EDP Sciences 1777041696 20260424 fre

laboutique.edpsciences.fr-001956 03 01 01 001956 03 9782759825738 15 9782759825738 00 BA 02 170 mm 01 240 mm 08 1 gr 10 01 02 Current Natural Sciences 01 01 What is Space-Time Made of ? 1 A01 01 A1961 David IZABEL IZABEL, David David IZABEL David Izabel est un ingénieur mécanicien Français (INSA Rennes - Major de promotion) et professeur au Centre des Hautes Etudes de la Construction. Il a publié différents articles scientifiques de physique sur l’analogie de relativité générale avec la théorie de l’élasticité via l’étude des caractéristiques mécaniques de l’espace-temps (déformations, module d’Young). Il a également publié 5 formulaires sur la théorie des poutres sandwiches et récemment sur l’élasticité de l’espace-temps « what is space time made off ? ». Après 7 ans passés à l’APPAVE comme contrôleur technique spécialiste en structure de bâtiments et de génie civil en acier, bois et béton, il est depuis 22 ans directeur technique de l’Enveloppe Métallique et de l’Institut de l’Enveloppe Métallique en tant que spécialiste en profils minces et panneaux sandwich en acier. Il a publié dans une revue mathématique américaine un article sur la loi de l’évolution du hasard. David Izabel is a French mechanical engineer (INSA Rennes - Valedictorian) and professor at the Center des Hautes Etudes de la Construction. He has published various scientific physics articles on the analogy of general relativity with the theory of elasticity through the study of the mechanical characteristics of space-time (deformations, Young's modulus). He has also published 5 forms on the theory of sandwich beams and recently on the elasticity of space-time “what is space time made off? ". After 7 years spent at APPAVE as a technical controller specializing in building structures and civil engineering in steel, wood and concrete, he has been technical director of the Metallic Envelope and the Institute of the Metallic Envelope for 22 years. as a specialist in thin profiles and steel sandwich panels. He published in an American mathematical journal an article on the law of the evolution of chance. 1 01 eng 00 366 03 01 24 Izibook:Subject Physique Générale 24 Izibook:SubjectAndCategoryAndTags |Physique Générale| 20 General relativity 10 2011 SCI055000 29 3051 29 3058 01 539 05 06 06 03 00 In the first part of this book, the author synthesizes the main results and formulas of physics–Albert Einstein’s, with general relativity, gravitational waves involving elastic deformable space-time, quantum field theory, Heisenberg’s principle, and Casimir’s force implying that a vacuum is not nothingness. In the second part, based on these scientific facts, the author re-studies the fundamental equation of general relativity in a weak gravitational field by unifying it with the theory of elasticity. He considers the Ligo and Virgo interferometers as strain gauges. It follows from this approach that the gravitational constant G, Einstein’s constant κ, can be expressed as a function of the physical, mechanical and elastic characteristics of space-time. He overlaps these results and in particular Young’s modulus of space-time, with publications obtained by renowned scientists. By imposing to satisfy the set of universal constants G, c, κ, ħ and by taking into account the vacuum data, he proposes a new quantum expression of G which is still compatible with existing serious publications. It appears that time becomes the lapse of time necessary to transmit information from one elastic sheet of space to another. Time also becomes elastic. Thus, space becomes an elastic material, with a particle size of the order of the Planck scale, a new deformable ether, therefore different from the non-existent luminiferous ether. Finally, in the third part, in appendices, the author demonstrates the fundamentals of general relativity, cosmology and the theory of elasticity 02 00 A Nice Addition to Looking at the Dynamics of General Relativity through the Window of Elasticity. 04 00 ContentsPreamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IIISymbology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIIIIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVIICHAPTER 1Where is Physics Today? – Synthetic Overview of the State of the Art of Physics Today . . . . . .  . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Newton’s Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Electromagnetism/GravitoElectroMagnetism. . . . . . . . . . . . . . . . . . . . 21.4 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 General Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.7 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.8 Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.9 Highlighting the Differences between the Two Pillars of Physics . . . . . 