Scale Transitions as Foundations of Physics

429 Pages·2021·13.031 MB·English

by  Ioan Merches, Maricel Agop, Nicolae Mazilu

Scale Transitions
as Foundations
of Physics
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Scale Transitions
as Foundations
of Physics
Nicolae Mazilu
University of Akron, Ohio, USA
Maricel Agop
Asachi Technical University, Iasi, Romania
Ioan Merches
Al. I. Cuza University, Iasi, Romania
World Scientific
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SCALE TRANSITIONS AS FOUNDATIONS OF PHYSICS
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“If I were again beginning my studies, I would follow the advice of
Plato and start with mathematics”
Galileo Galilei
v
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Contents
Foreword xi
Chapter 1. Classical Moments of Interpretation 1
1.1 Classical Ether as an Implicit Case
of Interpretation . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Physical Description of a Hertz Material Point
by Confinement . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Lorentz Matter: Poincar´e Interpretation
of Electromagnetic Ether . . . . . . . . . . . . . . . . . 24
1.4 Einstein’s Matter: Authentic Matter
Interpretation . . . . . . . . . . . . . . . . . . . . . . . . 45
1.5 Non-Euclidean Geometry as a Gauge
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
1.6 De Sitter’s Spacetime . . . . . . . . . . . . . . . . . . . 57
1.7 Schwarzschild Matter: Sphere of Ideal Fluid . . . . . 68
Chapter 2. Recovering Some Forgotten Roots 77
2.1 Introducing the Subject: Time, Space and the Idea
of Compass . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.2 Necessity of a Cosmology “Newton Himself would
Understand” . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.3 A Thermodynamical Argument: Classical
Ideal Gas as a Model. . . . . . . . . . . . . . . . . . . . 88
2.4 Sufficiency, as a Physical Concept . . . . . . . . . . . 94
2.5 A Statistical Interpretation of the Classical
Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
vii
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viii Scale Transitions as Foundations of Physics
2.6 Average Lagrangian as a Statistic: The Transition
Amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.7 The Motivation for a Space–Time
Transformation . . . . . . . . . . . . . . . . . . . . . . . 117
2.8 An Idea of Morton Lutzky . . . . . . . . . . . . . . . . 126
2.9 Conclusion: Asymptotic Freedom as a
Manifestation of Scale Transition . . . . . . . . . . . . 127
Chapter 3. Theory of Regularization of Kepler
Problem 137
3.1 The Distance of Action as a Physical Manifold . . . 140
3.2 The Analyticity Condition in Regularization
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.3 A Meaning only Newton would be
Able to Perceive . . . . . . . . . . . . . . . . . . . . . . . 154
3.4 Conclusion: The Coordinate Space and the
Ordinary Space . . . . . . . . . . . . . . . . . . . . . . . 167
Chapter 4. A Natural Condition of Analyticity 171
4.1 The Three-Dimensional Light Ray and
Fractality . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
4.2 A Three-Dimensional Regularization Procedure
and its Physical Meaning . . . . . . . . . . . . . . . . . 200
4.3 Coordinates as Measures . . . . . . . . . . . . . . . . . 203
4.4 On a Statistics Prompted by Appell’s
Coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.5 An Example of Yang–Mills Fields Related to the
Three-Dimensional Regularization . . . . . . . . . . . 214
Chapter 5. The Physical Structure of Rotating
Matter According to Go¨del 221
5.1 Classical Forces and Compass Indications . . . . . . 227
5.2 Bertrand’s Problem, Binary Stars and the
Compass of Inertia . . . . . . . . . . . . . . . . . . . . . 230
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Contents ix
5.3 Berry–Klein Equation of Motion: The Physical
Meaning of Regularization . . . . . . . . . . . . . . . . 246
Chapter 6. A Geometry of Reverse
Interpretation of a Fundamental
Physical Structure 255
6.1 The Case of Cubic Equation with Real Roots . . . . 258
6.2 The Connection between Phase and Time:
The Physics of a Compass . . . . . . . . . . . . . . . . 272
6.3 The Relativity as Absolute Geometry . . . . . . . . . 276
Chapter 7. Gravitation: The Case
of Anisotropic Relativity 289
7.1 The Group of Waves as an Ensemble . . . . . . . . . 296
7.2 A One-Dimensional Anisotropic Relativity . . . . . . 300
7.3 Vladimir Boltyanskii: A Way of Describing
the Gravitation . . . . . . . . . . . . . . . . . . . . . . . 307
7.4 A View to Celestial Matter . . . . . . . . . . . . . . . . 313
Chapter 8. Classical Theory of Affine Surfaces
in Space 323
8.1 Conditions of Physical Nature on a Surface:
The Fubini–Pick Cubic . . . . . . . . . . . . . . . . . . 330
8.2 General Theory of Equiaffine Reference Frames
in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
8.3 The Existing Physical Incentives . . . . . . . . . . . . 339
8.4 Conclusions: Historical Line for a Theoretical
Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
Conclusions: Historical Line for a Theoretical
Physics 359
Bibliography 375