1) The document proposes a theory of statistical geometrodynamics derived from novel statistical postulates about fundamental constituents of spacetime called "geomets".
2) Key results include deriving the Einstein field equations as a first law of geometrodynamics, and relating the Ricci curvature tensor to the entropy of a holographic surface bounding spacetime via a second law.
3) A third law and zeroeth law of geometrodynamics are also proposed, relating the mean curvature of the holographic surface to bit saturation in the bulk and on the surface.
Equation of a particle in gravitational field of spherical bodyAlexander Decker
1. This academic article presents an analysis of the motion of particles in the gravitational field of a spherical body based on a new theory of classical mechanics proposed by the authors.
2. The authors derive equations of motion for particles in the equatorial plane of the spherical body that contain corrections for relativistic effects up to all orders of c-2, where c is the speed of light.
3. They show that their equation for radial motion, to first order in c-2, is identical to Einstein's equation from general relativity for planetary motion in the solar system, and correctly predicts the anomalous orbital precession observed astronomically.
This document discusses the incompatibility between classical mechanics and electromagnetism. It shows that under a Galilean transformation, the wave equation governing electromagnetic waves takes on a different form in different reference frames, violating Galilean invariance. This means that the laws of electromagnetism depend on the choice of reference frame. As such, classical mechanics and electromagnetism cannot be unified without modifications to account for this issue.
Quantization of the Orbital Motion of a Mass In The Presence Of Einstein’s Gr...IOSR Journals
This document presents a theoretical model to explain the quantized nature of planetary orbits around the sun based on Einstein's general theory of relativity. It derives expressions for the Lagrangian and Hamiltonian of a unit mass moving in the curved spacetime around a massive body. Using these, it writes a Schrodinger-like quantum equation that includes variation of the wavefunction with respect to a curve parameter representing spacetime curvature. The solutions reveal the quantized energy levels and orbits determined by quantum numbers. When applied to planetary orbits, the model estimates distances from the sun in good agreement with observed values.
The document discusses Einstein's field equations and Heisenberg's uncertainty principle. It begins by providing background on Einstein's field equations, which relate the geometry of spacetime to the distribution of mass and energy within it. It then discusses some key mathematical aspects of the field equations, including their nonlinear partial differential form. Finally, it notes that the field equations can be consolidated with Heisenberg's uncertainty principle to provide a unified description of gravity and quantum mechanics.
1) The document summarizes the 100-year history of gravitational wave detection, from Einstein's theory of general relativity predicting their existence to the recent direct detection by the LIGO experiment.
2) It describes how LIGO uses laser interferometry to extremely sensitively measure tiny distortions in spacetime caused by passing gravitational waves.
3) The first detected gravitational waves in 2015 matched predictions for the inspiral and merger of two black holes, with the signal analyzed to determine properties of the black holes such as their masses.
A relationship between mass as a geometric concept and motion associated with a closed curve in spacetime (a notion taken from differential geometry) is investigated. We show that the 4-dimensional exterior Schwarzschild solution of the General Theory of Relativity can be mapped to a 4-dimensional Euclidean spacetime manifold. As a consequence of this mapping, the quantity M in the exterior Schwarzschild solution which is usually attributed to a massive central object is shown to correspond to a geometric property of spacetime. An additional outcome of this analysis is the discovery that, because M is a property of spacetime geometry, an anisotropy with respect to its spacetime components measured in a Minkowski tangent space defined with respect to a spacetime event P by an observer O who is stationary with respect to the spacetime event P, may be a sensitive measure of an anisotropic cosmic accelerated expansion. The presence of anisotropy in the cosmic accelerated expansion may contribute to the reason that there are currently two prevailing measured estimates of this quantity
1) The document provides an overview of the contents of Part II of a slideshow on modern physics, which covers topics such as charge and current densities, electromagnetic induction, Maxwell's equations, special relativity, tensors, blackbody radiation, photons, electrons, scattering problems, and waves.
2) It aims to provide a brief yet modern review of foundational concepts in electromagnetism and set the stage for introducing special relativity, quantum mechanics, and matter waves for undergraduate students.
3) The overview highlights that succeeding chapters will develop tensor formulations of electromagnetism and special relativity from first principles before discussing applications like blackbody radiation and early quantum models.
Gravity in general relativity and Einstein-Cartan-Sciama-Kibble theory is summarized. In general relativity, gravity is described using a symmetric connection and Riemannian geometry. The Einstein field equations relate the Ricci tensor and scalar to the stress-energy tensor. In ECSK theory, the connection is non-symmetric due to the inclusion of torsion. This leads to modifications in the covariant derivative, curvature, and Einstein field equations compared to general relativity. ECSK theory aims to extend general relativity to combine macroscopic and microscopic scales.
Equation of a particle in gravitational field of spherical bodyAlexander Decker
1. This academic article presents an analysis of the motion of particles in the gravitational field of a spherical body based on a new theory of classical mechanics proposed by the authors.
2. The authors derive equations of motion for particles in the equatorial plane of the spherical body that contain corrections for relativistic effects up to all orders of c-2, where c is the speed of light.
3. They show that their equation for radial motion, to first order in c-2, is identical to Einstein's equation from general relativity for planetary motion in the solar system, and correctly predicts the anomalous orbital precession observed astronomically.
This document discusses the incompatibility between classical mechanics and electromagnetism. It shows that under a Galilean transformation, the wave equation governing electromagnetic waves takes on a different form in different reference frames, violating Galilean invariance. This means that the laws of electromagnetism depend on the choice of reference frame. As such, classical mechanics and electromagnetism cannot be unified without modifications to account for this issue.
