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In the development of the old ideas of Stueckelberg-Wheeler-Feynman on the"one-electron Universe", we study the purely algebraic dynamics of the ensembleof(two kinds of) identical point-like particles. These are represented bythe(real and complex conjugate) roots of a generic polynomial system ofequations that implicitly defines a single "worldline". The dynamics includesevents of "merging" of a pair of particles modelling the annihilation/creationprocesses. Correlations in the location and motion of the particles-rootsrelate, in particular, to the Vieta formulas. After a special choice of theinertial-like reference frame, the linear Vieta formulas guarantee that, forany worldline, the law of (non-relativistic) momentum conservation isidentically satisfied. Thus, the general structure of Newtonian mechanicsfollows from the algebraic properties of a worldline alone. Some considerationson relativization of the scheme are presented. A simple example of,unexpectedly rich, "polynomial dynamics" is retraced in detail and illustratedvia an animation(available from ancillary file enclosed)

Algebraic roots of Newtonian mechanics: correlated dynamics of particles on a unique worldline