331.10 Nature Plays with Our Senses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.11 How to Reconcile the Two Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 37CHAPTER 2First Ask the Right Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.1 What is the State of the Art and the Issues that Arise from It? . . . . . 412.2 What is the Nature of Space-Time? . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3 Can Einstein’s Equation be Reconstructed without Passingthrough Newton’s Weak Field Limits? Without Using G? . . . . . . . . . . 422.4 What Brings Us Contemporary Data of the Vacuum? . . . . . . . . . . . . . 442.5 Space-Time as a Physical Object an Elastic Medium . . . . . . . . . . . . . . 45CHAPTER 3A Strange Analogy between S. Timoshenko’s Beam Theory and General Relativity . . . . . . . . . . . . . . . . . . . . 473.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Generalities on General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3 Analogy between Beam Theory and General Relativity fromthe Point of View of the General Principle Curvature = K × EnergyDensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4 Analogy between the Definition of Curvature in Strength of Materialand General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5 Extension of Curvature to Other Strength of Material Solicitations . . . 573.6 Analysis of Einstein’s Equation Applied to the Entire Universe(Case of Cosmology) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63CHAPTER 4The Stress Energy Tensor in Theory of General Relativity and the StressTensor in Elasticity Theory are Similar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Definition of the Stress Energy Tensor in General Relativity . . . . . . . . 654.2 Definition of Stress Tensor in Elasticity Theory . . . . . . . . . . . . . . . . . . 664.3 Demonstration of the Correlation between the Stress Tensor and the Stress Energy Tensor . . . . . . . . . .. . . . . . . . . . . 66CHAPTER 5Relationship between the Metric Tensor and the Strain Tensor in Low Gravitational Field . . . . . . . . . . . . . . . . . . . . 715.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Definition of Strain Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.3 Determination of the Link between the Metric and the Strain . . . . . . . 73CHAPTER 6Relationship between the Stress Tensor and the Strain Tensor in Elasticity(K) and between the Curvature and the Stress Energy Tensor (κ) in General Relativity in Weak Gravitational Fields . .. . . . . . . . 796.1 Reminder of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.2 Some Reminders about the Elasticity Theory . . . . . . . . . . . . . . . . . . . 806.3 Highlighting the Parallelism between Elasticity Theory and General Relativity . . . . . . . . . .  . . . . . . . . . . . . . 816.4 Consequence of Parallelism and Transversalism between the Elasticity Theory and General Relativity. . . .  . . . . . . 83CHAPTER 7Can Space-be Considered as an Elastic Medium? New Ether? . . . . . . . . . . . . 857.1 The Conclusions of Michelson and Morley’s Experiment . . . . . . . . . . . 857.2 Einstein’s View of the Ether . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.3 Observations Made Demonstrate the Elastic Behaviour of Space-Time . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 867.4 Consequence of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91CHAPTER 8And if We Reconstructed the Formula of Einstein’s Gravitational Field by no Longer Considering the Temporal Components of the Tensors, but the Spatial Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938.1 Let Us Step Back from Gravitation According to Newton . . . . . . . . . . 938.2 The Strengths and Weaknesses of Newton’s Gravitational Approach . . 948.3 G a Gravitational Constant of Strange Dimensions as a Combination of Underlying Parameters . . . . . . . . . . . . . . . . . . . . 958.4 How to Re-parameterize κ in Einstein’s Gravitational Field Equation . . 968.5 The Strengths and Weaknesses of Gravitation According to Einstein . . . 978.6 Approach to Reconstructing General Relativity from the Elasticity Theory . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 98CHAPTER 9Re-interpretation of the Results of the Theoretical Calculation of GeneralRelativity on Gravitational Waves in Weak Field from the Windows of Elasticity Theory . . . . . . . . . . . . . 1019.2 Re-interpretation of the 2 Gravitational Wave Polarizations in Terms of Space Deformation Tensors in the Sense of Elasticity Theory . . . . . 1019.3 Consequence in Terms of Oscillating Waves in the Arms of Interferometers . . . . . . . . . . . . . . . . . . . . . . . . 