  Consider a worldline of a pointlike particle parametrized by polynomial
functions, together with the light cone ("retardation") equation of an
inertially moving observer. Then a set of apparent copies, R- or C-particles,
defined by the (real or complex conjugate) roots of the retardation equation
will be detected by the observer. We prove that for any "polynomial" worldline
the induced collective dynamics of the system of R-C particles obeys a whole
set of canonical conservation laws (for total momentum, angular momentum and
the analogue of mechanical energy). Explicit formulas for the values of total
angular momentum and the analogue of total rest energy (rest mass) are
obtained; the latter is "self-quantized", i.e. for any worldline takes only
integer values. The dynamics is Lorentz invariant though different from the
canonical relativistic mechanics. Asymptotically, at large values of the
observer's proper time, the R-C particles gather themselves into pairs and then
assemble into compact incoming/outgoing clusters. As a whole, the evolution
resembles the process of (either elastic or inelastic) scattering of a beam of
composite particles. Throughout the paper the consideration is purely
algebraic, with no resort to differential equations of motion, field equations,
etc.
