Algebrodynamics: Super-Conservative Collective Dynamics on a “Unique Worldline” and the Hubble Law

We study the properties of roots of a polynomial system of equations which define a set of identical point particles located on a Unique Worldline (UW), in the spirit of the Wheeler–Feynman’s old conception. As a consequence of Vieta’s formulas, a great number of conservation laws are fulfilled for collective algebraic dynamics on the UW. These, besides the canonical ones, include the laws with higher derivatives and those containing multiparticle correlation terms as well. On the other hand, such a “super-conservative” dynamics turns out to be manifestly Lorentz invariant and quite nontrivial. At great values of “cosmic time” \(t\), the roots-particles demonstrate universal recession (resembling that in the Milne’s cosmology and simulating “expansion” of the Universe), for which the Hubble’s law holds true, with the Hubble parameter inversely proportional to \(t\).