  We discuss the feasibility of using astrophysical observations of white
dwarfs as probes of fundamental physics. We quantify the effects of varying
fundamental couplings on the white dwarf mass-radius relation in a broad class
of unification scenarios, both for the simple case of a polytropic stellar
structure model and for more general models. Independent measurements of the
mass and radius, together with direct spectroscopic measurements of the
fine-structure constant in white dwarf atmospheres lead to constraints on
combinations of the two phenomenological parameters describing the underlying
unification scenario (one of which is related to the strong sector of the
theory while the other is related to the electroweak sector). While currently
available measurements do not yet provide stringent constraints, we show that
forthcoming improvements, expected for example from the Gaia satellite, can
break parameter degeneracies and lead to constraints that ideally complement
those obtained from local laboratory tests using atomic clocks.
