Torsion Of Space Research Articles

FREE CURVILINEAR SPACE WITH TORSION

Under the classical field theory, a variant unification of gravity and electromagnetism on the basis of four-dimensional curved space with torsion is proposed. The connection between electromagnetic field and torsion of space is discovered, a physical interpretation of the space scalar curvature as the density of matter mass is proposed. The solution for the eigenstate of a curved space with torsion, corresponding to the electron is obtained. The identification of the field equations as the Schrodinger equation for the hydrogen atom is shown. Cosmological solutions for the expanding Universe are found, the average mass density in the Universe is estimated, and the results corresponding to the data of astronomical observations are obtained.

Geometrical interpretation of the pilot wave theory and manifestation of spinor fields

Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.

Einstein-Maxwell Theory without Symmetry and Examples of Geodesics in Space with Torsion

The propagation of light and electromagnetic-gravity field in Y n space is studied. Our aims are to obtain the equations that described gravitational field in vacuum from the principle of least action in Y n space, and derive the law of motion of free point particles in Y n ; we showed that free point particles move along geodesics of space. The geodesic in Y n are depended on metric and torsion and this situation are considered in several non-trivial examples of the geodesics in the three-dimensional space without gravitational force; as result, we obtained that even in space without gravity geodesics are depending on torsion of space.

Retraction: Einstein–Maxwell theory without symmetry and examples of geodesics in space with torsion

The propagation of light and electromagnetic-gravity field in Y n space is studied. Our aims are to obtain the equations that described gravitational field in vacuum from the principle of least action in Y n space, and derive the law of motion of free point particles in Y n ; we showed that free point particles move along geodesics of space. The geodesic in Y n are depended on metric and torsion and this situation are considered in several non-trivial examples of the geodesics in the three-dimensional space without gravitational force; as result, we obtained that even in space without gravity geodesics are depending on torsion of space.

An exact spherically symmetric space–time in Einstein–Cartan theory

By adopting the Newman–Penrose–Jogia–Griffith formalism, the field equations in Einstein–Cartan theory for matter with spin creating torsion in space–time are solved in a spherically symmetric space–time by assuming only one non-vanishing component of spin. The exact solution might be the prototype for more realistic models.

Torsion and electron motion in quantum dots with crystal lattice dislocations

The motion of a conducting electron in a quantum dot, with one or several dislocations in the underlying crystal lattice, is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of torsion are investigated on the levels of classical motion, on non-relativistic quantum motion, and on spin-torsion coupling terms derivable in the non-relativistic limit of generalizations of the Dirac equation in a space with torsion. Finally, phenomenological spin-torsion couplings analogous to Pauli terms are considered in the non-relativistic equations. Different prescriptions of classical and non-relativistic quantum motion in a space with torsion are shown to give effects that should, in principle, be observable. Semiclassical arguments are presented to show that torsion is not relevant for the classical motion of the centre of a wavepacket. The correct semiclassical limit can instead be described as classical trajectories in a Hamiltonian given by the band energy. In the special case of a spherically symmetric band this motion reduces to straight lines, independently of local crystal orientations. By dimensional analysis the coupling constants of the possible spin-torsion interactions are postulated to be proportional to a combination of the effective mass of the electron, , the lattice constant, a, and . The level splitting is then very small with transition frequencies of the order of 1 kHz, or smaller.

The Effect of Space Missions on Gravity-Responsive Torsional Eye Movements

Three astronauts underwent preflight, inflight, and postflight testing of spontaneous ocular torsion and of ocular counterrolling (OCR), reflexes governed by the gravity-responsive otolith organs in the inner ear. One astronaut, A, had a 30-day space mission on Euromir '94 and was examined monocularly with SensoMotoric Instruments video-oculography (VOG). The other two astronauts, B and C, were studied with a binocular VOG and flew an 180-day mission on Euromir '95. In space, spontaneous eye torsion in the upright position was found to be substantially offset from baseline Earth-based recordings in all three subjects for the duration of the flights. In addition, the binocular studies showed a marked torsional disconjugacy. On return to Earth, offset and torsional disconjugacy persisted for many days. OCR in response to 30 degrees right and left tilt was examined preflight and postflight. Compared to preflight, Astronaut A showed reduced OCR immediately postflight, which increased over the next few days. Both Astronauts B and C had increased OCR postflight, which gradually approached but did not achieve the preflight values over 13 days postflight. The adaptation of ocular torsion in space in one astronaut and not in the other two, and slow adaptation postflight, may reflect the lack of visual feed-back and the open loop nature of the otolith-ocular torsion reflex.

A new exact solution of classical supergravity

A new exact plane-wave type solution of classical supergravity is presented. It depends on two arbitrary, complex anti-commuting functions G( U) and H( U, X + i Y). The vector part of the gravitino field is directed along the propagation vector of the wave. The space torsion and the energy-momentum tensor of the gravitino field are both zero.

Spacetime of the Elementary Particles

The possibility is examined that physical space is characterized by a torsion, or an asymmetric connection, which is determined by the matter field. There exists a space with uniform torsion with the same metrical properties as conventional microspace; it is isotropic and homogeneous with a very large radius of curvature (R≅1028 cm). The momentum operators form a group and for practical purposes commute. The torsion defines at every point two kinds of parallel transfer or two screw motions of opposite helicity. There are, consequently, two kinds of spinor field associated with the space; they are distinguished by opposite coupling to the torsion. Viewed from within the Lorentz group the torsion produces an axial vector interaction. To interpret the given mathematical model, it is suggested that there exists a universal axial vector coupling between fermions represented by the spinor fields and bosons associated with the torsion; and that this interaction manifests itself macroscopically as a torsion of space, in the same general way that gravitational interactions correspond to a curvature of space. This general assumption leads to cosmological models characterized by relations connecting the average density of matter and the strength of the assumed interaction. For the observed average density of matter in the known universe (∼10−30 g/cm3) the proposed axial vector coupling turns out, for a space of uniform torsion, to be of the order of the strong interactions.