Scale Transitions as Foundations of Physics

Description

The scale transitions are essential to physical knowledge. The book describes the history of essential moments of physics, viewed as necessary consequences of the unavoidable process of scale transition, and provides the mathematical techniques for the construction of a theoretical physics founded on scale transition. The indispensable mathematical technique is analyticity, helping in the construction of space coordinate systems. The indispensable theoretical technique from physical point of view is the affine theory of surfaces. The connection between the two techniques is provided by a duality in defining the physical properties. Contents Foreword Chapter 1. Classical Moments of Interpretation 1.1 Classical Ether as an Implicit Case of Interpretation 1.2 Physical Description of a Hertz Material Point by Confinement 1.3 Lorentz Matter: Poincar´e Interpretation of Electromagnetic Ether 1.4 Einstein’s Matter: Authentic Matter Interpretation 1.5 Non-Euclidean Geometry as a Gauge Geometry 1.6 De Sitter’s Spacetime 1.7 Schwarzschild Matter: Sphere of Ideal Fluid Chapter 2. Recovering Some Forgotten Roots 2.1 Introducing the Subject: Time, Space and the Idea of Compass 2.2 Necessity of a Cosmology “Newton Himself would Understand” 2.3 A Thermodynamical Argument: Classical Ideal Gas as a Model 2.4 Sufficiency, as a Physical Concept 2.5 A Statistical Interpretation of the Classical Action 2.6 Average Lagrangian as a Statistic: The Transition Amplitude 2.7 The Motivation for a Space–Time Transformation 2.8 An Idea of Morton Lutzky 2.9 Conclusion: Asymptotic Freedom as a Manifestation of Scale Transition Chapter 3. Theory of Regularization of Kepler Problem 3.1 The Distance of Action as a Physical Manifold 3.2 The Analyticity Condition in Regularization Theory 3.3 A Meaning only Newton would be Able to Perceive 3.4 Conclusion: The Coordinate Space and the Ordinary Space Chapter 4. A Natural Condition of Analyticity 4.1 The Three-Dimensional Light Ray and Fractality 4.2 A Three-Dimensional Regularization Procedure and its Physical Meaning 4.3 Coordinates as Measures 4.4 On a Statistics Prompted by Appell’s Coordinates 4.5 An Example of Yang–Mills Fields Related to the Three-Dimensional Regularization Chapter 5. The Physical Structure of Rotating Matter According to Gödel 5.1 Classical Forces and Compass Indications 5.2 Bertrand’s Problem, Binary Stars and the Compass of Inertia 5.3 Berry–Klein Equation of Motion: The Physical Meaning of Regularization Chapter 6. A Geometry of Reverse Interpretation of a Fundamental Physical Structure 6.1 The Case of Cubic Equation with Real Roots 6.2 The Connection between Phase and Time: The Physics of a Compass 6.3 The Relativity as Absolute Geometry Chapter 7. Gravitation: The Case of Anisotropic Relativity 7.1 The Group of Waves as an Ensemble 7.2 A One-Dimensional Anisotropic Relativity 7.3 Vladimir Boltyanskii: A Way of Describing the Gravitation 7.4 A View to Celestial Matter Chapter 8. Classical Theory of Affine Surfaces in Space 8.1 Conditions of Physical Nature on a Surface: The Fubini–Pick Cubic 8.2 General Theory of Equiaffine Reference Frames in Space 8.3 The Existing Physical Incentives 8.4 Conclusions: Historical Line for a Theoretical Physics Conclusions: Historical Line for a Theoretical Physics Bibliography