Gravitation theory in a fractal space-time

2006 ◽  
Vol 47 (5) ◽  
pp. 053503 ◽  
Author(s):  
M. Agop ◽  
I. Gottlieb
Keyword(s):  
Space Time ◽  
Gravitation Theory ◽  
Fractal Space

FRACTALS AND THE QUANTUM THEORY OF SPACETIME

1989 ◽  
Vol 04 (19) ◽  
pp. 5047-5117 ◽  
Author(s):  
LAURENT NOTTALE
Keyword(s):  
Fractal Dimension ◽  
Heavy Ion ◽  
Space Time ◽  
Curvilinear Coordinates ◽  
Fractal Structures ◽  
Ion Collisions ◽  
Principle Of Relativity ◽  
First Results ◽  
Fractal Space ◽  
Dimension 2

We review in this paper the first results obtained in an attempt at understanding quantum space-time based on a new extension of the principle of relativity and on the geometrical concept of fractals. We present methods for dealing with the nondifferentiability and the infinities of fractals, as a first step towards the definition and intrinsic description of a fractal space. After having recalled that the Heisenberg relations imply a transition of spatial coordinates of a particle to fractal dimension 2 about the de Broglie length λ = ħ/p, it is suggested that a similar transition occurs for temporal coordinates about the de Broglie time τ = ħ/E. We then investigate the hypothesis that the microstructure of space-time is of fractal nature, and that the observed properties of the quantum world at a given resolution result from the smoothing of curvilinear coordinates of such a spacetime projected into classical spacetime. Along this road, we successively study the link of fractal dimension 2 to spin, we give first hints on the expected behavior of families of fractal geodesics, and we exhibit a general class of fractal structures which is assumed to yield a lowest order description of the quantum vacuum. The links between the new approach and both special and general relativity are touched upon. We finally suggest that the anomalous peaks recently observed in the spectra of positrons from supercritical heavy ion collisions may be understood in this context.

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

THE MICROSCOPIC-MACROSCOPIC SCALE TRANSFORMATION THROUGH A CHAOS SCENARIO IN THE FRACTAL SPACE-TIME THEORY

2011 ◽  
Vol 21 (02) ◽  
pp. 603-618 ◽  
Author(s):  
G. V. MUNCELEANU ◽  
V.-P. PAUN ◽  
I. CASIAN-BOTEZ ◽  
M. AGOP
Keyword(s):  
Vacuum Polarization ◽  
Plasma Plume ◽  
Space Time ◽  
Time Dependent ◽  
Scale Transformation ◽  
Particle Movement ◽  
Specific Mechanism ◽  
Macroscopic Scale ◽  
Fractal Space ◽  
Time Theory

Considering that the particle movement takes place on fractal curves, the mathematical and physical aspects in fractal space-time theory are analyzed. In such context, the harmonic oscillator problem implies that the microscopic-macroscopic scale transition could be associated with an evolution scenario towards chaos. The splitting of the plasma plume, generated by laser ablation, into two patterns, has been successfully reproduced through a numerical simulation using the fractal hydrodynamic model. For the free time-dependent particle in a fractal space-time, the uniform movement is naturally obtained by a specific mechanism of vacuum polarization.

scholarly journals Some Physical Implications of the Gravitoelectromagnetic Field in Fractal Space - Time Theory

1998 ◽  
Vol 51 (1) ◽  
pp. 9 ◽  
Author(s):  
M. Agop ◽  
V. Griga ◽  
C. Gh. Buzea ◽  
N. Rezlescu ◽  
C. Buzea ◽  
...  
Keyword(s):  
Space Time ◽  
Cosmic Scale ◽  
Gravitomagnetic Field ◽  
Fractal Space ◽  
Binary Galaxy ◽  
The Universe ◽  
Time Theory

It is shown that in terms of the fractal space–time theory the gravitoelectric potential is responsible for the quantisation of the planetary and binary galaxy motions. On a cosmic scale a homogeneous gravitomagnetic field allows not only an ordering of the Universe, but a ‘global’ redshift quantisation of galaxies as well.

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