Quantization of the Orbital Motion of a Mass In The Presence Of Einstein’s Gr...IOSR Journals
This document presents a theoretical model to explain the quantized nature of planetary orbits around the sun based on Einstein's general theory of relativity. It derives expressions for the Lagrangian and Hamiltonian of a unit mass moving in the curved spacetime around a massive body. Using these, it writes a Schrodinger-like quantum equation that includes variation of the wavefunction with respect to a curve parameter representing spacetime curvature. The solutions reveal the quantized energy levels and orbits determined by quantum numbers. When applied to planetary orbits, the model estimates distances from the sun in good agreement with observed values.
The document discusses Einstein's field equations and Heisenberg's uncertainty principle. It begins by providing background on Einstein's field equations, which relate the geometry of spacetime to the distribution of mass and energy within it. It then discusses some key mathematical aspects of the field equations, including their nonlinear partial differential form. Finally, it notes that the field equations can be consolidated with Heisenberg's uncertainty principle to provide a unified description of gravity and quantum mechanics.
1) The document summarizes the 100-year history of gravitational wave detection, from Einstein's theory of general relativity predicting their existence to the recent direct detection by the LIGO experiment.
2) It describes how LIGO uses laser interferometry to extremely sensitively measure tiny distortions in spacetime caused by passing gravitational waves.
3) The first detected gravitational waves in 2015 matched predictions for the inspiral and merger of two black holes, with the signal analyzed to determine properties of the black holes such as their masses.
A relationship between mass as a geometric concept and motion associated with a closed curve in spacetime (a notion taken from differential geometry) is investigated. We show that the 4-dimensional exterior Schwarzschild solution of the General Theory of Relativity can be mapped to a 4-dimensional Euclidean spacetime manifold. As a consequence of this mapping, the quantity M in the exterior Schwarzschild solution which is usually attributed to a massive central object is shown to correspond to a geometric property of spacetime. An additional outcome of this analysis is the discovery that, because M is a property of spacetime geometry, an anisotropy with respect to its spacetime components measured in a Minkowski tangent space defined with respect to a spacetime event P by an observer O who is stationary with respect to the spacetime event P, may be a sensitive measure of an anisotropic cosmic accelerated expansion. The presence of anisotropy in the cosmic accelerated expansion may contribute to the reason that there are currently two prevailing measured estimates of this quantity
1) The document provides an overview of the contents of Part II of a slideshow on modern physics, which covers topics such as charge and current densities, electromagnetic induction, Maxwell's equations, special relativity, tensors, blackbody radiation, photons, electrons, scattering problems, and waves.
2) It aims to provide a brief yet modern review of foundational concepts in electromagnetism and set the stage for introducing special relativity, quantum mechanics, and matter waves for undergraduate students.
3) The overview highlights that succeeding chapters will develop tensor formulations of electromagnetism and special relativity from first principles before discussing applications like blackbody radiation and early quantum models.
Gravity in general relativity and Einstein-Cartan-Sciama-Kibble theory is summarized. In general relativity, gravity is described using a symmetric connection and Riemannian geometry. The Einstein field equations relate the Ricci tensor and scalar to the stress-energy tensor. In ECSK theory, the connection is non-symmetric due to the inclusion of torsion. This leads to modifications in the covariant derivative, curvature, and Einstein field equations compared to general relativity. ECSK theory aims to extend general relativity to combine macroscopic and microscopic scales.
Geometry of Noninertial Bases in Relativistic Mechanics of Continua and Bell'...ijrap
From obtained equations of structure (integrability conditions of continuum equations) the elemental noninertial reference frames (NRF) are investigated: relativistic global uniformly accelerated Born’s hard NRF, relativistic Born’s rigid uniformly rotating RF free of horizon, rigid vortex-free spherically symmetrical NRF. All these systems are not described in Minkowski space. Riemann space-time of these RF does not directly connect with general theory of relativity (GR). However the exact equations of structure restrict the possibilities of application of the Einstein's equations.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
1) The document discusses the classical theory of electromagnetic radiation confined within an isothermal enclosure and the discrepancies with experimental observations.
2) It analyzes the temperature dependence of the energy density and pressure of the radiation using thermodynamic considerations.
3) This leads to the derivation of the Stefan-Boltzmann law relating the emissive power of a black body to the fourth power of its temperature.
The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
DOI: 10.13140/RG.2.2.22006.45124/1
Five-Dimensional Cosmological Model with Time-Dependent G and Lamda for Const...IOSR Journals
In this paper we have consider five-dimensional cosmological model in presence of perfect fluid
source with time dependent G and .The Einstein field equations are solvable with the help of constant
deceleration parameter. Physical and kinematical properties of this model are investigated. It has been shown
that the solutions are comparable with recent observations. The behavior of gravitational constant,
cosmological constant, density, critical density and pressure is discussed for dust, radiation dominated and stiff matter of the Universe. It is also examined the behavior of gravitational constant and cosmological constant for expansion law and exponential law for stiff matter
To the Issue of Reconciling Quantum Mechanics and General RelativityIOSRJAP
The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 1042G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature Λ. If the numerical values of K 5.11031 Nm2 kg-2 and =4.41029 m -2 , there is a spectrum of stationary states of the electron in its own gravitational field (0.511 MeV ... 0.681 MeV).Adjusting according to the known mechanisms of broadening does not disclose the broadening of the registered portion of the emission spectrum of the micropinch. It indicates the presence of an additional mechanism of broadening the registered portion of the spectrum of the characteristic radiation due to the contribution of the excited states of electrons in their own gravitational field. The energy spectrum of the electron in its own gravitational field and the energy spectra of multielectron atoms are such that there is a resonance of these spectra. As obvious, the consequence of such resonant interaction is appearance, including new lines, of electromagnetic transitions not associated with atomic transitions. The manuscript is the review of previously published papers cited in the references.
