  Weyl fermions are massless chiral particles first predicted in 1929 and once
thought to describe neutrinos. Although never observed as elementary particles,
quasiparticles with Weyl dispersion have recently been experimentally
discovered in solid-state systems causing a furore in the research community.
Systems with Weyl excitations can display a plethora of fascinating phenomena
and offer great potential for improved quantum technologies. Here we show that
Weyl excitations generically exist in three-dimensional systems of dipolar
particles with weakly broken time-reversal symmetry (for example, by a magnetic
field). They emerge as a result of dipolar-interaction-induced transfer of
angular momentum between the $J=0$ and $J=1$ internal particle levels. We also
discuss momentum-resolved Ramsey spectroscopy methods for observing Weyl
quasiparticles in cold alkaline-earth-atom systems. Our results provide a
pathway for a feasible experimental realisation of Weyl quasiparticles and
related phenomena in clean and controllable atomic systems.
