Symmetry rules [Texte imprimé] : how science and nature are founded on symmetry / by Joseph Rosen

Bibliogr. p. [289]-295

Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance.

1 The Concept of Symmetry 1 -- 1.1 The Essence of Symmetry 1 -- 1.2 Symmetry Implies Asymmetry 8 -- 1.3 Analogy and Classification Are Symmetry 10 -- 2 Science Is Founded on Symmetry 17 -- 2.1 Science 17 -- 2.2 Reduction Is Symmetry 20 -- 2.2.1 Reduction to Observer and Observed 22 -- 2.2.2 Reduction to Quasi-Isolated System and Environment 25 -- 2.2.3 Reduction to Initial State and Evolution 26 -- 2.3 Reproducibility Is Symmetry 29 -- 2.4 Predictability Is Symmetry 32 -- 2.5 Analogy in Science 35 -- 2.6 Symmetry at the Foundation of Science 37 -- 3 Symmetry in Physics 39 -- 3.1 Symmetry of Evolution 40 -- 3.2 Symmetry of States 44 -- 3.3 Reference Frame 49 -- 3.4 Global, Inertial, and Local Reference Frames 53 -- 3.5 Gauge Transformation 55 -- 3.6 Gauge Symmetry 58 -- 3.7 Symmetry and Conservation 65 -- 3.7.1 Conservation of Energy 66 -- 3.7.2 Conservation of Linear Momentum 67 -- 3.7.3 Conservation of Angular Momentum 68 -- 3.8 Symmetry at the Foundation of Physics 70 -- 3.9 Symmetry at the Foundation of Quantum Theory 71 -- 3.9.1 Association of a Hilbert Space with a Physical System 71 -- 3.9.2 Correspondence of Observables to Hermitian Operators 73 -- 3.9.3 Complete Set of Compatible Observables 74 -- 3.9.4 Heisenberg Commutation Relations 75 -- 3.9.5 Operators for Canonical Variables 75 -- 3.9.6 A Measurement Result Is an Eigenvalue 75 -- 3.9.7 Expectation Values and Probabilities 76 -- 3.9.8 The Hamiltonian Operator 76 -- 3.9.9 Planck's Constant as a Parameter 77 -- 3.9.10 The Correspondence Principle 77 -- 4 The Symmetry Principle 81 -- 4.1 Causal Relation 81 -- 4.2 Equivalence Relation, Equivalence Class 86 -- 4.3 The Equivalence Principle 89 -- 4.4 The Symmetry Principle 97 -- 4.5 Cause and Effect in Quantum Systems 102 -- 5 Application of Symmetry 107 -- 5.1 Minimalistic Use of the Symmetry Principle 107 -- 5.2 Maximalistic Use of the Symmetry Principle 125 -- 6 Approximate Symmetry, Spontaneous Symmetry Breaking 131 -- 6.1 Approximate Symmetry 131 -- 6.2 Spontaneous Symmetry Breaking 135 -- 7 Cosmic Considerations 141 -- 7.1 Symmetry of the Laws of Nature 141 -- 7.2 Symmetry of the Universe 144 -- 7.3 No Cosmic Symmetry Breaking or Restoration 147 -- 7.4 The Quantum Era and The Beginning 155 -- 8 The Mathematics of Symmetry: Group Theory 161 -- 8.1 Group 161 -- 8.2 Mapping 176 -- 8.3 Isomorphism 180 -- 8.4 Homomorphism 186 -- 8.5 Subgroup 192 -- 9 Group Theory Continued 195 -- 9.1 Conjugacy, Invariant Subgroup, Kernel 195 -- 9.2 Coset Decomposition 203 -- 9.3 Factor Group 207 -- 9.4 Anatomy of Homomorphism 209 -- 9.5 Generator 215 -- 9.6 Direct Product 217 -- 9.7 Permutation, Symmetric Group 220 -- 9.8 Cayley's Theorem 224 -- 10 The Formalism of Symmetry 227 -- 10.1 System, State 227 -- 10.2 Transformation, Transformation Group 229 -- 10.3 Transformations in Space, Time, and Space-Time 236 -- 10.4 State Equivalence 240 -- 10.5 Symmetry Transformation, Symmetry Group 243 -- 10.6 Approximate Symmetry Transformation 251 -- 10.7 Quantification of Symmetry 253 -- 10.8 Quantum Systems 255 -- 11 Symmetry in Processes 261 -- 11.1 Symmetry of the Laws of Nature 261 -- 11.2 Symmetry of Initial and Final States, the General Symmetry Evolution Principle 270 -- 11.3 The Special Symmetry Evolution Principle and Entropy 274 -- 12 Summary of Principles 283 -- 12.1 Symmetry and Asymmetry 283 -- 12.2 Symmetry Implies Asymmetry 283 -- 12.3 No Exact Symmetry of the Universe 284 -- 12.4 Cosmological Implications 285 -- 12.5 The Equivalence Principle 285 -- 12.6 The Symmetry Principle 285 -- 12.7 The Equivalence Principle for Processes 286 -- 12.8 The Symmetry Principle for Processes 286 -- 12.9 The General Symmetry Evolution Principle 286 -- 12.10 The Special Symmetry Evolution Principle 286.