Einstein's General Theory of Relativity interpreted in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to an apparent space contraction as a result of a spectral energy density gradient.
1) John Nash presents an equation that is a 4th order covariant tensor partial differential equation applicable to the metric tensor of spacetime. This equation is formally divergence free like the Einstein vacuum equation.
2) The equation can be derived from a specific Lagrangian involving terms quadratic in the scalar curvature and Ricci tensor. Previous theorists had considered such Lagrangians in attempts at quantum gravity theories but had not focused on this specific choice.
3) The equation may allow a wider variety of gravitational waves, including compressional waves not excluded in electromagnetic theory. Standard GR only allows transverse gravitational waves.
A new universal formula for atoms, planets, and galaxiesIOSR Journals
In this paper a new universal formula about the rotation velocity distribution of atoms, planets, and galaxies is presented. It is based on a new general formula based on the relativistic Schwarzschild/Minkowski metric, where it has been possible to obtain expressions for the rotation velocity - and mass distribution versus the distance to the atomic nucleus, planet system centre, and galactic centre. A mathematical proof of this new formula is also given. This formula is divided into a Keplerian(general relativity)-and a relativistic(special relativity) part. For the atomic-and planet systems the Keplerian distribution is followed, which is also in accordance with observations.
According to the rotation velocity distribution of the galaxies the rotation velocity increases very rapidly from the centre and reaches a plateau which is constant out to a great distance from the centre. This is in accordance with observations and is also in accordance with the main structure of rotation velocity versus distance from different galaxy measurements.
Computer simulations were also performed to establish and verify the rotation velocity distributions in the atomic – planetary- and galaxy system, according to this paper. These computer simulations are in accordance with observations in two and three dimensions. It was also possible to study the matching percentage in these calculations showing a much higher matching percentage between theoretical and observational values by this new formula.
Backreaction of hawking_radiation_on_a_gravitationally_collapsing_star_1_blac...Sérgio Sacani
The document summarizes a study investigating the backreaction of Hawking radiation on the interior of a gravitationally collapsing star. It finds that due to the negative energy Hawking radiation inside the star, the collapse stops at a finite radius before a black hole singularity or event horizon can form, meaning the star bounces instead of collapsing fully. The interior metric of a collapsing star is equivalent to that of a closed Friedmann-Robertson-Walker universe. The Oppenheimer-Snyder model of stellar collapse is described, which provides context for analyzing the dynamics involving Hawking radiation.
Evaluation of post-Einsteinian gravitational theories through parameterized p...Nicolae Sfetcu
Right after the elaboration and success of general relativity (GR), alternative theories for gravity began to appear. In order to verify and classify all these theories, specific tests have been developed, based on self-consistency and on completeness. In the field of experimental gravity, one of the important applications is formalism. For the evaluation of gravity models, several sets of tests have been proposed. Parameterized post-Newtonian formalism considers approximations of Einstein's gravity equations by the lowest order deviations from Newton's law for weak fields.
DOI: 10.13140/RG.2.2.25994.82881
Why Does the Atmosphere Rotate? Trajectory of a desorbed moleculeJames Smith
As a step toward understanding why the Earth's atmosphere "rotates" with the Earth, we use using Geometric (Clifford) Algebra to investigate the trajectory of a single molecule that desorbs vertically upward from the Equator, then falls back to Earth without colliding with any other molecules. Sample calculations are presented for a molecule whose vertical velocity is equal to the surface velocity of the Earth at the Equator (463 m/s) and for one with a vertical velocity three times as high. The latter velocity is sufficient for the molecule to reach the Kármán Line (100,000 m). We find that both molecules fall to Earth behind the point from which they desorbed: by 0.25 degrees of latitude for the higher vertical velocity, but by only 0.001 degrees for the lower.
Motions for systems and structures in space, described by a set denoted Avd. ...Premier Publishers
In order to describe general motions and matter in space, functions for angular velocity and density are assumed and denoted Avd, as an abbreviation. The framework provides a unified approach to motions at different scales. It is analysed how Avd enters and rules, in terms of results from equations, in field experiments and observations at Earth. Chaos may organize according to Avd, such that more order, Cosmos, appear in complex nonlinear dynamical systems. This reveals that Avd may be governing and that deterministic systems can be created without assuming boundaries and conditions for initial values and forces from outside. A mathematical model for the initiation of Logos (when a paper accelerates into a narrow circular orbit), was described, and denoted local implosion; Li. The theorem for dl, provides discrete solutions to a power law, and this is related to locations of satellites and moons.
1) The document discusses testing modifications to general relativity (GR) to explain the observed accelerated expansion of the universe. Two representative modified gravity (MG) models are studied: f(R) theories and the Bean-Tangmatitham parametrization.
2) These MG models modify the gravitational potentials in GR through additional parameters that can generate different gravitational behaviors, including those described by GR.
3) The MG parameters are constrained using CosmoSIS, a cosmological parameter estimation code, with data from the Cosmic Microwave Background and weak lensing surveys. Estimates of the MG parameters suggest no deviation from GR predictions.
Complete solution for particles of nonzero rest mass in gravitational fieldsAlexander Decker
This academic article presents research on deriving the equation of motion and calculating the angle of deflection for photons in a gravitational field.
