  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, could be tested in the next installment of the
neutrino speed experiments. We also show that 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
larger-than-GR shifts of the clock frequencies and clock non-universality. This
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.
