Symmetry Rules (eBook)

A theoretical physicist, Joe Rosen was for many years a member of the School of Physics and Astronomy of Tel Aviv University and also served as chair of the Department of Physics and Astronomy of the University of Central Arkansas. He has authored or edited eleven books, and many of his publications have dealt with various aspects of symmetry in physics and in science. Now semi-retired from academe, Joe Rosen is involved in research, writing, and physics teaching as adjunct professor at universities and colleges in the Washington DC area.

Preface 7
Contents 11
1 The Concept of Symmetry 15
1.1 The Essence of Symmetry 15
1.2 Symmetry Implies Asymmetry 22
1.3 Analogy and Classi.cation Are Symmetry 24
1.4 Summary 29
2 Science Is Founded on Symmetry 30
2.1 Science 30
2.2 Reduction Is Symmetry 33
2.3 Reproducibility Is Symmetry 42
2.4 Predictability Is Symmetry 45
2.5 Analogy in Science 48
2.6 Symmetry at the Foundation of Science 50
2.7 Summary 51
3 Symmetry in Physics 52
3.1 Symmetry of Evolution 53
3.2 Symmetry of States 57
3.3 Reference Frame 62
3.4 Global, Inertial, and Local Reference Frames 66
3.5 Gauge Transformation 68
3.6 Gauge Symmetry 71
3.7 Symmetry and Conservation 78
3.8 Symmetry at the Foundation of Physics 83
3.9 Symmetry at the Foundation of Quantum Theory 84
3.10 Summary 90
4 The Symmetry Principle 93
4.1 Causal Relation 93
4.2 Equivalence Relation, Equivalence Class 98
4.3 The Equivalence Principle 101
4.4 The Symmetry Principle 109
4.5 Cause and E.ect in Quantum Systems 114
4.6 Summary 116
5 Application of Symmetry 118
5.1 Minimalistic Use of the Symmetry Principle 118
5.2 Maximalistic Use of the Symmetry Principle 136
5.3 Summary 141
6 Approximate Symmetry, Spontaneous Symmetry Breaking 142
6.1 Approximate Symmetry 142
6.2 Spontaneous Symmetry Breaking 146
6.3 Summary 151
7 Cosmic Considerations 152
7.1 Symmetry of the Laws of Nature 152
7.2 Symmetry of the Universe 155
7.3 No Cosmic Symmetry Breaking or Restoration 158
7.4 The Quantum Era and The Beginning 166
7.5 Summary 170
8 The Mathematics of Symmetry: Group Theory 172
8.1 Group 172
8.2 Mapping 187
8.3 Isomorphism 191
8.4 Homomorphism 197
8.5 Subgroup 203
8.6 Summary 205
9 Group Theory Continued 206
9.1 Conjugacy, Invariant Subgroup, Kernel 206
9.2 Coset Decomposition 214
9.3 Factor Group 218
9.4 Anatomy of Homomorphism 220
9.5 Generator 226
9.6 Direct Product 228
9.7 Permutation, Symmetric Group 231
9.8 Cayley’s Theorem 235
9.9 Summary 237
10 The Formalism of Symmetry 238
10.1 System, State 238
10.2 Transformation, Transformation Group 240
10.3 Transformations in Space, Time, and Space-Time 247
10.4 State Equivalence 251
10.5 Symmetry Transformation, Symmetry Group 254
10.6 Approximate Symmetry Transformation 262
10.7 Quanti.cation of Symmetry 264
10.8 Quantum Systems 266
10.9 Summary 269
11 Symmetry in Processes 271
11.1 Symmetry of the Laws of Nature 271
11.2 Symmetry of Initial and Final States, the General Symmetry Evolution Principle 280
11.3 The Special Symmetry Evolution Principle and Entropy 284
11.4 Summary 290
12 Summary of Principles 292
12.1 Symmetry and Asymmetry 292
12.2 Symmetry Implies Asymmetry 292
12.3 No Exact Symmetry of the Universe 293
12.4 Cosmological Implications 294
12.5 The Equivalence Principle 294
12.6 The Symmetry Principle 294
12.7 The Equivalence Principle for Processes 295
12.8 The Symmetry Principle for Processes 295
12.9 The General Symmetry Evolution Principle 295
12.10 The Special Symmetry Evolution Principle 295
References 297
Index 304