arXiv subjects

Ildus Sh. Khasanov

Publications and source records attributed to Ildus Sh. Khasanov.

3 recordsLinked to original sources

arXiv2023

The algebrodynamics: super-conservative collective dynamics on a "Unique Worldline'' and the Hubble's 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 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 $t$.

gr-qc↗

arXiv2015

Collective Lorentz invariant dynamics on a single "polynomial" worldline

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.

physics.gen-ph↗

arXiv2013

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

In the development of the old ideas of Stueckelberg-Wheeler-Feynman on the "one-electron Universe", we study the purely algebraic dynamics of the ensemble of(two kinds of) identical point-like particles. These are represented by the(real and complex conjugate) roots of a generic polynomial system of equations that implicitly defines a single "worldline". The dynamics includes events of "merging" of a pair of particles modelling the annihilation/creation processes. Correlations in the location and motion of the particles-roots relate, in particular, to the Vieta formulas. After a special choice of the inertial-like reference frame, the linear Vieta formulas guarantee that, for any worldline, the law of (non-relativistic) momentum conservation is identically satisfied. Thus, the general structure of Newtonian mechanics follows from the algebraic properties of a worldline alone. Some considerations on relativization of the scheme are presented. A simple example of, unexpectedly rich, "polynomial dynamics" is retraced in detail and illustrated via an animation(available from ancillary file enclosed)

physics.gen-ph↗