1079.4 Expression of Einstein’s Linearized Gravitational Equation in the Form of Strains . . . . . . . . . . . . . . . . . . . . . 110CHAPTER 10Determination of Poisson’s Ratio of the Elastic Space Material . . . . . . . . . . . 11310.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11310.2 First Approach: Analysis of the Movements of Particles Positioned in Space on a Circle Undergoing the Passage of a Gravitational Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11410.3 Second Approach: In the z Direction, the Gravitational Wave is a Transverse Wave and is Not a Compression Wave .  . 11410.4 Third Approach: Based on Available Datas . . . . . . . . . . . . . . . . . . . . 115CHAPTER 11Dynamic Study of the Elastic Space Strains in an Arm of an Interferometer . . . 11711.1 Study of an Interferometric Arm Subjected to Gravitational WavesCausing Compressions and Tractions of the Volume of Empty Space within It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11711.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11711.1.2 Determination of Tensorial Equations Associated with Each Arm of the Interferometer . . . . . . . . . . . . . . . . . . 119CHAPTER 12Dynamic Study of Simultaneous Elastic Space Strains in the 2 Arms of an Interferometer . . . . .. . . . . . . . . . . 12512.1 Study of Two Interferometric Arms Subjected to Gravitational Waves Resulting in Compression/Traction of the Volume of Space within Them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12612.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12612.1.2 Determination of Tensorial Equation Associated with the Two Arms of the Interferometer . . . . . . . . . . . . . . . 127CHAPTER 13Study of an Elastic Space Cylinder Twisted by the Coalescence of Two Black Holes . . . . . . . .. . . . . . . . . . . . . 13713.1 Study of a Vertical Space Cylinder in Pure Twisting – Use of Shear Speed of the Shear Wave Correlated with the Shear Strains .  13813.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13813.1.2 Determination of Tensorial Equation Associated with Twisting Space Tube . . . . . . . . . . . 139CHAPTER 14New Mechanical Expression of Einstein’s Constant κ . . . . . . . . . . . . . . . . . . 14714.1 Steps to Obtain the Mechanical Conversion of κ . . . . . . . . . . . . . . . . 14814.2 Case where We Consider Only One Interferometer Arm . . . . . . . . . . 14814.3 Cases where the Two Arms of the Interferometer and Poisson’s Ratio are Considered . . . . . . . . . . . . . . . . . . . . . . . . . . 14914.4 Case of a Pure Torsion of Space Tube . . . . . . . . . . . . . . . . . . . . . . . . 149CHAPTER 15Vacuum Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15115.1 Physical Approach or Mathematical Artifact? . . . . . . . . . . . . . . . . . . 15115.2 The Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15215.3 Consistency of Results with Vacuum Data. . . . . . . . . . . . . . . . . . . . . 152CHAPTER 16Calibrating the New Mechanical Expression of κ with the Vacuum Data . . . . 15516.1 Numerical Application to Vacuum Energy – Longitudinal Waves in Interferometric Tubes . . . . . . . . 15616.1.1 Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 15616.1.2 Intensity Obtained for the New G Parameters Based on Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15916.2 Numerical Application to Vacuum Energy – Global Approachby Twist Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15916.2.1 Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 15916.2.2 Intensities Obtained for New G Parameters Based on Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162CHAPTER 17Let’s Go Back to the Time Components Based on the New Results . . . . . . . 16517.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16617.2 Impact on the Time of this Search . . . . . . . . . . . . . . . . . . . . . . . . . . 16617.2.1 Time Behaviour as an Elastic Material . . . . . . . . . . . . . . . . . 16617.2.2 Relating the Time Intervals with the Thickness Fibers of Spatial Space Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169CHAPTER 18Analogy of Mohr’s Circle with Graviton Spin . . . . . . . . . . . . . . . . . . . . . . . . 17518.1 Possible Constitution of Space Material. . . . . . . . . . . . . . . . . . . . . . . 17518.2 Analogy of Mohr’s Circle with Graviton Spin . . . . . . . . . . . . . . . . . . 176CHAPTER 19What if We Gave Up the Constant Character of G? . . . . . . . . . . . . . . . . . . . 179CHAPTER 20How to Test the New Theory? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18120.1 Experimental Test of Young’s Modulus of the Space Medium . . . . . . 18120.2 Experimental Test of Pure Space Shear Behavior . . . . . . . . . . . . . . . 182CHAPTER 21Other Points in Link with the Strength of Material. . . . . . . . . . . . . . . . . . . . 