What is Space-Time Made of ?

Name: What is Space-Time Made of ?
Brand: EDP sciences
Price: 294.78 EUR
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David Izabel(Autor*in)

EDP sciences (Verlag)

1. Auflage

Erschienen am 20. Mai 2021

366 Seiten

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978-2-7598-2574-5 (ISBN)

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Inhalt

Intro
What is Space-Time Made of?
Preamble
Symbology
Introduction
What is the Problem with 21st Century Physics?
Where is Physics Today? - Synthetic Overview of the State of the Art of Physics Today
Introduction
Newton's Gravitation
Electromagnetism/GravitoElectroMagnetism
Special Relativity
General Relativity
Black Holes
Gravitational Waves
Quantum Mechanics
Highlighting the Differences between the Two Pillars of Physics
Nature Plays with Our Senses
How to Reconcile the Two Physics
First Ask the Right Question
What is the State of the Art and the Issues that Arise from It?
What is the Nature of Space-Time?
Can Einstein's Equation be Reconstructed without Passing through Newton's Weak Field Limits? Without Using G?
What Brings Us Contemporary Data of the Vacuum?
Space-Time as a Physical Object an Elastic Medium
A Strange Analogy between S. Timoshenko's Beam Theory and General Relativity
Introduction
Generalities on General Relativity
Analogy between Beam Theory and General Relativity from the Point of View of the General Principle Curvature=K &hx00D7
Energy Density
Analogy between the Definition of Curvature in Strength of Material and General Relativity
Extension of Curvature to Other Strength of Material Solicitations
Analysis of Einstein's Equation Applied to the Entire Universe (Case of Cosmology)
Conclusions
The Stress Energy Tensor in Theory of General Relativity and the Stress Tensor in Elasticity Theory are Similar
Definition of the Stress Energy Tensor in General Relativity
Definition of Stress Tensor in Elasticity Theory
Demonstration of the Correlation between the Stress Tensor and the Stress Energy Tensor
Relationship between the Metric Tensor and the Strain Tensor in Low Gravitational Field
Introduction
Definition of Strain Tensor
Determination of the Link between the Metric and the Strain
Relationship between the Stress Tensor and the Strain Tensor in Elasticity (K) and between the Curvature and the Stress Energy Tensor (?) in General Relativity in Weak Gravitational Fields
Reminder of Results
Some Reminders about the Elasticity Theory
Highlighting the Parallelism between Elasticity Theory and General Relativity
Consequence of Parallelism and Transversalism between the Elasticity Theory and General Relativity
And if We Reconstructed the Formula of Einstein's Gravitational Field by No Longer Considering the Temporal Components of the Tensors, but the Spatial Components
Let Us Step Back from Gravitation According to Newton
The Strengths and Weaknesses of Newton's Gravitational Approach
G a Gravitational Constant of Strange Dimensions as a Combination of Underlying Parameters
How to Re-parameterize ? in Einstein's Gravitational Field Equation
The Strengths and Weaknesses of Gravitation According to Einstein
Approach to Reconstructing General Relativity from the Elasticity Theory
Re-interpretation of the Results of the Theoretical Calculation of General Relativity on Gravitational Waves in Weak Field from the Windows of Elasticity Theory
Introduction
Re-interpretation of the 2 Gravitational Wave Polarizations in Terms of Space Deformation Tensors in the Sense of Elasticity Theory
Consequence in Terms of Oscillating Waves in the Arms of Interferometers
Expression of Einstein's Linearized Gravitational Equation in the Form of Strains
Determination of Poisson's Ratio of the elastic Space Material
Introduction
First Approach: Analysis of the Movements of Particles Positioned in Space on a Circle Undergoing the Passage of a Gravitational Wave
Second Approach: In the z Direction, the Gravitational Wave is a Transverse Wave and is Not a Compression Wave
Third Approach: Based on Available Datas
Dynamic Study of the elastic Space Strains in an Arm of an Interferometer
Study of an Interferometric Arm Subjected to Gravitational Waves Causing Compressions and Tractions of the Volume of Empty Space within It
Assumptions
Determination of Tensorial Equations Associated with Each Arm of the Interferometer
Dynamic Study of Simultaneous Elastic Space Strains in the 2 Arms of an Interferometer
Study of Two Interferometric Arms Subjected to Gravitational Waves Resulting in Compression/Traction of the Volume of Space within Them
Assumptions
Determination of Tensorial Equation Associated with the Two Arms of the Interferometer
Study of an Elastic Space Cylinder Twisted by the Coalescence of Two Black Holes
Study of a Vertical Space Cylinder in Pure Twisting - Use of Shear Speed of the Shear Wave Correlated with the Shear Strains
Assumptions
Determination of Tensorial Equation Associated with Twisting Space Tube
New Mechanical Expression of Einstein's Constant ?
Steps to Obtain the Mechanical Conversion of ?
Case where We Consider Only One Interferometer Arm
Cases where the Two Arms of the Interferometer and Poisson's Ratio are Considered
Case of a Pure Torsion of Vacuum Space Tube
Vacuum Data
Physical Approach or Mathematical Artifact?
The Vacuum Energy
Consistency of Results with Vacuum Data
Calibrating the New Mechanical Expression of ? with the Vacuum Data
Numerical Application to Vacuum Energy - Longitudinal Waves in Interferometric Tubes
Theoretical Development
Intensity Obtained for the New G Parameters Based on Vacuum Energy
Numerical Application to Vacuum Energy - Global Approach by Twist Wave
Theoretical Development
Intensities Obtained for New G Parameters Based on Vacuum Energy
