scholarly journals Geometry and general relativity in the groupoid model with a finite structure group

2015 ◽  
Vol 93 (1) ◽  
pp. 43-54 ◽  
Author(s):  
Michael Heller ◽  
Tomasz Miller ◽  
Leszek Pysiak ◽  
Wiesław Sasin
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Lorentz Group ◽  
Space Time ◽  
Einstein Equations ◽  
Diagonal Form ◽  
Frame Bundle ◽  
Relativistic Limit ◽  
Theor Phys ◽  
A Finite Group

In a series of papers (M. Heller et al. J. Math. Phys. 38, 5840 (1997). doi:10.1063/1.532186 ; M. Heller and W. Sasin. Int. J. Theor. Phys. 38, 1619 (1999). doi:10.1023/A:1026617913754 ; M. Heller et al. Int. J. Theor. Phys. 44, 619 (2005). doi:10.1007/s10773-005-3992-7 ) we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra, [Formula: see text], defined on a transformation groupoid Γ determined by the action of the Lorentz group on the frame bundle (E, πM, M) over space–time M. In the present work, we construct a simplified version of the gravitational sector of this model in which the Lorentz group is replaced by a finite group, G, and the frame bundle is trivial E = M × G. The model is fully computable. We define the Einstein–Hilbert action, with the help of which we derive the generalized vacuum Einstein equations. When the equations are projected to space–time (giving the “general relativistic limit”), the extra terms that appear due to our generalization can be interpreted as “matter terms”, as in Kaluza–Klein-type models. To illustrate this effect we further simplify the metric matrix to a block diagonal form, compute for it the generalized Einstein equations and find two of their “Friedman-like” solutions for the special case when G = [Formula: see text]. One of them gives the flat Minkowski space–time (which, however, is not static), another, a hyperbolic, linearly expanding universe.

scholarly journals Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

GENERALIZED BELINSKY–RUFFINI GEOMETRY

1991 ◽  
Vol 06 (24) ◽  
pp. 2189-2195
Author(s):  
AMIR LEVINSON ◽  
AHARON DAVIDSON
Keyword(s):  
Electric Charge ◽  
Magnetic Moment ◽  
Extra Dimension ◽  
Space Time ◽  
Einstein Equations ◽  
Axially Symmetric ◽  
Relativistic Limit ◽  
Kaluza Klein

Stationary, axially symmetric solutions of Einstein equations in a free 5-dimensional Kaluza–Klein space-time are derived. The electric charge and magnetic moment are generated by a fictitious boost involving the extra dimension. The associated gyromagnetic factor tends to unity at the ultra-relativistic limit. The solution derived interpolates between the Kerr and the Belinsky–Ruffini solutions.

scholarly journals Theory of Discrete Gravity

2018 ◽  
Author(s):  
Mihir Kumar Jha
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Loop Quantum Gravity ◽  
Riemannian Metric ◽  
Space Time ◽  
Final Theory ◽  
Theory Of Everything ◽  
Single Field ◽  
Fundamental Forces ◽  
New Framework

Theory of everything (T.O.E), final theory or ultimate theory is a theoretical framework in the field of physics, which holds an ultimate key to unify all the fundamental forces of nature in a single field. In other words such theory can glue quantum mechanics with general relativity into a single framework. Many theories have been postulated over the decades but the dominant one includes string theory and loop quantum gravity. In this paper I would like to present a new framework which can unify quantum mechanics with general relativity by showing that the change in Riemannian metric or the bend in space time is always an integral multiple of planks constant and since gravity is the result due to bend in space-time, gravity itself is a discrete force

scholarly journals Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces

2018 ◽  
Author(s):  
Jae-Kwang Hwang
Keyword(s):  
General Relativity ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Energy Transition ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Dimensional Space Time

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=tq). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

scholarly journals LORENTZ GAUGE THEORY AND SPINOR INTERACTION

2008 ◽  
Vol 23 (08) ◽  
pp. 1282-1285 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Lorentz Group ◽  
Flat Space ◽  
Stationary Solutions ◽  
Space Time ◽  
Pauli Equation ◽  
Relativistic Limit ◽  
Curved Space

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.

scholarly journals Unitary representations of the Lorentz group

1945 ◽  
Vol 183 (994) ◽  
pp. 284-295 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quadratic Form ◽  
Lorentz Group ◽  
Positive Definite ◽  
Space Time ◽  
Unitary Representations ◽  
Positive Definite Quadratic Form ◽  
Number Of Components

Certain quantities are introduced which are like tensors in space-time with an infinite enumerable number of components and with an invariant positive definite quadratic form for their squared length. Some of the main properties of these quantities are dealt with, and some applications to quantum mechanics are pointed out

scholarly journals Multiversal SpaceTime (MSpaceTime) Not Neural Network as Source of Intelligence in Generalized Quantum Mechanics, Extended General Relativity, Darwin Dynamics for Artificial Super Intelligence Synthesis

