  Up until now, a consistent causal theory of point charged particles (for
example electrons) interacting with electromagnetic field is not known. The
well-known problem is that the standard Lorentz force alone (in the case of
point particles) does not lead to a theory in which momentum and energy are
conserved. The need of radiation reaction force (or self-force) thus arises.
The well known candidate for such force, the Lorentz-Abraham-Dirac reaction
force, gives non-causal particle behavior, i.e., the particle starts to move
before the arrival of external electromagnetic fields. Alternative, causal
proposals provide non-physical behavior of the particle -- the particle moves
with non-zero acceleration long after any external forces acted on it. Below,
we question the existence of a causal theory. We show that for certain
electromagnetic pulse of radiation and point particle being initially at rest,
there {\it does not exists} a causal particle trajectory, such that the
particle ends up moving with constant velocity (when no external
electromagnetic fields act on it for very long time). This shows that the
proper, causal electrodynamics of point particles does not exist.
