The unification of the laws of physics – a legitimate and long-standing aspiration – is undertaken here using the framework of discrete mechanics. Towards a Unification of the Laws of Physics in Classical Fields Theory extends these concepts to classical field physics.
This book examines and revisits the fundamental principles of physics to derive a unified law of motion capable of modeling the phenomena observed, which are currently described by disparate laws. The global reference frames of classical mechanics and relativity are abandoned: space is defined from a one-dimensional local reference frame, and time is considered discrete. Applying the principle of parsimony to the derivation of this single law leads to the rejection of many concepts from classical mechanics and relativity, retaining only proper acceleration as the sole absolute quantity.
The construction of this unified law of motion paves the way for a rational resolution of phenomena relating to mechanics, special and general relativity, electromagnetism and, more broadly, physics as a whole
Table of Contents:
Preface xi
List of Symbols xv
Chapter 1. Objections and Rebuttals of Current Laws 1
1.1. Discussion on the general concepts 1
1.2. Objections to the equations of classical mechanics 8
Chapter 2. A Different View of Space and Time 15
2.1. Maxwell's local frame of reference 15
2.2. Length and time 17
2.3. The local notion of vector in an n-dimensional space 18
2.4. Acceleration, velocity and celerity 22
2.5. Galileo and Lorentz transformations 26
2.6. The genesis of a unified law 27
2.7. Mass or energy 36
2.8. The quantities of a unified physics 38
2.9. A one-dimensional model of space and time 45
Chapter 3. Unified Law of Motion 49
3.1. Dynamics of accelerated motions 49
3.2. Dynamics of uniform expansion and rotational motion 50
3.3. Kinematics of motion in discrete mechanics 54
3.4. Laws of conservation of compressive and rotational energy 57
3.5. Total energy conservation law 59
3.6. Principle of inertia 62
3.7. Helmholtz–Hodge decomposition 69
3.8. Properties of the law of motion 74
3.9. Potential couplings and interaction 77
Chapter 4. Consequences of the Law of Motion 83
4.1. Weak equivalence principle revisited 83
4.2. Velocity limit 89
4.3. Advection 95
4.4. Local primal and dual forms of Bernoulli's law 97
4.5. Invariances and Noether's theorem 101
4.6. Absence of constitutive laws 105
Chapter 5. Fluid Mechanics 107
5.1. Inertia, a concept at the heart of mechanics 107
5.2. Incompressible fluid mechanics 120
5.3. Two-phase flows 133
5.4. Compressible flows 152
Chapter 6. Fluid–Structure Interactions and Porous Media 175
6.1. Equation of motion for a solid 176
6.2. Connection conditions 179
6.3. Some examples 182
6.4. Other constitutive laws 187
6.5. Porous media 190
Chapter 7. Heat Transfer 203
7.1. Introduction 203
7.2. Analysis of the heat transfer equations 204
7.3. An alternative law of heat propagation 208
7.4. A law of discrete transfer 215
7.5. Test cases 226
Chapter 8. Electromagnetism 241
8.1. Introduction 241
8.2. A few remarks about Maxwell's equations 242
8.3. An alternative law of propagation of electromagnetic waves 245
8.4. Some examples 265
8.5. Propagation of light 275
Chapter 9. Relativity, Gravitation 281
9.1. An alternative to the theory of relativity 281
9.2. Wave–energy duality 283
9.3. Photon velocity 286
9.4. Gravitation 291
9.5. Two typical examples 301
9.6. Gravitational redshift 303
9.7. Quantification 309
References 315
Index 327
About the Author :
Jean-Paul Caltagirone is Professor Emeritus at the National Polytechnic Institute of the University of Bordeaux, France. His research focuses on the conservation of acceleration in the field of mechanics, the basis of discrete mechanics, which has now been extended to all classical field physics.