2019 ◽  
Author(s):  
Yang Zhang
Keyword(s):  
Neural Network ◽  
Hilbert Space ◽  
General Relativity ◽  
Quantum Mechanics ◽  
Riemannian Manifold ◽  
Conformal Geometry ◽  
Logic Synthesis ◽  
Einstein Equations ◽  
Biological Synthesis ◽  
Agent Intelligence

AbstractFrom Synthesis perspective, whether Logic Synthesis, Physical Synthesis, Chemical Synthesis, or Biological Synthesis, Physical Geometry such as Universal Geometry and Quantum Geometry, and Biological Geometry like Conformal Geometry supported by Tensors and Manifolds, are the outcome of physical laws and biological laws in modeling non-linear physical and biological dynamics as opposed to traditional partial differential/difference equation way. We discover that Multiversal SpaceTime instead of Neural Network, governing physical and biological world at macroscopic and microscopic level, is the ultimate source of intelligence. With that we propose Multiversal Synthesis-based Artificial Design Automation (ADA), a bio-physical inspired model based on Multiverse in Darwin Dynamics, Generalized Quantum Mechanics, and Extended General Relativity, for Artificial Super Intelligence (ASI) implementation. Based on Schrodinger Equation of Quantum Mechanics, we generalize the 4-Dimensional Hilbert Space based Discrete Quantum SpaceTime to N-Dimensional (1 ≪ N < M, with M is limited by Planck Length) Hilbert Space based Discrete MSpaceTime as part of MSpaceTime, in modeling both Micro-Environment Intelligence and Micro-Agent Intelligence of ASI; likewise based on Einstein Equations of General Relativity, we make a T-Symmetry extension first, and then extend the 4-Dimensional Pseudo-Riemannian Manifold based Continuous Curved SpaceTime as part of MSpaceTime to N-Dimensional (1 ≪ N < ∞) Pseudo-Riemannian Manifold based Continuous MSpaceTime extension, in modeling both Macro-Environment Intelligence and Macro-Agent Intelligence of ASI. Our discovery only solves the black box puzzle of AI, but also paves the way in achieving ASI through ADA. Of course, our Multiverse Endeavor will never stop from there.

Non-radial oscillations of stars in general relativity: a scattering problem

1992 ◽  
Vol 340 (1658) ◽  
pp. 423-445 ◽  
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Waves ◽  
Potential Barrier ◽  
Scattering Problem ◽  
Relativistic Effects ◽  
Resonant Scattering ◽  
Space Time ◽  
Rotating Stars

The problem of non-radial oscillations of stars can be formulated as a problem of resonant scattering of gravitational waves incident on the potential barrier generated by the space-time curvature. This approach discloses some unexpected correspondences between the theory of perturbations of stars and the theory of quantum mechanics. New relativistic effects are predicted, as the resonant behaviour of the axial modes in slowly rotating stars, due to the coupling with the polar modes induced by the Lense-Thirring effect.

LIMIT TO SPACE-TIME MEASUREMENT

1994 ◽  
Vol 09 (04) ◽  
pp. 335-340 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Time Measurement ◽  
Space Time ◽  
Quantum Measurements ◽  
Quantum Decoherence ◽  
Planck Mass ◽  
The One

Applying simultaneously the principles of quantum mechanics and general relativity we find an intrinsic limitation to quantum measurements of space-time distances. The intrinsic uncertainty of a length is shown to be proportional to the one third power of the length itself. This uncertainty in space-time measurements implies an intrinsic uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass.

Singularities in general relativity

1970 ◽  
Vol 48 (8) ◽  
pp. 970-980 ◽  
Author(s):  
J. Pachner
Keyword(s):  
High Pressure ◽  
General Relativity ◽  
Angular Velocity ◽  
Mass Density ◽  
Rest Mass ◽  
First Integrals ◽  
Einstein Equations ◽  
Rotating Fluid ◽  
Relativistic Limit ◽  
Local Observer

The problem of singularities is examined from the standpoint of a local observer. A singularity is defined as a state with an infinite proper rest mass density. It is proved that any inhomogeneity and anisotropy in the distribution and motion of a nonrotating ideal fluid accelerates collapse. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In order to investigate the influence of rotation on the existence of singularities in incoherent matter the Einstein equations together with their first integrals are written out for the points on a vortex filament. They show that rotation decelerates the contraction of space not only in the direction perpendicular to the vector of the angular velocity, but indirectly also along this vector and can prevent the occurrence of a singularity. This conclusion is confirmed by the numerical integration of the Einstein equations. The paper concludes with a discussion of some cosmological implications.

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