  That the laws of physics are the same at all times and places throughout the
Universe is one of the basic assumptions of physics. Astronomical observations
provide the only means to test this basic assumption on cosmological time and
distance scales. The possibility of variations in the dimensionless physical
constant {\mu} - the proton-to-electron mass ratio, can be tested by comparing
astronomical measurements of the rest frequency of certain spectral lines at
radio wavelengths with laboratory determinations. Different types of molecular
transitions have different dependencies on {\mu} and so observations of two or
more spectral lines towards the same astronomical source can be used to test
whether there is any evidence for either temporal or spatial changes in the
physical fundamental constants. {\mu} will change if the relative strength of
the strong nuclear force compared to the electromagnetic force varies.
Theoretical studies have shown that the rotational transitions of some
molecules which have transitions in the frequency range that will be covered by
FAST (e.g., CH3OH, OH and CH) are sensitive to changes in {\mu}. A number of
studies looking for possible variations in {\mu} have been undertaken with
existing telescopes, however, the greater sensitivity of FAST means it will
open new opportunities to significantly improve upon measurements made to date.
In this paper, we discuss which molecular transitions and sources (both in the
Galaxy and external galaxies) are likely targets for providing improved
constraints on {\mu} with FAST.