18321.1 An Analysis of the Vibrations of the Space Medium at the Timeof the Big Bang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18321.2 The Plastic Behavior of the Space Medium in Strong Fields . . . . . . . 183CHAPTER 22Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Appendix A – Chronological Order of Progress of the Author’s Reflection and Related Discoveries. . . . . . . . . 193Appendix B – Measurements of Space-Time Material Deformations (Strains and Angles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Appendix C – History of Physics and Related Formulas . . . . . . . . . . . . . . 205Appendix D – Calculating the Scalar Curvature R of a Sphere. . . . . . . . . 207Appendix E – Application of Einstein’s Equation in Cosmology – Demonstration of Friedmann–Lemaitre Equations . . . . . . . 233Appendix F – Can-We Understand a Black Hole from the Strength of the Materials? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279Appendix G – Proof of the Relation between Speed c and the Shear Modulus μ of the Elastic Medium in the Case of Gravitational Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289Appendix H – Proof of Curvature in Beam Theory . . . . . . . . . . . . . . . . . . 297Appendix I – Proof of Quantum Value of Young’s Modulus of Space Space-Time Obtained in Tables 16.1 and 16.2 . . . . . . . . . . 305Appendix J – Young’s Modulus of the Space Time from the Energy Density of the Gravitational Wave . . . . . . . . . 309References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 21 00 06 01 https://laboutique.edpsciences.fr/produit/1190/9782759825745/what-is-space-time-made-of 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/982/431/original/9782759825738-Space-time_couv-sofedis.jpg 17 14 20240913T172645+0200 15 00 04 02 01 E107 04 9782759825738-Space-time_sommaire.pdf 05 0.07 06 2385c0514965d8a5f749cee7a0fcc046 https://laboutique.edpsciences.fr/extract/1533?filename=9782759825738-Space-time_sommaire.pdf&md5sum=2385c0514965d8a5f749cee7a0fcc046&size=71739&title=Sommaire+de+l%27ouvrage 17 14 20210525T133521+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 01 00 20210520 19 00 20210520 2026 06 3052868830012 01 WORLD 27 03 9782759825745 15 9782759825745 WORLD 08 EDP Sciences & Science Press 04 01 00 20210520 03 01 D1 EDP Sciences 21 04 05 01 02 1 00 128.00 01 5.50 6.67 EUR 01 laboutique.edpsciences.fr-R001534 03 01 01 R001534 00 ED E107 02 01 01 What is Space-Time Made of ? 01 eng 08 366 03 22 37341302 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 02 01 001957 03 9782759825745 15 9782759825745 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-001957 03 01 01 001957 03 9782759825745 15 9782759825745 10 EA E107 10 02 01 R001534 ED E107 1 10 01 02 Current Natural Sciences 01 01 What is Space-Time Made of ? 1 A01 01 A1961 David IZABEL IZABEL, David David IZABEL David Izabel est un ingénieur mécanicien Français (INSA Rennes - Major de promotion) et professeur au Centre des Hautes Etudes de la Construction. Il a publié différents articles scientifiques de physique sur l’analogie de relativité générale avec la théorie de l’élasticité via l’étude des caractéristiques mécaniques de l’espace-temps (déformations, module d’Young). Il a également publié 5 formulaires sur la théorie des poutres sandwiches et récemment sur l’élasticité de l’espace-temps « what is space time made off ? ». Après 7 ans passés à l’APPAVE comme contrôleur technique spécialiste en structure de bâtiments et de génie civil en acier, bois et béton, il est depuis 22 ans directeur technique de l’Enveloppe Métallique et de l’Institut de l’Enveloppe Métallique en tant que spécialiste en profils minces et panneaux sandwich en acier. Il a publié dans une revue mathématique américaine un article sur la loi de l’évolution du hasard. David Izabel is a French mechanical engineer (INSA Rennes - Valedictorian) and professor at the Center des Hautes Etudes de la Construction. He has published various scientific physics articles on the analogy of general relativity with the theory of elasticity through the study of the mechanical characteristics of space-time (deformations, Young's modulus). He has also published 5 forms on the theory of sandwich beams and recently on the elasticity of space-time “what is space time made off? ". After 7 years spent at APPAVE as a technical controller specializing in building structures and civil engineering in steel, wood and concrete, he has been technical director of the Metallic Envelope and the Institute of the Metallic Envelope for 22 years. as a specialist in thin profiles and steel sandwich panels. He published in an American mathematical journal an article on the law of the evolution of chance. 