The algebrodynamics: super-conservative collective dynamics on a "Unique Worldline'' and the Hubble's law

TL;DR

This paper explores algebraic collective dynamics on a unique worldline, revealing conservation laws, Lorentz invariance, and a universe expansion model consistent with Hubble's law, derived from polynomial roots representing particles.

Contribution

It introduces a novel algebraic framework for particle dynamics on a worldline, uncovering conservation laws and a universe expansion model aligned with Hubble's law.

Findings

Conservation laws include higher derivatives and multi-particle correlations.

Dynamics are Lorentz invariant and nontrivial.

Recession of roots-particles follows Hubble's law with inverse proportionality to time.

Abstract

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 old Wheeler-Feynman's conception. As a consequence of the Vieta's formulas, a great number of conservation laws is fulfilled for collective algebraic dynamics on the UW. These, besides the canonical ones, include the laws with higher derivatives and those containing multi-particle correlation terms as well. On the other hand, such a ``super-conservative'' dynamics turns to be manifestly Lorentz invariant and quite nontrivial. At great values of ``cosmic time'' $t$ roots-particles demonstrate universal recession (resembling that in the Milne's cosmology and simulating ``expansion'' of the Universe) for which the Hubble's law does hold true, with Hubble parameter being inversely proportional to $t$.