  Time evolution generically entangles a quantum state with environmental
degrees of freedom. The resulting increase in entropy changes the properties of
that quantum system leading to "aging". It is interesting to ask if this
familiar property also applies to simple, single particle quantum systems such
as the decay of a radioactive particle. We propose a test of such aging in an
ion clock setup where we probe for temporal changes to the energies of the
electronic state of an ion containing a radioactive nucleus. Such effects are
absent in standard quantum mechanics and this test is thus a potent null test
for violations of quantum mechanics. As a proof of principle, we show that
these effects exist in causal non-linear modifications of quantum mechanics.