Let's Go Back to the Time Components Based on the New Results
Introduction
Impact on the Time of this Search
Time Behaviour as an Elastic Material
Relating the Time Intervals with the Thickness Fibers of Spatial Space Sheets
Analogy of Mohr's Circle with Graviton Spin
Possible Constitution of Space Material
Analogy of Mohr's Circle with Graviton Spin
What if We Gave Up the Constant Character of G?
How to Test the New Theory?
Experimental Test of Young's Modulus of the Elastic Space Medium
Experimental Test of Pure Space Shear Behavior
Other Points in Link with the Strength of Material
An Analysis of the Vibrations of the Space Medium at the Time of the Big Bang
The Plastic Behavior of the Space Medium in Strong Fields
Conclusions
Chronological Order of Progress of the Author's Reflection and Related Discoveries
Measurements of Space-Time Material Deformations (Strains and Angles)
The Distortion of Space-Time by Lense-Thirring Effect (Frame Dragging) {142}
The Distortion of Space-Time by the Sun
Space-Time Strains Measured in the Interferometers Ligo and Virgo
History of Physics and Related Formulas
Calculating the Scalar Curvature R of a Sphere
Introduction
Metric Definition
Calculation of the First Derivatives of the Metric
Calculation of the Different Christoffel Symbols
Calculation of the Components of Riemann's Curvature Tensor
Scalar Curvature Calculation
Einstein's Tensor Expression
Application of Einstein's Equation in Cosmology - Demonstration of Friedmann-Lemaitre Equations
Expression of Metric and Stress Energy Tensor
Steps 1 Determination of the Affine Connections
Step 2
Steps 3 Determination of Scalar R
Steps 4 Expression of Einstein's Equation of General Relativity and Deduction of Friedmann-Lemaitre's Equations [52] and [53]
Reminder of Einstein's Equation
Time-Related Equation No. 1 (µ and t)
Space-Related Equation No. 2 (µ and t)
Can-We Understand a Black Hole from the Strength of the Materials?
Preamble
Determination of the Maximum Elastic Moment Me that can Withstand a Single Bending Beam
Determination of the Maximum Plastic Moment Mp that can Withstand a Single Bending Beam
Relationship Between the Curvature and Elastic Curvature of a Single Bending Beam with a Moment Less than the Elastic Moment
Determination of the Elastic-Plastic Moment that can Support a Single Bending Beam
Relationship Between the Curvature and the Elasto-Plastic Curvature of a Single Bending Beam with a Moment Greater or Equal to the Elastic Moment
Interpretation of the Relationship between Curves and Plastic Moment
Energy Deformation of the Elasto-Plastic Beam
Analogy with the General Relativity and Singularity of Black Holes
Proof of the Relation Between Speed c and the Shear Modulus µ of the Elastic Medium in the Case of Gravitational Wave
Expression Issued of the General Relativity Linearized
Formula Issued of the Elastic Wave in Elasticity Theory
Comparison of the Results Between General Relativity and Elasticity Theory
Proof of Curvature in Beam Theory
General Geometric Curvature in One Dimension
Case of the Beam (Sources see [1] à [3])
Relation Between the Bending Moment and the Curvature in One Dimension
Proof of Quantum Value of Young's Modulus of Space Space-Time Obtained in Tables 16.1 and 16.2
Introduction
Determination of Young's Modulus Formula from the Expressions of the Table 16.1 of Chapter 16
Determination of Young's Modulus Formula from the Expression of the Table 16.2 of Chapter 16
Young's Modulus of the Space Time from the Energy Density of the Gravitational Wave
Origin of This Topic
Strain Energy Density in Strength of Material
Strain Energy Density for a Gravitational Wave
Expression of the Young Modulus Y (See [13])
References from the Author and from the Article Published at PRAMANA on August 13, 2020
References Bibliographies - General Culture and Sources of this Book Noted {xx} in the Body of the Text
For the Mechanics of Structures
Strength of Material of Beams
Strength of Material Plate
Matrix Calculations of Structures
Eigen Period of String Vibration, Beams and Plates
For General Relativity
For Quantum Mechanics
Quantum Curvature
General Lectures in Quantum Mechanics
Quantum Mechanics and Schrodinger in 1-3 Dimensions and Bohr Atom
Spontaneous Symmetry Break
Particles and Waves
For the Waves
For All Subjects
For the Author David Izabel Hal Publications
For Casimir's Force
For Demonstration of Friedmann's Equations
For Special Relativity
For the Concept of Eigen Value and Eigen Mode of Space-Time
For Quantum Field Theory Klein-Gordon-Dirac
For Gravitational Waves
For Laplacian's Own values in Hyper-Spherical Coordinates
Overview of the Topics
Vibrations of the Universe and Space-Time
Duality Waves Particles
Acoustic Sound Energy
Yukawa's Potential
String Theory and Quantum Qravity
Cosmological Diffuse Background
Higgs Boson
Ether
Expansion of Space-Time
Distortion of Space-Time by the Rotation of the Earth - Lense Thirring Effect
Moment of Inertia and Kinetic Energy of Rotating Bodies
Einstein Cartan Kibble Sciama Theory
Twist in RDM
Superfluid Space-Time Without Viscosity
Stiffness of the Space Time
Global Warming of the Universe
Number of Dimensions in the Universe (4) According to Gravitational Waves
Black Hole
Wave Particle Duality - Thermal Fluctuation
Wave Equations in Elasticity
Human Brain Frame and Frame of the Univers
About the Expression of G as a Function of c, f and Y
Terms and Definitions
Definition of the Main General Relativity Terms (Source e-Lecture of General Relativity Initiation of Richard Taillet Teacher-Researcher at Savoie Mont Blanc University)
Synthesis of Formula Links in Einstein's Equation
Key Formula of this Book
About the Author
Summary

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