Holdings: Symmetry rules :: THWS Bibkatalog

Symmetry rules: how science and nature are founded on symmetry

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.

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Bibliographic Details
Main Author:	Rosen, Joe (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2008
Series:	The frontiers collection
Subjects:	Symmetry Symmetrie
Online Access:	Inhaltsverzeichnis
Summary:	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.
Physical Description:	XIV, 304 S. graph. Darst.
ISBN:	9783540759720

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MARC


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_version_	1804137486561050624
adam_text	CONTENTS 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 1.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 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 2.7 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 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 XII CONTENTS 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 PLANCKS CONSTANT AS A PARAMETER . . . . . . . . . . . 77 3.9.10 THE CORRESPONDENCE PRINCIPLE. . . . . . . . . . . . . . . 77 3.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 4.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5 APPLICATION OF SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.1 MINIMALISTIC USE OF THE SYMMETRY PRINCIPLE . . . . . . . . . 107 5.2 MAXIMALISTIC USE OF THE SYMMETRY PRINCIPLE. . . . . . . . . 125 5.3 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 CONTENTS XIII 6 APPROXIMATE SYMMETRY, SPONTANEOUS SYMMETRY BREAKING . . . . . . . . . . . . . . . . . . . 131 6.1 APPROXIMATE SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.2 SPONTANEOUS SYMMETRY BREAKING . . . . . . . . . . . . . . . . . . 135 6.3 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 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 7.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 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 8.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 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 CAYLEYS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 10 THE FORMALISM OF SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . 227 10.1 SYSTEM, STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 10.2 TRANSFORMATION, TRANSFORMATION GROUP . . . . . . . . . . . . . 229 XIV CONTENTS 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 10.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 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 11.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 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 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
adam_txt	CONTENTS 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 1.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 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 2.7 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 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 XII CONTENTS 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 PLANCKS CONSTANT AS A PARAMETER . . . . . . . . . . . 77 3.9.10 THE CORRESPONDENCE PRINCIPLE. . . . . . . . . . . . . . . 77 3.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 4.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5 APPLICATION OF SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.1 MINIMALISTIC USE OF THE SYMMETRY PRINCIPLE . . . . . . . . . 107 5.2 MAXIMALISTIC USE OF THE SYMMETRY PRINCIPLE. . . . . . . . . 125 5.3 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 CONTENTS XIII 6 APPROXIMATE SYMMETRY, SPONTANEOUS SYMMETRY BREAKING . . . . . . . . . . . . . . . . . . . 131 6.1 APPROXIMATE SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.2 SPONTANEOUS SYMMETRY BREAKING . . . . . . . . . . . . . . . . . . 135 6.3 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 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 7.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 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 8.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 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 CAYLEYS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 10 THE FORMALISM OF SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . 227 10.1 SYSTEM, STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 10.2 TRANSFORMATION, TRANSFORMATION GROUP . . . . . . . . . . . . . 229 XIV CONTENTS 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 10.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 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 11.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 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 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
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spelling	Rosen, Joe Verfasser aut Symmetry rules how science and nature are founded on symmetry Joe Rosen Berlin [u.a.] Springer 2008 XIV, 304 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The frontiers collection 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. Symmetry Symmetrie (DE-588)4058724-1 gnd rswk-swf Symmetrie (DE-588)4058724-1 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016392982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Rosen, Joe Symmetry rules how science and nature are founded on symmetry Symmetry Symmetrie (DE-588)4058724-1 gnd
subject_GND	(DE-588)4058724-1
title	Symmetry rules how science and nature are founded on symmetry
title_auth	Symmetry rules how science and nature are founded on symmetry
title_exact_search	Symmetry rules how science and nature are founded on symmetry
title_exact_search_txtP	Symmetry rules how science and nature are founded on symmetry
title_full	Symmetry rules how science and nature are founded on symmetry Joe Rosen
title_fullStr	Symmetry rules how science and nature are founded on symmetry Joe Rosen
title_full_unstemmed	Symmetry rules how science and nature are founded on symmetry Joe Rosen
title_short	Symmetry rules
title_sort	symmetry rules how science and nature are founded on symmetry
title_sub	how science and nature are founded on symmetry
topic	Symmetry Symmetrie (DE-588)4058724-1 gnd
topic_facet	Symmetry Symmetrie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016392982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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