What is Space-Time Made of ?, livre ebook

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

Contents

Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III

Symbology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIII

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVII

CHAPTER 1

Where is Physics Today? – Synthetic Overview of the State of the Art of Physics Today . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Newton’s Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Electromagnetism/GravitoElectroMagnetism. . . . . . . . . . . . . . . . . . . . 2

1.4 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 General Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.7 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.8 Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.9 Highlighting the Differences between the Two Pillars of Physics . . . . . 33

1.10 Nature Plays with Our Senses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.11 How to Reconcile the Two Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

CHAPTER 2

First Ask the Right Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.1 What is the State of the Art and the Issues that Arise from It? . . . . . 41

2.2 What is the Nature of Space-Time? . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.3 Can Einstein’s Equation be Reconstructed without Passing

through Newton’s Weak Field Limits? Without Using G? . . . . . . . . . . 42

2.4 What Brings Us Contemporary Data of the Vacuum? . . . . . . . . . . . . . 44

2.5 Space-Time as a Physical Object an Elastic Medium . . . . . . . . . . . . . . 45

CHAPTER 3

A Strange Analogy between S. Timoshenko’s Beam Theory and General Relativity . . . . . . . . . . . . . . . . . . . . 47

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Generalities on General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.3 Analogy between Beam Theory and General Relativity from

the Point of View of the General Principle Curvature = K × Energy

Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.4 Analogy between the Definition of Curvature in Strength of Material

and General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5 Extension of Curvature to Other Strength of Material Solicitations . . . 57

3.6 Analysis of Einstein’s Equation Applied to the Entire Universe

(Case of Cosmology) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

CHAPTER 4

The Stress Energy Tensor in Theory of General Relativity and the Stress

Tensor in Elasticity Theory are Similar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.1 Definition of the Stress Energy Tensor in General Relativity . . . . . . . . 65

4.2 Definition of Stress Tensor in Elasticity Theory . . . . . . . . . . . . . . . . . . 66

4.3 Demonstration of the Correlation between the Stress Tensor and the Stress Energy Tensor . . . . . . . . . .. . . . . . . . . . . 66

CHAPTER 5

Relationship between the Metric Tensor and the Strain Tensor in Low Gravitational Field . . . . . . . . . . . . . . . . . . . . 71

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.2 Definition of Strain Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.3 Determination of the Link between the Metric and the Strain . . . . . . . 73

CHAPTER 6

Relationship 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 . .. . . . . . . . 79

6.1 Reminder of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.2 Some Reminders about the Elasticity Theory . . . . . . . . . . . . . . . . . . . 80

6.3 Highlighting the Parallelism between Elasticity Theory and General Relativity . . . . . . . . . . . . . . . . . . . . . . . 81

6.4 Consequence of Parallelism and Transversalism between the Elasticity Theory and General Relativity. . . . . . . . . . 83

CHAPTER 7

Can Space-be Considered as an Elastic Medium? New Ether? . . . . . . . . . . . . 85

7.1 The Conclusions of Michelson and Morley’s Experiment . . . . . . . . . . . 85

7.2 Einstein’s View of the Ether . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.3 Observations Made Demonstrate the Elastic Behaviour of Space-Time . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 86

7.4 Consequence of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

CHAPTER 8

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

8.1 Let Us Step Back from Gravitation According to Newton . . . . . . . . . . 93

8.2 The Strengths and Weaknesses of Newton’s Gravitational Approach . . 94

8.3 G a Gravitational Constant of Strange Dimensions as a Combination of Underlying Parameters . . . . . . . . . . . . . . . . . . . . 95

8.4 How to Re-parameterize κ in Einstein’s Gravitational Field Equation . . 96

8.5 The Strengths and Weaknesses of Gravitation According to Einstein . . . 97

8.6 Approach to Reconstructing General Relativity from the Elasticity Theory . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 98

CHAPTER 9

Re-interpretation of the Results of the Theoretical Calculation of General

Relativity on Gravitational Waves in Weak Field from the Windows of Elasticity Theory . . . . . . . . . . . . . 101

9.2 Re-interpretation of the 2 Gravitational Wave Polarizations in Terms of Space Deformation Tensors in the Sense of Elasticity Theory . . . . . 101

9.3 Consequence in Terms of Oscillating Waves in the Arms of Interferometers . . . . . . . . . . . . . . . . . . . . . . . . 107

9.4 Expression of Einstein’s Linearized Gravitational Equation in the Form of Strains . . . . . . . . . . . . . . . . . . . . . 110

CHAPTER 10

Determination of Poisson’s Ratio of the Elastic Space Material . . . . . . . . . . . 113

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

10.2 First Approach: Analysis of the Movements of Particles Positioned in Space on a Circle Undergoing the Passage of a Gravitational Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

10.3 Second Approach: In the z Direction, the Gravitational Wave is a Transverse Wave and is Not a Compression Wave . . 114

10.4 Third Approach: Based on Available Datas . . . . . . . . . . . . . . . . . . . . 115

CHAPTER 11

Dynamic Study of the Elastic Space Strains in an Arm of an Interferometer . . . 117

