  In the standard model of particle physics, all fermions are fundamentally
massless and only acquire their effective bare mass when the Higgs field
condenses. Therefore, in a fundamental de Broglie-Bohm pilot-wave quantum field
theory (valid before and after the Higgs condensation), position beables should
be attributed to massless fermions. In our endeavour to build a pilot-wave
theory of massless fermions, which would be relevant for the study of quantum
non-equilibrium in the early universe, we are naturally led to Weyl spinors and
to particle trajectories which give meaning to the `zig-zag' picture of the
electron discussed recently by Penrose. We show that a positive-energy massive
Dirac electron of given helicity can be thought of as a superposition of
positive and negative energy Weyl particles of the same helicity and that a
single massive Dirac electron can in principle move luminally at all times.
This is however not true for the many body situation required by quantum field
theory and we conclude that a more natural theory arises from attributing
beable status to the positions of massless Dirac particles instead of to Weyl
particles.
