  M dwarfs are prime targets in the hunt for habitable worlds around other
stars. This is due to their abundance as well as their small radii and low
masses and temperatures, which facilitate the detection of temperate, rocky
planets in orbit around them. However, the fundamental properties of M dwarfs
are difficult to constrain, often limiting our ability to characterise the
planets they host. Here we test several theoretical relationships for M dwarfs
by measuring 23 high precision, model-independent masses and radii for M dwarfs
in binaries with white dwarfs. We find a large scatter in the radii of these
low-mass stars, with 25 per cent having radii consistent with theoretical
models while the rest are up to 12 per cent over-inflated. This scatter is seen
in both partially- and fully-convective M dwarfs. No clear trend is seen
between the over-inflation and age or metallicity, but there are indications
that the radii of slowly rotating M dwarfs are more consistent with
predictions, albeit with a similar amount of scatter in the measurements
compared to more rapidly rotating M dwarfs. The sample of M dwarfs in close
binaries with white dwarfs appears indistinguishable from other M dwarf
samples, implying that common envelope evolution has a negligible impact on
their structure. We conclude that theoretical and empirical mass-radius
relationships lack the precision and accuracy required to measure the
fundamental parameters of M dwarfs well enough to determine the internal
structure and bulk composition of the planets they host.