11.1 Study of an Interferometric Arm Subjected to Gravitational Waves

Causing Compressions and Tractions of the Volume of Empty Space within It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

11.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

11.1.2 Determination of Tensorial Equations Associated with Each Arm of the Interferometer . . . . . . . . . . . . . . . . . . 119

CHAPTER 12

Dynamic Study of Simultaneous Elastic Space Strains in the 2 Arms of an Interferometer . . . . .. . . . . . . . . . . 125

12.1 Study of Two Interferometric Arms Subjected to Gravitational Waves Resulting in Compression/Traction of the Volume of Space within Them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

12.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

12.1.2 Determination of Tensorial Equation Associated with the Two Arms of the Interferometer . . . . . . . . . . . . . . . 127

CHAPTER 13

Study of an Elastic Space Cylinder Twisted by the Coalescence of Two Black Holes . . . . . . . .. . . . . . . . . . . . . 137

13.1 Study of a Vertical Space Cylinder in Pure Twisting – Use of Shear Speed of the Shear Wave Correlated with the Shear Strains . 138

13.1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

13.1.2 Determination of Tensorial Equation Associated with Twisting Space Tube . . . . . . . . . . . 139

CHAPTER 14

New Mechanical Expression of Einstein’s Constant κ . . . . . . . . . . . . . . . . . . 147

14.1 Steps to Obtain the Mechanical Conversion of κ . . . . . . . . . . . . . . . . 148

14.2 Case where We Consider Only One Interferometer Arm . . . . . . . . . . 148

14.3 Cases where the Two Arms of the Interferometer and Poisson’s Ratio are Considered . . . . . . . . . . . . . . . . . . . . . . . . . . 149

14.4 Case of a Pure Torsion of Space Tube . . . . . . . . . . . . . . . . . . . . . . . . 149

CHAPTER 15

Vacuum Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

15.1 Physical Approach or Mathematical Artifact? . . . . . . . . . . . . . . . . . . 151

15.2 The Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

15.3 Consistency of Results with Vacuum Data. . . . . . . . . . . . . . . . . . . . . 152

CHAPTER 16

Calibrating the New Mechanical Expression of κ with the Vacuum Data . . . . 155

16.1 Numerical Application to Vacuum Energy – Longitudinal Waves in Interferometric Tubes . . . . . . . . 156

16.1.1 Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

16.1.2 Intensity Obtained for the New G Parameters Based on Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

16.2 Numerical Application to Vacuum Energy – Global Approach

by Twist Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

16.2.1 Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

16.2.2 Intensities Obtained for New G Parameters Based on Vacuum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

CHAPTER 17

Let’s Go Back to the Time Components Based on the New Results . . . . . . . 165

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

17.2 Impact on the Time of this Search . . . . . . . . . . . . . . . . . . . . . . . . . . 166

17.2.1 Time Behaviour as an Elastic Material . . . . . . . . . . . . . . . . . 166

17.2.2 Relating the Time Intervals with the Thickness Fibers of Spatial Space Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

CHAPTER 18

Analogy of Mohr’s Circle with Graviton Spin . . . . . . . . . . . . . . . . . . . . . . . . 175

18.1 Possible Constitution of Space Material. . . . . . . . . . . . . . . . . . . . . . . 175

18.2 Analogy of Mohr’s Circle with Graviton Spin . . . . . . . . . . . . . . . . . . 176

CHAPTER 19

What if We Gave Up the Constant Character of G? . . . . . . . . . . . . . . . . . . . 179

CHAPTER 20

How to Test the New Theory? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

20.1 Experimental Test of Young’s Modulus of the Space Medium . . . . . . 181

20.2 Experimental Test of Pure Space Shear Behavior . . . . . . . . . . . . . . . 182

CHAPTER 21

Other Points in Link with the Strength of Material. . . . . . . . . . . . . . . . . . . . 183

21.1 An Analysis of the Vibrations of the Space Medium at the Time

of the Big Bang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

21.2 The Plastic Behavior of the Space Medium in Strong Fields . . . . . . . 183

CHAPTER 22

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Appendix A – Chronological Order of Progress of the Author’s Reflection and Related Discoveries. . . . . . . . . 193

Appendix B – Measurements of Space-Time Material Deformations (Strains and Angles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Appendix C – History of Physics and Related Formulas . . . . . . . . . . . . . . 205

Appendix D – Calculating the Scalar Curvature R of a Sphere. . . . . . . . . 207

Appendix E – Application of Einstein’s Equation in Cosmology – Demonstration of Friedmann–Lemaitre Equations . . . . . . . 233

Appendix F – Can-We Understand a Black Hole from the Strength of the Materials? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

Appendix G – Proof of the Relation between Speed c and the Shear Modulus μ of the Elastic Medium in the Case of Gravitational Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Appendix H – Proof of Curvature in Beam Theory . . . . . . . . . . . . . . . . . . 297

Appendix I – Proof of Quantum Value of Young’s Modulus of Space Space-Time Obtained in Tables 16.1 and 16.2 . . . . . . . . . . 305

Appendix J – Young’s Modulus of the Space Time from the Energy Density of the Gravitational Wave . . . . . . . . . 309

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343