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Media type:
Book
Title:
Symmetry rules
:
how science and nature are founded on symmetry ; with 4 tables
Other titles:
Angekündigt u.d.T.: Science as symmetry
Contains:
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.
Description:
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