The researchers used a series method to solve the planetary orbital equation of motion for particles with nonzero rest mass in gravitational fields. Their results for the deflection angle of photons grazing the sun's edge matched predictions from general relativity and fell within experimental measurements.
The paper aims to provide a complete solution to the dynamical equation of motion that incorporates corrections for all orders of c-2, the speed of light. This generalized equation is supported by experimental evidence and opens opportunities for further theoretical and experimental applications.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
This paper explores dimensional reduction of 4D general relativity to a (1+1) gravity model using a Kaluza-Klein type approach. It begins with the Einstein-Hilbert action in 4D and defines a fundamental metric that encodes the metric for a (1+1) spacetime. This allows obtaining an effective (1+1) gravity action coupled to a scalar field. The equations of motion for the metric and scalar field in the (1+1) spacetime are then derived. A solution to the metric is presented where the scalar field is the radius of a 2-sphere.
This document presents new ideas in loop quantum gravity, including:
1. Deriving a relationship between time and vorticity using wavefunction continuity.
2. Introducing a new "Eikonal constraint" and showing how it removes acausality by gauging time to light cones.
3. Proposing a new form of the Hamiltonian constraint in the style of the Dirac equation, which reduces state fuzziness in line with Penrose's ideas.
Vasil Penchev. Cyclic mechanics. The principle of cyclicityVasil Penchev
1) The document discusses a theory of cyclic mechanics intended to unify quantum mechanics and general relativity.
2) It proposes several foundational principles, including that the universe can return to any point, time is not uniformly flowing, and all laws must be invariant to discrete and continuous transformations.
3) A key concept is introducing the notion of "quantum measure" and "quantum information" to provide a common measure to equate equations from different theories, with the goal of unifying them.
Anti-Universe And Emergent Gravity and the Dark UniverseSérgio Sacani
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a0 = cH0, and provide evidence for the fact that this additional ‘dark gravity force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Geometry of Noninertial Bases in Relativistic Mechanics of Continua and Bell'...ijrap
From obtained equations of structure (integrability conditions of continuum equations) the elemental noninertial reference frames (NRF) are investigated: relativistic global uniformly accelerated Born’s hard NRF, relativistic Born’s rigid uniformly rotating RF free of horizon, rigid vortex-free spherically symmetrical NRF. All these systems are not described in Minkowski space. Riemann space-time of these RF does not directly connect with general theory of relativity (GR). However the exact equations of structure restrict the possibilities of application of the Einstein's equations.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
1) The document discusses the classical theory of electromagnetic radiation confined within an isothermal enclosure and the discrepancies with experimental observations.
2) It analyzes the temperature dependence of the energy density and pressure of the radiation using thermodynamic considerations.
3) This leads to the derivation of the Stefan-Boltzmann law relating the emissive power of a black body to the fourth power of its temperature.
The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
DOI: 10.13140/RG.2.2.22006.45124/1
Five-Dimensional Cosmological Model with Time-Dependent G and Lamda for Const...IOSR Journals
In this paper we have consider five-dimensional cosmological model in presence of perfect fluid
source with time dependent G and .The Einstein field equations are solvable with the help of constant
deceleration parameter. Physical and kinematical properties of this model are investigated. It has been shown
that the solutions are comparable with recent observations. The behavior of gravitational constant,
cosmological constant, density, critical density and pressure is discussed for dust, radiation dominated and stiff matter of the Universe. It is also examined the behavior of gravitational constant and cosmological constant for expansion law and exponential law for stiff matter
To the Issue of Reconciling Quantum Mechanics and General RelativityIOSRJAP
The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 1042G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature Λ. If the numerical values of K 5.11031 Nm2 kg-2 and =4.41029 m -2 , there is a spectrum of stationary states of the electron in its own gravitational field (0.511 MeV ... 0.681 MeV).Adjusting according to the known mechanisms of broadening does not disclose the broadening of the registered portion of the emission spectrum of the micropinch. It indicates the presence of an additional mechanism of broadening the registered portion of the spectrum of the characteristic radiation due to the contribution of the excited states of electrons in their own gravitational field. The energy spectrum of the electron in its own gravitational field and the energy spectra of multielectron atoms are such that there is a resonance of these spectra. As obvious, the consequence of such resonant interaction is appearance, including new lines, of electromagnetic transitions not associated with atomic transitions. The manuscript is the review of previously published papers cited in the references.
Einstein's General Theory of Relativity interpreted in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to an apparent space contraction as a result of a spectral energy density gradient.
1) John Nash presents an equation that is a 4th order covariant tensor partial differential equation applicable to the metric tensor of spacetime. This equation is formally divergence free like the Einstein vacuum equation.
2) The equation can be derived from a specific Lagrangian involving terms quadratic in the scalar curvature and Ricci tensor. Previous theorists had considered such Lagrangians in attempts at quantum gravity theories but had not focused on this specific choice.
3) The equation may allow a wider variety of gravitational waves, including compressional waves not excluded in electromagnetic theory. Standard GR only allows transverse gravitational waves.
A new universal formula for atoms, planets, and galaxiesIOSR Journals
In this paper a new universal formula about the rotation velocity distribution of atoms, planets, and galaxies is presented. It is based on a new general formula based on the relativistic Schwarzschild/Minkowski metric, where it has been possible to obtain expressions for the rotation velocity - and mass distribution versus the distance to the atomic nucleus, planet system centre, and galactic centre. A mathematical proof of this new formula is also given. This formula is divided into a Keplerian(general relativity)-and a relativistic(special relativity) part. For the atomic-and planet systems the Keplerian distribution is followed, which is also in accordance with observations.
