Rosen Symmetry Rules

How Science and Nature Are Founded on Symmetry
2008
ISBN: 978-3-540-75973-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 305 Seiten

Reihe: The Frontiers Collection

When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. Written by a renowned expert, this book will convince all interested readers of the importance of symmetry in science.

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.

Autoren/Hrsg.

Rosen, Joseph

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;1 The Concept of Symmetry;15
3.1;1.1 The Essence of Symmetry;15
3.2;1.2 Symmetry Implies Asymmetry;22
3.3;1.3 Analogy and Classi.cation Are Symmetry;24
3.4;1.4 Summary;29
4;2 Science Is Founded on Symmetry;30
4.1;2.1 Science;30
4.2;2.2 Reduction Is Symmetry;33
4.3;2.3 Reproducibility Is Symmetry;42
4.4;2.4 Predictability Is Symmetry;45
4.5;2.5 Analogy in Science;48
4.6;2.6 Symmetry at the Foundation of Science;50
4.7;2.7 Summary;51
5;3 Symmetry in Physics;52
5.1;3.1 Symmetry of Evolution;53
5.2;3.2 Symmetry of States;57
5.3;3.3 Reference Frame;62
5.4;3.4 Global, Inertial, and Local Reference Frames;66
5.5;3.5 Gauge Transformation;68
5.6;3.6 Gauge Symmetry;71
5.7;3.7 Symmetry and Conservation;78
5.8;3.8 Symmetry at the Foundation of Physics;83
5.9;3.9 Symmetry at the Foundation of Quantum Theory;84
5.10;3.10 Summary;90
6;4 The Symmetry Principle;93
6.1;4.1 Causal Relation;93
6.2;4.2 Equivalence Relation, Equivalence Class;98
6.3;4.3 The Equivalence Principle;101
6.4;4.4 The Symmetry Principle;109
6.5;4.5 Cause and E.ect in Quantum Systems;114
6.6;4.6 Summary;116
7;5 Application of Symmetry;118
7.1;5.1 Minimalistic Use of the Symmetry Principle;118
7.2;5.2 Maximalistic Use of the Symmetry Principle;136
7.3;5.3 Summary;141
8;6 Approximate Symmetry, Spontaneous Symmetry Breaking;142
8.1;6.1 Approximate Symmetry;142
8.2;6.2 Spontaneous Symmetry Breaking;146
8.3;6.3 Summary;151
9;7 Cosmic Considerations;152
9.1;7.1 Symmetry of the Laws of Nature;152
9.2;7.2 Symmetry of the Universe;155
9.3;7.3 No Cosmic Symmetry Breaking or Restoration;158
9.4;7.4 The Quantum Era and The Beginning;166
9.5;7.5 Summary;170
10;8 The Mathematics of Symmetry: Group Theory;172
10.1;8.1 Group;172
10.2;8.2 Mapping;187
10.3;8.3 Isomorphism;191
10.4;8.4 Homomorphism;197
10.5;8.5 Subgroup;203
10.6;8.6 Summary;205
11;9 Group Theory Continued;206
11.1;9.1 Conjugacy, Invariant Subgroup, Kernel;206
11.2;9.2 Coset Decomposition;214
11.3;9.3 Factor Group;218
11.4;9.4 Anatomy of Homomorphism;220
11.5;9.5 Generator;226
11.6;9.6 Direct Product;228
11.7;9.7 Permutation, Symmetric Group;231
11.8;9.8 Cayley’s Theorem;235
11.9;9.9 Summary;237
12;10 The Formalism of Symmetry;238
12.1;10.1 System, State;238
12.2;10.2 Transformation, Transformation Group;240
12.3;10.3 Transformations in Space, Time, and Space-Time;247
12.4;10.4 State Equivalence;251
12.5;10.5 Symmetry Transformation, Symmetry Group;254
12.6;10.6 Approximate Symmetry Transformation;262
12.7;10.7 Quanti.cation of Symmetry;264
12.8;10.8 Quantum Systems;266
12.9;10.9 Summary;269
13;11 Symmetry in Processes;271
13.1;11.1 Symmetry of the Laws of Nature;271
13.2;11.2 Symmetry of Initial and Final States, the General Symmetry Evolution Principle;280
13.3;11.3 The Special Symmetry Evolution Principle and Entropy;284
13.4;11.4 Summary;290
14;12 Summary of Principles;292
14.1;12.1 Symmetry and Asymmetry;292
14.2;12.2 Symmetry Implies Asymmetry;292
14.3;12.3 No Exact Symmetry of the Universe;293
14.4;12.4 Cosmological Implications;294
14.5;12.5 The Equivalence Principle;294
14.6;12.6 The Symmetry Principle;294
14.7;12.7 The Equivalence Principle for Processes;295
14.8;12.8 The Symmetry Principle for Processes;295
14.9;12.9 The General Symmetry Evolution Principle;295
14.10;12.10 The Special Symmetry Evolution Principle;295
15;References;297
16;Index;304