Rosen Symmetry Rules

How Science and Nature Are Founded on Symmetry
1. Auflage 2008
ISBN: 978-3-540-75973-7
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 305 Seiten

Ernest Rutherford (New Zealand–British physicist, 1871–1937), the 1908 Nobel Laureate who discovered the existence of atomic nuclei, is famously quoted as having said: “Physics is the only real science. All the rest is butter?y collecting.” Or something to that e?ect. I like to include this quote in my introductory remarks at the ?rst class meetings of the physics courses I teach. I have seen that there are those whointerpret this as a put-down of amateurs (butter?y collectors) in science. However, my own interp- tation of Rutherford’s statement is that he is claiming that, except for physics, all of the rest of science is involved merely in collecting facts and classifying them (butter?y collecting). It is physics, uniqueamong the sciences, that is attempting to ?nd explanations for the classi?ed data. The periodic table of the chemical elements, originally proposed by DmitriIvanovichMendeleev(Russianchemist,1834–1907), presentsan example of this. Chemists toiled to discover the chemical elements and their properties and then classi?ed the elements in the scheme that is expressed by the periodic table. Here was the chemists’ butter?y collecting. It took physicists to explaintheperiodictablebymeansof quantum theory.

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