1 01 eng 08 366 03 01 24 Izibook:Subject Physique Générale 24 Izibook:SubjectAndCategoryAndTags |Physique Générale| 20 General relativity 10 2011 SCI055000 29 3051 29 3058 01 539 05 06 06 03 00 In the first part of this book, the author synthesizes the main results and formulas of physics–Albert Einstein’s, with general relativity, gravitational waves involving elastic deformable space-time, quantum field theory, Heisenberg’s principle, and Casimir’s force implying that a vacuum is not nothingness. In the second part, based on these scientific facts, the author re-studies the fundamental equation of general relativity in a weak gravitational field by unifying it with the theory of elasticity. He considers the Ligo and Virgo interferometers as strain gauges. It follows from this approach that the gravitational constant G, Einstein’s constant κ, can be expressed as a function of the physical, mechanical and elastic characteristics of space-time. He overlaps these results and in particular Young’s modulus of space-time, with publications obtained by renowned scientists. By imposing to satisfy the set of universal constants G, c, κ, ħ and by taking into account the vacuum data, he proposes a new quantum expression of G which is still compatible with existing serious publications. It appears that time becomes the lapse of time necessary to transmit information from one elastic sheet of space to another. Time also becomes elastic. Thus, space becomes an elastic material, with a particle size of the order of the Planck scale, a new deformable ether, therefore different from the non-existent luminiferous ether. Finally, in the third part, in appendices, the author demonstrates the fundamentals of general relativity, cosmology and the theory of elasticity 02 00 A Nice Addition to Looking at the Dynamics of General Relativity through the Window of Elasticity. 04 00 ContentsPreamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IIISymbology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIIIIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVIICHAPTER 1Where is Physics Today? – Synthetic Overview of the State of the Art of Physics Today . . . . . .  . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Newton’s Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Electromagnetism/GravitoElectroMagnetism. . . . . . . . . . . . . . . . . . . . 21.4 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 General Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.7 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.8 Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.9 Highlighting the Differences between the Two Pillars of Physics . . . . . 331.10 Nature Plays with Our Senses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.11 How to Reconcile the Two Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 37CHAPTER 2First Ask the Right Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.1 What is the State of the Art and the Issues that Arise from It? . . . . . 412.2 What is the Nature of Space-Time? . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3 Can Einstein’s Equation be Reconstructed without Passingthrough Newton’s Weak Field Limits? Without Using G? . . . . . . . . . . 422.4 What Brings Us Contemporary Data of the Vacuum? . . . . . . . . . . . . . 442.5 Space-Time as a Physical Object an Elastic Medium . . . . . . . . . . . . . . 45CHAPTER 3A Strange Analogy between S. Timoshenko’s Beam Theory and General Relativity . . . . . . . . . . . . . . . . . . . . 473.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Generalities on General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3 Analogy between Beam Theory and General Relativity fromthe Point of View of the General Principle Curvature = K × EnergyDensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4 Analogy between the Definition of Curvature in Strength of Materialand General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5 Extension of Curvature to Other Strength of Material Solicitations . . . 573.6 Analysis of Einstein’s Equation Applied to the Entire Universe(Case of Cosmology) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63CHAPTER 4The Stress Energy Tensor in Theory of General Relativity and the StressTensor in Elasticity Theory are Similar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Definition of the Stress Energy Tensor in General Relativity . . . . . . . . 654.2 Definition of Stress Tensor in Elasticity Theory . . . . . . . . . . . . . . . . . . 664.3 Demonstration of the Correlation between the Stress Tensor and the Stress Energy Tensor . . . . . . . . . .. . . . . . . . . . . 66CHAPTER 5Relationship between the Metric Tensor and the Strain Tensor in Low Gravitational Field . . . . . . . . . . . . . . . . . . . . 