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

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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 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 \(t\).

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Notes

  1. see also the works by E.C.G. Stueckelberg [4, 5].

  2. “… why all electrons have the same charge and mass?” – “Because they are all the same electron!” [9].

  3. It results after elimination of the other two components \(y,z\) from (1).

  4. It follows from (2) that for any pair of complex conjugate roots the mass of the corresponding C-particle should be twice as large as for R-particles.

  5. A manifestly Lorentz-invariant form of the conservation laws can be presented, see, e.g., [8].

  6. We may ignore, in the incidence relation (9), the frequently used factor \(i\).

  7. A worldline located on \(\mathbb{C}\mathbf{M}\), a complex generalization of \(\mathbf{M}\), generates an NSFC with nonzero torsion, a familiar example of which being represented by the Kerr congruence.

  8. Remarkably, in the previous papers [6, 8] we considered the UW construction based on (1) as a nonrelativistic one, with \(t\) playing the role of absolute Newtonian time.

  9. In the procedure, the ratio of spinor components \(G\) transforms according to a linear-fractional law.

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Funding

V.K. acknowledges support from Project no. FSSF-2023-0003.

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Authors and Affiliations

  1. Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, 117198, Moscow, Russia

    V. V. Kassandrov

  2. Scientific and Technological Center of Unique Instrumentation of Russian Academy of Sciences, 117342, Moscow, Russia

    Ildus Sh. Khasanov

Authors
  1. V. V. Kassandrov
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  2. Ildus Sh. Khasanov
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Correspondence to V. V. Kassandrov or Ildus Sh. Khasanov.

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Kassandrov, V.V., Khasanov, I.S. Algebrodynamics: Super-Conservative Collective Dynamics on a “Unique Worldline” and the Hubble Law. Gravit. Cosmol. 29, 50–56 (2023). https://doi.org/10.1134/S0202289323010048

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