  The intersections of topology, geometry and strong correlations offer many
opportunities for exotic quantum phases to emerge in condensed matter systems.
Weyl fermions, in particular, provide an ideal platform for exploring the
dynamical instabilities of single-particle physics under interactions. Despite
its fundamental role in relativistic field theory, the concept of causality and
the associated spacetime light cone and event horizon has not been considered
in connection with interacting Weyl fermionic excitations in quantum matter.
Here, by using charge-density wave (CDW) as an example, we unveil the behavior
of interacting Weyl fermions and show that a Weyl fermion in a system can open
a band gap by interacting only with other Weyl fermions that lie within its
energy-momentum dispersion cone. In this sense, causal connections or
interactions are only possible within overlapping dispersion cones and each
dispersion cone thus constitutes a solid-state analogue of the more
conventional `event horizon' of high-energy physics. Our study provides a
universal framework for considering interacting relativistic quasiparticles in
condensed matter by separating them into energy-like and momentum-like
relationships in analogy with the time-like and space-like events in
high-energy physics. Finally, we consider two different candidate materials for
hosting the Weyl CDW phase: (TaSe$_4$)$_2$I and Mo$_3$Al$_2$C. Our study
greatly enriches the phenomenology and unveils new connections between
condensed matter and high-energy physics.