715.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Definition of Strain Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.3 Determination of the Link between the Metric and the Strain . . . . . . . 73CHAPTER 6Relationship between the Stress Tensor and the Strain Tensor in Elasticity(K) and between the Curvature and the Stress Energy Tensor (κ) in General Relativity in Weak Gravitational Fields . .. . . . . . . . 796.1 Reminder of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.2 Some Reminders about the Elasticity Theory . . . . . . . . . . . . . . . . . . . 806.3 Highlighting the Parallelism between Elasticity Theory and General Relativity . . . . . . . . . .  . . . . . . . . . . . . . 816.4 Consequence of Parallelism and Transversalism between the Elasticity Theory and General Relativity. . . .  . . . . . . 83CHAPTER 7Can Space-be Considered as an Elastic Medium? New Ether? . . . . . . . . . . . . 857.1 The Conclusions of Michelson and Morley’s Experiment . . . . . . . . . . . 857.2 Einstein’s View of the Ether . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.3 Observations Made Demonstrate the Elastic Behaviour of Space-Time . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 867.4 Consequence of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91CHAPTER 8And if We Reconstructed the Formula of Einstein’s Gravitational Field by no Longer Considering the Temporal Components of the Tensors, but the Spatial Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938.1 Let Us Step Back from Gravitation According to Newton . . . . . . . . . . 938.2 The Strengths and Weaknesses of Newton’s Gravitational Approach . . 948.3 G a Gravitational Constant of Strange Dimensions as a Combination of Underlying Parameters . . . . . . . . . . . . . . . . . . . . 958.4 How to Re-parameterize κ in Einstein’s Gravitational Field Equation . . 968.5 The Strengths and Weaknesses of Gravitation According to Einstein . . . 978.6 Approach to Reconstructing General Relativity from the Elasticity Theory . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 98CHAPTER 9Re-interpretation of the Results of the Theoretical Calculation of GeneralRelativity on Gravitational Waves in Weak Field from the Windows of Elasticity Theory . . . . . . . . . . . . . 1019.2 Re-interpretation of the 2 Gravitational Wave Polarizations in Terms of Space Deformation Tensors in the Sense of Elasticity Theory . . . . . 1019.3 Consequence in Terms of Oscillating Waves in the Arms of Interferometers . . . . . . . . . . . . . . . . . . . . . . . . 1079.4 Expression of Einstein’s Linearized Gravitational Equation in the Form of Strains . . . . . . . . . . . . . . . . . . . . . 110CHAPTER 10Determination of Poisson’s Ratio of the Elastic Space Material . . . . . . . . . . . 11310.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11310.2 First Approach: Analysis of the Movements of Particles Positioned in Space on a Circle Undergoing the Passage of a Gravitational Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11410.3 Second Approach: In the z Direction, the Gravitational Wave is a Transverse Wave and is Not a Compression Wave .  . 11410.4 Third Approach: Based on Available Datas . . . . . . . . . . . . . . . . . . . . 115CHAPTER 11Dynamic Study of the Elastic Space Strains in an Arm of an Interferometer . . . 11711.1 Study of an Interferometric Arm Subjected to Gravitational WavesCausing Compressions and Tractions of the Volume of Empty Space within It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11711.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11711.1.2 Determination of Tensorial Equations Associated with Each Arm of the Interferometer . . . . . . . . . . . . . . . . . . 119CHAPTER 12Dynamic Study of Simultaneous Elastic Space Strains in the 2 Arms of an Interferometer . . . . .. . . . . . . . . . . 12512.1 Study of Two Interferometric Arms Subjected to Gravitational Waves Resulting in Compression/Traction of the Volume of Space within Them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12612.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12612.1.2 Determination of Tensorial Equation Associated with the Two Arms of the Interferometer . . . . . . . . . . . . . . . 127CHAPTER 13Study of an Elastic Space Cylinder Twisted by the Coalescence of Two Black Holes . . . . . . . .. . . . . . . . . . . . . 13713.1 Study of a Vertical Space Cylinder in Pure Twisting – Use of Shear Speed of the Shear Wave Correlated with the Shear Strains .  13813.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13813.1.2 Determination of Tensorial Equation Associated with Twisting Space Tube . . . . . . . . . . . 139CHAPTER 14New Mechanical Expression of Einstein’s Constant κ . . . . . . . . . . . . . . . . . . 