According to the rotation velocity distribution of the galaxies the rotation velocity increases very rapidly from the centre and reaches a plateau which is constant out to a great distance from the centre. This is in accordance with observations and is also in accordance with the main structure of rotation velocity versus distance from different galaxy measurements.
Computer simulations were also performed to establish and verify the rotation velocity distributions in the atomic – planetary- and galaxy system, according to this paper. These computer simulations are in accordance with observations in two and three dimensions. It was also possible to study the matching percentage in these calculations showing a much higher matching percentage between theoretical and observational values by this new formula.
Backreaction of hawking_radiation_on_a_gravitationally_collapsing_star_1_blac...Sérgio Sacani
The document summarizes a study investigating the backreaction of Hawking radiation on the interior of a gravitationally collapsing star. It finds that due to the negative energy Hawking radiation inside the star, the collapse stops at a finite radius before a black hole singularity or event horizon can form, meaning the star bounces instead of collapsing fully. The interior metric of a collapsing star is equivalent to that of a closed Friedmann-Robertson-Walker universe. The Oppenheimer-Snyder model of stellar collapse is described, which provides context for analyzing the dynamics involving Hawking radiation.
Evaluation of post-Einsteinian gravitational theories through parameterized p...Nicolae Sfetcu
Right after the elaboration and success of general relativity (GR), alternative theories for gravity began to appear. In order to verify and classify all these theories, specific tests have been developed, based on self-consistency and on completeness. In the field of experimental gravity, one of the important applications is formalism. For the evaluation of gravity models, several sets of tests have been proposed. Parameterized post-Newtonian formalism considers approximations of Einstein's gravity equations by the lowest order deviations from Newton's law for weak fields.
DOI: 10.13140/RG.2.2.25994.82881
Why Does the Atmosphere Rotate? Trajectory of a desorbed moleculeJames Smith
As a step toward understanding why the Earth's atmosphere "rotates" with the Earth, we use using Geometric (Clifford) Algebra to investigate the trajectory of a single molecule that desorbs vertically upward from the Equator, then falls back to Earth without colliding with any other molecules. Sample calculations are presented for a molecule whose vertical velocity is equal to the surface velocity of the Earth at the Equator (463 m/s) and for one with a vertical velocity three times as high. The latter velocity is sufficient for the molecule to reach the Kármán Line (100,000 m). We find that both molecules fall to Earth behind the point from which they desorbed: by 0.25 degrees of latitude for the higher vertical velocity, but by only 0.001 degrees for the lower.
Motions for systems and structures in space, described by a set denoted Avd. ...Premier Publishers
In order to describe general motions and matter in space, functions for angular velocity and density are assumed and denoted Avd, as an abbreviation. The framework provides a unified approach to motions at different scales. It is analysed how Avd enters and rules, in terms of results from equations, in field experiments and observations at Earth. Chaos may organize according to Avd, such that more order, Cosmos, appear in complex nonlinear dynamical systems. This reveals that Avd may be governing and that deterministic systems can be created without assuming boundaries and conditions for initial values and forces from outside. A mathematical model for the initiation of Logos (when a paper accelerates into a narrow circular orbit), was described, and denoted local implosion; Li. The theorem for dl, provides discrete solutions to a power law, and this is related to locations of satellites and moons.
1) The document discusses testing modifications to general relativity (GR) to explain the observed accelerated expansion of the universe. Two representative modified gravity (MG) models are studied: f(R) theories and the Bean-Tangmatitham parametrization.
2) These MG models modify the gravitational potentials in GR through additional parameters that can generate different gravitational behaviors, including those described by GR.
3) The MG parameters are constrained using CosmoSIS, a cosmological parameter estimation code, with data from the Cosmic Microwave Background and weak lensing surveys. Estimates of the MG parameters suggest no deviation from GR predictions.
Complete solution for particles of nonzero rest mass in gravitational fieldsAlexander Decker
This academic article presents research on deriving the equation of motion and calculating the angle of deflection for photons in a gravitational field.
The researchers used a series method to solve the planetary orbital equation of motion for particles with nonzero rest mass in gravitational fields. Their results for the deflection angle of photons grazing the sun's edge matched predictions from general relativity and fell within experimental measurements.
The paper aims to provide a complete solution to the dynamical equation of motion that incorporates corrections for all orders of c-2, the speed of light. This generalized equation is supported by experimental evidence and opens opportunities for further theoretical and experimental applications.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
This paper explores dimensional reduction of 4D general relativity to a (1+1) gravity model using a Kaluza-Klein type approach. It begins with the Einstein-Hilbert action in 4D and defines a fundamental metric that encodes the metric for a (1+1) spacetime. This allows obtaining an effective (1+1) gravity action coupled to a scalar field. The equations of motion for the metric and scalar field in the (1+1) spacetime are then derived. A solution to the metric is presented where the scalar field is the radius of a 2-sphere.
This document presents new ideas in loop quantum gravity, including:
1. Deriving a relationship between time and vorticity using wavefunction continuity.
2. Introducing a new "Eikonal constraint" and showing how it removes acausality by gauging time to light cones.
3. Proposing a new form of the Hamiltonian constraint in the style of the Dirac equation, which reduces state fuzziness in line with Penrose's ideas.
Vasil Penchev. Cyclic mechanics. The principle of cyclicityVasil Penchev
1) The document discusses a theory of cyclic mechanics intended to unify quantum mechanics and general relativity.
