  Context. It is possible to accurately measure the masses of the white dwarfs
(WDs) in the Hyades cluster using gravitational redshift, because the radial
velocity of the stars can be obtained independently of spectroscopy from
astrometry and the cluster has a low velocity dispersion. Aims. We aim to
obtain an accurate measurement of the Hyades WD masses by determining the
mass-to-radius ratio (M/R) from the observed gravitational redshift, and to
compare them with masses derived from other methods. Methods. We analyse
archive high-resolution UVES-VLT spectra of six WDs belonging to the Hyades to
measure their Doppler shift, from which M/R is determined after subtracting the
astrometric radial velocity. We estimate the radii using Gaia photometry as
well as literature data. Results. The M/R error associated to the gravitational
redshift measurement is about 5%. The radii estimates, evaluated with different
methods, are in very good agreement, though they can differ by up to 4%
depending on the quality of the data. The masses based on gravitational
redshift are systematically smaller than those derived from other methods, by a
minimum of $\sim 0.02$ up to 0.05 solar masses. While this difference is within
our measurement uncertainty, the fact that it is systematic indicates a likely
real discrepancy between the different methods. Conclusions. We show that the
M/R derived from gravitational redshift measurements is a powerful tool to
determine the masses of the Hyades WDs and could reveal interesting properties
of their atmospheres. The technique can be improved by using dedicated
spectrographs, and can be extended to other clusters, making it unique in its
ability to accurately and empirically determine the masses of WDs in open
clusters. At the same time we prove that gravitational redshift in WDs agrees
with the predictions of stellar evolution models to within a few percent.
