  Motivated by recent astrophysical observations of quasar absorption systems,
we formulate a simple theory where the electron to proton mass ratio $\mu
=m_{e}/m_{p}$ is allowed to vary in space-time. In such a minimal theory only
the electron mass varies, with $\alpha $ and $m_{p}$ kept constant. We find
that changes in $\mu $ will be driven by the electronic energy density after
the electron mass threshold is crossed. Particle production in this scenario is
negligible. The cosmological constraints imposed by recent astronomical
observations are very weak, due to the low mass density in electrons. Unlike in
similar theories for spacetime variation of the fine structure constant, the
observational constraints on variations in $\mu $ imposed by the weak
equivalence principle are much more stringent constraints than those from
quasar spectra. Any time-variation in the electron-proton mass ratio must be
less than one part in $10^{9}$since redshifts $z\approx 1.$This is more than
one thousand times smaller than current spectroscopic sensitivities can
achieve. Astronomically observable variations in the electron-proton must
therefore arise directly from effects induced by varying fine structure
'constant' or by processes associated with internal proton structure. We also
place a new upper bound of $2\times 10^{-8}$ on any large-scale spatial
variation of $\mu $ that is compatible with the isotropy of the microwave
background radiation.