2) It proposes several foundational principles, including that the universe can return to any point, time is not uniformly flowing, and all laws must be invariant to discrete and continuous transformations.
3) A key concept is introducing the notion of "quantum measure" and "quantum information" to provide a common measure to equate equations from different theories, with the goal of unifying them.
Anti-Universe And Emergent Gravity and the Dark UniverseSérgio Sacani
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a0 = cH0, and provide evidence for the fact that this additional ‘dark gravity force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Quantization of photonic energy and photonic wave lengthEran Sinbar
The document proposes that if space is quantized at the Planck length, then photonic energy and wavelength must also be quantized. It suggests that future experiments could detect these quantization levels in cosmic radiation or particle collisions. It also puts forward a "grid dimensions" theory that proposes extra non-local dimensions between Planck length pieces of space that could explain quantum non-local effects like entanglement. Key equations presented quantify proposed quantized limits for momentum, mass, velocity of particles if space-time is quantized.
Energy in form of space may solve the dark energy problemPremier Publishers
A review of recent observations suggests a universe that is light weight (matter density is 1/3rd of the critical value), accelerating and flat. This implies the existence of a cosmic Dark Energy that overcomes the gravitational self-attraction force of matter and causes the accelerating expansion. Finding out the cause of expansion and acceleration of the universe is a challenging job in present day cosmology. Cosmological models with different types of dark energy are becoming viable standard models to analyze and simulate experimental data from a number of high red shift supernovae. In this article, physical significance and analytical expression for dark energy related to total energy (or energy density) and matter (or matter density) in the universe is presented. It is assumed that 'space' or 'vacuum' is another form of energy (other form is mass which is related as E = mc2). With this assumption new cosmological equation of state is constructed which is in very good agreement with present observations. Thus energy evolves from matter to radiation to space. It is also predicted that the existence of a fundamental particle with mass less than the mass of a quark is possible.
Universal constants like Planck's constant h, the speed of light c, gravitational constant G, and Boltzmann's constant k can be used to structure theoretical physics. They lead to three main theories: quantum field theory (h and c), general relativity (c and G), and quantum statistics (h and k). While not fully unified, these theories underlie the standard models of particle physics and cosmology. Fundamental metrology provides reliable standards by determining the values of dimensionless constants that depend on h, c, k, and G. Metrology exists at the intersection of fundamental physics described by these theories and emergent physics involving statistical mechanics.
Albert Einstein (1879-1955) developed the theories of special and general relativity. Special relativity, published in 1905, established that the laws of physics are the same in all inertial frames of reference and that the speed of light in a vacuum is constant. General relativity, published in 1915, introduced gravitation as a result of the curvature of spacetime caused by the uneven distribution of mass and energy. One of Einstein's most famous equations is E=mc2, which shows that mass and energy are equivalent and interconvertible.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Hamiltonian formulation project Sk Serajuddin.pdfmiteshmohanty03
This document appears to be a student's project dissertation on the Hamiltonian formulation of classical mechanics. It includes an acknowledgements section thanking the student's supervisor, a certificate from the supervisor, and a declaration by the student. The abstract provides a short overview stating that the project will review classical mechanics and introduce the Euler-Lagrange and Hamiltonian formulations of mechanics. It will examine the relationship between symmetry and conservation laws and introduce quantization rules.
This document discusses whether quantum mechanics is involved in the early evolution of the universe and if a Machian relationship between gravitons and gravitinos can help answer this question. It proposes that:
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2) A minimum amount of initial information, such as a small value for Planck's constant, is needed to set fundamental cosmological parameters and could be transferred from a prior universe.
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As we are all aware,therecent discovery of the Higgs boson has revealed a highly massive particle, the value of which lies between 125and 126.5 GeV/c2.. According to the basic concepts of Quantum Mechanics, and in full compliance with the Uncertainty Principle and Yukawa intuitions, we were able to calculate the maximum limit of the Higgs boson‟s field of action. From the calculations show that the Higgs boson presents a range of action really very small, namely 9.8828∙10-16[cm], that is slightly smaller than 10-15[cm]. This value is justified by the considerable mass that the Higgs bosonacquires, in perfect agreement with the Uncertainty Principle.
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3) The model aims to replace the standard LambdaCDM model, treating the expanding universe as a dynamically stable "biking" Einstein universe where the running cosmological constant compensates for the effect of gravity at all epochs.
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before we can build a unified physical theory.
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Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. He developed the special theory of relativity, which describes the laws of motion at high speeds and led to his famous equation, and the general theory of relativity, which describes gravity as a geometric property of space and time.
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. The document provides background on Einstein's life and work, and summarizes his theories of special relativity, which describes physics at high speeds, and general relativity, which proposes that gravity results from the curvature of spacetime.
FROM THE PRINCIPLE OF LEAST ACTION TO THE CONSERVATION OF QUANTUM INFORMATION...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to
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what (if any) is conserved? An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
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The electromagnetism and gravity are unified where, while the first originates from the electric charges in a
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explanation of masses in the Universe 100 % inclusive, to solving the hackneyed yet equally elusive puzzle
of why the inertial mass is equal to the gravitational mass.
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Geometry and Probablity: Statistical
Geometrodynamics with Holography
Koustubh Kabe†
(Affiliation): Department of Mathematics, Gogte Institute of Technology, Udyambag,
Belgaum(Belgavi)- 590 008 Karnataka, INDIA.
