Version 1
: Received: 25 November 2023 / Approved: 27 November 2023 / Online: 27 November 2023 (07:48:01 CET)
How to cite:
Sbitnev, V. Quaternion Algebra on 4D Spacetime: The Lorentz Gauge Is a Door to the Invisible World of Dark Matter and Dark Energy. Preprints2023, 2023111673. https://doi.org/10.20944/preprints202311.1673.v1
Sbitnev, V. Quaternion Algebra on 4D Spacetime: The Lorentz Gauge Is a Door to the Invisible World of Dark Matter and Dark Energy. Preprints 2023, 2023111673. https://doi.org/10.20944/preprints202311.1673.v1
Sbitnev, V. Quaternion Algebra on 4D Spacetime: The Lorentz Gauge Is a Door to the Invisible World of Dark Matter and Dark Energy. Preprints2023, 2023111673. https://doi.org/10.20944/preprints202311.1673.v1
APA Style
Sbitnev, V. (2023). Quaternion Algebra on 4D Spacetime: The Lorentz Gauge Is a Door to the Invisible World of Dark Matter and Dark Energy. Preprints. https://doi.org/10.20944/preprints202311.1673.v1
Chicago/Turabian Style
Sbitnev, V. 2023 "Quaternion Algebra on 4D Spacetime: The Lorentz Gauge Is a Door to the Invisible World of Dark Matter and Dark Energy" Preprints. https://doi.org/10.20944/preprints202311.1673.v1
Abstract
Quaternion algebra is used both for the description of the motion of material objects in 4D space-time and for the representation of the energy-momentum density tensor in the same quaternion basis, accurate to some arbitrary scalar fields. Quaternionic generating operators applied repeatedly to the energy-momentum density tensor lead to the gravitomagnetic equations that are parent equations for the series of physical equations ranging from the wave equations up to the quantum mechanical ones. Before finally deducing the gravitomagnetic equations, it is necessary to use the Lorentz gauge at a certain stage to cut off the arbitrary scalar fields. We declare that these superfluous scalar fields, inaccessible to direct observation, represent dark matter and dark energy. We show in what way the dark matter can provide a flat profile of the orbital speed of the galaxy's arm rotations.
Keywords
Navier-Stokes equation; vorticity equation; toroidal vortex; irrotational velocity; solenoidal velocity; spiral galaxies; dark matter; dark energy
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