14714.1 Steps to Obtain the Mechanical Conversion of κ . . . . . . . . . . . . . . . . 14814.2 Case where We Consider Only One Interferometer Arm . . . . . . . . . . 14814.3 Cases where the Two Arms of the Interferometer and Poisson’s Ratio are Considered . . . . . . . . . . . . . . . . . . . . . . . . . . 14914.4 Case of a Pure Torsion of Space Tube . . . . . . . . . . . . . . . . . . . . . . . . 149CHAPTER 15Vacuum Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15115.1 Physical Approach or Mathematical Artifact? . . . . . . . . . . . . . . . . . . 15115.2 The Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15215.3 Consistency of Results with Vacuum Data. . . . . . . . . . . . . . . . . . . . . 152CHAPTER 16Calibrating the New Mechanical Expression of κ with the Vacuum Data . . . . 15516.1 Numerical Application to Vacuum Energy – Longitudinal Waves in Interferometric Tubes . . . . . . . . 15616.1.1 Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 15616.1.2 Intensity Obtained for the New G Parameters Based on Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15916.2 Numerical Application to Vacuum Energy – Global Approachby Twist Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15916.2.1 Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 15916.2.2 Intensities Obtained for New G Parameters Based on Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162CHAPTER 17Let’s Go Back to the Time Components Based on the New Results . . . . . . . 16517.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16617.2 Impact on the Time of this Search . . . . . . . . . . . . . . . . . . . . . . . . . . 16617.2.1 Time Behaviour as an Elastic Material . . . . . . . . . . . . . . . . . 16617.2.2 Relating the Time Intervals with the Thickness Fibers of Spatial Space Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169CHAPTER 18Analogy of Mohr’s Circle with Graviton Spin . . . . . . . . . . . . . . . . . . . . . . . . 17518.1 Possible Constitution of Space Material. . . . . . . . . . . . . . . . . . . . . . . 17518.2 Analogy of Mohr’s Circle with Graviton Spin . . . . . . . . . . . . . . . . . . 176CHAPTER 19What if We Gave Up the Constant Character of G? . . . . . . . . . . . . . . . . . . . 179CHAPTER 20How to Test the New Theory? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18120.1 Experimental Test of Young’s Modulus of the Space Medium . . . . . . 18120.2 Experimental Test of Pure Space Shear Behavior . . . . . . . . . . . . . . . 182CHAPTER 21Other Points in Link with the Strength of Material. . . . . . . . . . . . . . . . . . . . 18321.1 An Analysis of the Vibrations of the Space Medium at the Timeof the Big Bang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18321.2 The Plastic Behavior of the Space Medium in Strong Fields . . . . . . . 183CHAPTER 22Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Appendix A – Chronological Order of Progress of the Author’s Reflection and Related Discoveries. . . . . . . . . 193Appendix B – Measurements of Space-Time Material Deformations (Strains and Angles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Appendix C – History of Physics and Related Formulas . . . . . . . . . . . . . . 205Appendix D – Calculating the Scalar Curvature R of a Sphere. . . . . . . . . 207Appendix E – Application of Einstein’s Equation in Cosmology – Demonstration of Friedmann–Lemaitre Equations . . . . . . . 233Appendix F – Can-We Understand a Black Hole from the Strength of the Materials? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279Appendix G – Proof of the Relation between Speed c and the Shear Modulus μ of the Elastic Medium in the Case of Gravitational Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289Appendix H – Proof of Curvature in Beam Theory . . . . . . . . . . . . . . . . . . 297Appendix I – Proof of Quantum Value of Young’s Modulus of Space Space-Time Obtained in Tables 16.1 and 16.2 . . . . . . . . . . 305Appendix J – Young’s Modulus of the Space Time from the Energy Density of the Gravitational Wave . . . . . . . . . 309References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 21 00 06 01 https://laboutique.edpsciences.fr/produit/1190/9782759825745/what-is-space-time-made-of 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/982/431/original/9782759825738-Space-time_couv-sofedis.jpg 17 14 20240913T172645+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 01 00 20210520 19 00 20210520 2026 06 3052868830012 01 WORLD 13 03 9782759825738 15 9782759825738 WORLD 08 EDP Sciences & Science Press 04 01 00 20210520 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 88.99 01 5.50 4.64 EUR 01 04 06 01 02 1 00 310.99 01 5.50 4.64 EUR 01 04 06 01 02 1 00 342.09 01 5.50 17.83 USD