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 Schrodinger equation in the non-relativistic limit and to the Dirac equation in the relativistic limit. The Ginsburg-Landau theory of superfluidity resulting from the Schrodinger 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, non-ferromagnetic 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.