.