Email: kkabe8@gmail.com
Abstract
The following paper makes an endeavor to derive from scratch, the Einstein gravity from purely
novel and subtle set of statistical ansatz. The theory developed is that of statistical
geometrodynamics in close conjunction with the standard statistical thermodynamics, thereby
extending the Einstein theory to three laws involving the Holographic Principle in a totally
different way. A Boltzmann-like formula is derived right after the second law of
geometrodynamics. The author hopes that the following work will shed some light on the
fundamental understanding of the underpinnings of gravity and information in a non-
conventional way. The rest of the latter part of the paper consists of discussions and possible
conclusions that could be drawn by the author at thye time of writing the paper.
PACS Nos.: 04.70.Dy, 04.60.Ds, 11.25.Mj, 97.60.Lf
Keywords: statistical thermodynamics, statistical geometrodynamics, holographic principle,
Einstein gravity, bit saturation.
The Holographic Principle worked out by „tHooft and independently by Susskind [1] has
played out a vital role in the understanding of gravity. The works of Bousso (see for example for
a good survey [2] and also references therein for an exhaustive study of the Holographic
Principle) has given a definitive direction to the study of the entropy bounds. Starting from the
Bekenstein bound arising from the Geroch process to the work of Susskind through his own
process of transforming any thermodynamic system into a blackhole and the application of this
transformation to the Bekenstein‟s Generalized Second Law (GSL) yielding the more rigorous
and general spherical entropy bound, one finds a rather subtle and elegant formulation through
the light-sheet formalism to the Bousso covariant entropy conjecture (also look up in [2] in the
reference section under B for Bousso), now a theorem due to the proof provided by Flanagan et.
al. [3]. Recently, Verlinde has made a revelation in gravitational physics [4] by demonstrating
the emergence of Newtonian and Einsteinean gravity in steps of approximations from the laws of
thermodynamics by the application of the Holographic Principle and bit dynamics. The work of
Caticha [5](check also references in [5]) has taken definitive steps in the direction of
construction of a statistical theory of geometrodynamics. The present work takes a completely
different route to derive the Einstein gravity and further extends the theory. The
geometrodynamic theory is considered from statistical postulates applied to hypothetical
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fundamental constituents of curved spacetime. The theory of geometrodynamics thus derived is
considered independent of thermodynamics and yet a similar theory in its own right with a set of
quantities analogous to entropy, thermodynamic probability, temperature, etc. There is thus no
such entropy bound here. Everything is in terms of curvature and statistical geometrodynamics.
The paper is a bold attempt to pave way in the positive direction of a fundamental understanding
of the origins of space and time [6].
One always arrives at the Einstein field equations and his law of gravitation through the
Principle of equivalence which asserts the equivalence of acceleration and gravitation. Then,
there is the Einstein-Hilbert variational principle from which also one gets the Einstein field
equations of gravitation which read
, (1)
where, is the Ricci curvature tensor, the corresponding scalar, is the fundamental or
metric tensor and is the energy momentum tensor. The above equation embodies the fact
that spacetime is curved by the presence of matter and mass is made to move by the curved
spacetime according to the warp of the spacetime.
This involves tensor analytic manipulation of the Christoffel symbols of the second kind thereby
defining the Ricci tensor. Yet another approach is that of the Bianchi identity of the second type
which exhibit the principle of geometrodynamics that the boundary of a boundary of a boundary
is zero. All these approaches involve deterministic and generically predictive propositions and
interpretations. On the other hand, energy-momentum tensor represents matter and energy and
these obey quantum statistical laws. There are quantum transitions involved in the matter
represented by . This quantum behavior should correspondingly be accounted for by the
spacetime geometry as well. If matter fluctuates statistically then so should geometry. If matter
obeys statistical laws then so should geometry at the quantum scales. The laws of physical
statistics obeyed by lead to statistical thermodynamics. The laws of physical statistics
obeyed by the geometric part of the Einstein law viz., the l.h.s. of eq (1) should lead to statistical
geometrodynamics. Still, it is the aim of this paper to not argue this way by starting with the
Einstein law and the eq (1). The aim is to rather start with a subtle and simple set of statistical
postulates and ansatz and arrive at various results.
We begin by proposing the existence of geomets – hypothetical quantum or fundamental objects
of spacetime geometry which occupy different available geometrodynamic states in the statistical
manner of speaking. The various geometrodynamic distributions are then arrived at by the gas of
geomets. The resulting spacetime geometry is a direct consequence of the ensemble of the gas of
geomets occupying the geometrodynamic states of different curvature probabilities. This is our
first ansatz. So, now there are two hypothetical objects – (i) geomets – the fundamental
constituents of curved spacetime and (ii) the geometrodynamic states. Since entropy for gravity
as a thermodynamic system is non-concave, there are many possible geometrodynamic states and
end-states. As such, the geometrodynamic probability and the geometrodynamic distribution
function for a given ensemble of a gas of geomets determining the curvature in the bulk of
spacetime become functions and are tensors of rank two. We denote them
respectively by and . Even though the number, , of the bits available for the description
of the individual species of geomets is the same (is equivalent to the number of matter or
radiation particles) the non-concave nature of entropy for gravity makes these tensors. Now from
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our simple hypothesis, we derive: (i) the Einstein law of geometrodynamics and follow it up with
two additional laws based on the holographic principle in analogy with the laws of
thermodynamics and (ii) we derive a formula connecting the Gauss-Bonnet mean curvature of
the holographic surface bounding the bulk of the spacetime and the geometrodynamic probability
in the bulk.
