Quaternion Algebra on 4D Superfluid Quantum Space-Time: Can Dark Matter Be a Manifestation of the Superfluid Ether?

Abstract

Quaternions are a natural framework of 4D space-time, where the unit element relates to time, and three others relate to 3D space. We define a quaternion set of differential torsion operators (shifts with rotations) that act to the energy-momentum tensor written on the same quaternion basis. It results in the equations of gravity-torsion (gravitomagnetic) fields that are similar to Maxwell’s equations. These equations are parent equations, generating the following equations: (a) equations of the transverse gravity-torsion waves; (b) the vorticity equation describing vortices orbital speed of which grows monotonically in the vortex core but far from it, it goes to a permanent level; (c) the modified Navier–Stokes equation leading to the Schrödinger equation in the nonrelativistic limit and to the Dirac equation in the relativistic limit. The Ginsburg–Landau theory of superfluidity resulting from the Schrödinger equation shows the emergence of coupled proton-antiproton pairs forming the Bose–Einstein condensate. In the final part of the article, we describe Samokhvalov’s experiment with rotating nonelectric, nonferromagnetic massive disks in a vacuum. It demonstrates an unknown force transferring the rotational moment from the driving disk to a driven one. It can be a manifestation of the dark matter. For studying this phenomenon, we propose a neutron interference experiment that is like the Aharonov–Bohm one.

Matter Waves in the Talbot-Lau Interferometry

“…( 14), λdB is de Broglie wavelength of the particle passing through the slit grating, and d is the slit spacing. Calculations of the interference patter gives perfect results [37]. Fig.…”

“…As soon as all reductions have been done, we obtain the wave function in the paraxial approximation, i.e., the source remote onto innity. It has the following view (37) Here a factor A ∞ replaces Since at T → ∞ the quadratic root tends to zero, then A ∞ t ends to zero as well. We will ignore this fact, and suppose let A ∞ be some innitesimal constant.…”

Untitled

“…Their energy consists partly of EM and partly of the energy of their excitations of the hexagonal lattice. Equations disclosing such a binding EM wave with optical phonons generated by thermal fluctuations of the matter lattice stem easily from the gravitomagnetic equations [76,77]:…”

“…The first equations resulting from the gravitomagnetic ones are the wave equations loaded by internal and external sources of acoustic and EM oscillations [77] as follows from (3):…”

Mass Gap Problem Solution in the Superfluid Quantum Space Model

“…is an ordered n-uple of real numbers ((xi, yi)∈ℝ n ); for the purpose of this paper, we consider its subset ℂ 4 where all elementary particles are different structures of ℂ 4-SQS and have four complex dimensions zi " [2]. The model of the superfluid quantum space is close to the model of 4D superfluid quantum space-time, also named "superfluid ether" which uses quaternions as its mathematical background [3].…”