Neutrino velocity and the variability of fundamental constants

Neutrino speed experiments could be viewed not only as tests of Lorentz invariance but also as measurements of limiting propagation speed for all standard model species below certain depth where no direct metrological information is available. The latter option, hypothetically caused by some chameleon-type background, is tested by the neutrino speed experiments. We show that complementary constraints on the same class of models can be obtained with experiments testing clock universality in deep underground/underwater experiments. By considering the explicit QED model with particle-universal modification of propagation speed by a depth-dependent tensor background, we show that, in general, one should expect shifts of the clock frequencies and clock nonuniversality. Such effects can be larger than predicted by general relativity and can be tested by comparison of the narrow transitions in atomic clocks, which for a generic model could deliver a superior accuracy compared to the neutrino speed experiments.