author = { Rosen, Joseph AND Rosen, Joe },

title = { Symmetry rules how science and nature are founded on symmetry ; with 4 tables },

publisher = {Springer},

isbn = {3540759727},

isbn = {9783540759720},

keywords = { Symmetry , Symmetrie },

year = {2008},

abstract = {Literaturverz. S. [289] - 295},

abstract = {1The Concept of Symmetry1 -- 1.1The Essence of Symmetry1 -- 1.2Symmetry Implies Asymmetry8 -- 1.3Analogy and Classification Are Symmetry10 -- 2Science Is Founded on Symmetry17 -- 2.1Science17 -- 2.2Reduction Is Symmetry20 -- 2.2.1Reduction to Observer and Observed22 -- 2.2.2Reduction to Quasi-Isolated System and Environment25 -- 2.2.3Reduction to Initial State and Evolution26 -- 2.3Reproducibility Is Symmetry29 -- 2.4Predictability Is Symmetry32 -- 2.5Analogy in Science35 -- 2.6Symmetry at the Foundation of Science37 -- 3Symmetry in Physics39 -- 3.1Symmetry of Evolution40 -- 3.2Symmetry of States44 -- 3.3Reference Frame49 -- 3.4Global, Inertial, and Local Reference Frames53 -- 3.5Gauge Transformation55 -- 3.6Gauge Symmetry58 -- 3.7Symmetry and Conservation65 -- 3.7.1Conservation of Energy66 -- 3.7.2Conservation of Linear Momentum67 -- 3.7.3Conservation of Angular Momentum68 -- 3.8Symmetry at the Foundation of Physics70 -- 3.9Symmetry at the Foundation of Quantum Theory71 -- 3.9.1Association of a Hilbert Space with a Physical System71 -- 3.9.2Correspondence of Observables to Hermitian Operators73 -- 3.9.3Complete Set of Compatible Observables74 -- 3.9.4Heisenberg Commutation Relations75 -- 3.9.5Operators for Canonical Variables75 -- 3.9.6A Measurement Result Is an Eigenvalue75 -- 3.9.7Expectation Values and Probabilities76 -- 3.9.8The Hamiltonian Operator76 -- 3.9.9Planck's Constant as a Parameter77 -- 3.9.10The Correspondence Principle77 -- 4The Symmetry Principle81 -- 4.1Causal Relation81 -- 4.2Equivalence Relation, Equivalence Class86 -- 4.3The Equivalence Principle89 -- 4.4The Symmetry Principle97 -- 4.5Cause and Effect in Quantum Systems102 -- 5Application of Symmetry107 -- 5.1Minimalistic Use of the Symmetry Principle107 -- 5.2Maximalistic Use of the Symmetry Principle125 -- 6Approximate Symmetry, Spontaneous Symmetry Breaking131 -- 6.1Approximate Symmetry131 -- 6.2Spontaneous Symmetry Breaking135 -- 7Cosmic Considerations141 -- 7.1Symmetry of the Laws of Nature141 -- 7.2Symmetry of the Universe144 -- 7.3No Cosmic Symmetry Breaking or Restoration147 -- 7.4The Quantum Era and The Beginning155 -- 8The Mathematics of Symmetry: Group Theory161 -- 8.1Group161 -- 8.2Mapping176 -- 8.3Isomorphism180 -- 8.4Homomorphism186 -- 8.5Subgroup192 -- 9Group Theory Continued195 -- 9.1Conjugacy, Invariant Subgroup, Kernel195 -- 9.2Coset Decomposition203 -- 9.3Factor Group207 -- 9.4Anatomy of Homomorphism209 -- 9.5Generator215 -- 9.6Direct Product217 -- 9.7Permutation, Symmetric Group220 -- 9.8Cayley's Theorem224 -- 10The Formalism of Symmetry227 -- 10.1System, State227 -- 10.2Transformation, Transformation Group229 -- 10.3Transformations in Space, Time, and Space-Time236 -- 10.4State Equivalence240 -- 10.5Symmetry Transformation, Symmetry Group243 -- 10.6Approximate Symmetry Transformation251 -- 10.7Quantification of Symmetry253 -- 10.8Quantum Systems255 -- 11Symmetry in Processes261 -- 11.1Symmetry of the Laws of Nature261 -- 11.2Symmetry of Initial and Final States, the General Symmetry Evolution Principle270 -- 11.3The Special Symmetry Evolution Principle and Entropy274 -- 12Summary of Principles283 -- 12.1Symmetry and Asymmetry283 -- 12.2Symmetry Implies Asymmetry283 -- 12.3No Exact Symmetry of the Universe284 -- 12.4Cosmological Implications285 -- 12.5The Equivalence Principle285 -- 12.6The Symmetry Principle285 -- 12.7The Equivalence Principle for Processes286 -- 12.8The Symmetry Principle for Processes286 -- 12.9The General Symmetry Evolution Principle286 -- 12.10The Special Symmetry Evolution Principle286.},

booktitle = {The frontiers collection},

address = { Berlin },

url = { http://slubdd.de/katalog?TN_libero_mab2 }