The quantity appearing in statistics is inversely proportional to the absolute
temperature in statistical thermodynamics. In statistical geometrodynamics, we define the
geometrodynamic probability by
∑ (2)
Now, we fix the following ansatz,
∑ and ∑ (3)
Here, is the kinetic geometry of the species of the geomets. The kinetic geometry is
defined as the geometry possessed by the geomet on account of its motion. This is a simple
definition: moving bodies possess kinetic energy and moving elements of curved spacetime
geometry – the geomets – possess kinetic geometry. This fixes up an exact yet abstruse analogy
between thermodynamics and geometrodynamics and further strengthens ansatz (3) above. Pure
statistical geometrodynamics should be geometrical in character. Any energy should be
translated into geometry and vice-versa.
So, we fix up tensor multipliers as,
. (4)
Then,
∑ ∑
∑ ∑ (5)
Since is fixed by ansatz (3),
∑ . (6)
And from the second part of (3),
∑ ∑ . (7)
The first term in (7) represents the stretch in the spacetime; that is, the geometric work or in
other words, the stressing curvature mathematically equal to ; that is
∑ ∑ , (8)
so that
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∑ . (9)
Also taking local derivatives w.r.t. time we have by Hamilton‟s Ricci flow
∑ (10)
so
∑ . (11)
Now, the second term – ∑ is the Ricci curvature which is the geometrodynamic
“warp” accrued by the bulk of the spacetime, i.e., the curvature inside the holographic screen.
Thus,
∑ . (12)
From (7), (8) and (12), we have for the first law of geometrodynamics, the Einstein field
equations (1) which we rewrite here as
(1) The first law of geometrodynamics: .
Also,
∑ ∑
or
.
(13)
On the other hand,
∑ . (14)
Therefore, is a total differential and , the intergrating factor of the Ricci curvature. The
statistical theory leads naturally to the second law of geometrodynamics which we enunciate as
follows:
(2) has an integrating factor namely,
, (15)
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where, is the Gauss-Bonnet mean curvature of the horizon or the holographic
screen/surface. is the bit saturation. Bit saturation is the ratio of the number of bits required
to describe the system, in the bulk of the spacetime including the bulk spacetime itself, to the
number of bits available on the holographic screen.
Hence, for quantum gravitational nature of the theory and for dimensional consistency, we insert
the Planck length, , as
. (16)
So,
, (17)
or
. (18)
According to Verlinde [4], where represents the Newtonian gravitational
potential. This is a positive number that vanishes at large distances. So, this coincides with
the fact that the temperature also decreases with the expanding universe. Therefore, we extend
the analogy with the third law of thermodynamics and propose that
(3) The Gauss-Bonnet mean curvature of the evolving holographic surface tends to zero
for pure gravity as the bit saturation tends to zero and becomes zero at zero bit
saturation for the pure gravity situation.
Thus, we now have three laws of statistical geometrodynamics. The first law is the Einstein law
of gravitation as given by the Einstein field equations. The second law connects the Ricci
curvature (tensor) in the Einstein theory to the holographic screen/surface encompassing the
Einstein bulk spacetime. And the third law is (more or less) purely about the holographic surface
enclosing the Einstein bulk. Another statement for the third law of thermodynamics is that,
“in every irreversible thermodynamic process, the total entropy of the universe always
increases”. Similarly,
(3‟) In every irreversible geometrodynamic process, the Gauss-Bonnet mean curvature of the
holographic screen bounding the bulk spacetime always increases.
Now, for empty spacetime, the number of bits available in the bulk will be constant and
that on the holographic screen will also stay the same. So, we have the zeroeth law of
geometrodynamics, viz.,
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(0) The bit saturation for a system of empty spacetime bulk bounded by a holographic
screen, is a constant.
Just as temperature is a concept that holds macroscopically and breaks down at the
individual molecular/atomic level, the bit saturation is a concept that plays out a similar role.
Now, temperature is defined as the average kinetic energy of all the particles in a thermodynamic
system. At the particle level, there is the individual kinetic energy of the moving particles. For
the whole bulk of spacetime and its enclosing Holographic screen, the bit saturation reduces to
individual bits and thereby plays out an equivalent role. The definite physical boundaries of the
object (matter) are blurred in the fine graining limit and vanish completely in the completely fine
grained structure. Similarly, the spacetime manifold defined by the l.h.s. of (1) will also
disappear at the quantum scales where the structure is sufficiently finely grained. Actually the
ansatz (3) somehow seems to show a fundamental equivalence between quantum geometry and
quantum matter and radiation by establishing an exact relationship between quanta of geometry
and quanta of matter.
Reference
1. „tHooft, G. Dimensional Reduction in Quantum Gravity,Utrecht Preprint THU-93/26,
gr-qc/9310026; Susskind, L. The World as a Hologram, hep-th/9409089; „tHooft, G. The
Holographic Principle,hep-th/0003004.
2. Bousso, R. The Holographic Principle, hep-th/0203101.
3. Flanagan, E. E., D. Marolf and R. M. Wald, Proof of Classical Versions of the Bousso
Entropy Bound and of the Generalized Second Law, Phys. Rev. D62, 084035.
hep-th/9908070.
4. Verlinde, E. On the Origin of Gravity and the Laws of Newton, hep-th/1001.0785.
5. Caticha, A. Towards a Statistical Geometrodynamics, in Decoherence and Entropy in
Complex Systems ed. By H.-T. Elze (Springer Verlag, 2004). gr-qc/0301061.ibid., The
Information Geometry of Space and Time, gr-qc/0508108.
6. Merali, Z. The Origins of Space and Time, Nature 500, 516, 29 Aug 2013.