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Symmetry Rules How Science and Nature Are Founded on Symmetry

:	Joseph Rosen
:	Symmetry Rules How Science and Nature Are Founded on Symmetry
:	Springer-Verlag
:	9783540759737
:	1
:	CHF 47.70
:

:	Allgemeines, Lexika
:	English

:	305
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	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