The Symmetry Principle
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This chapter derives the symmetry principle, which is the fundamental principle in the application of symmetry considerations to problem solving in science and engineering and devising theories in physics. It starts with the discussion of the concept of causal relation in physical systems, whereby certain correlations exist between states of cause subsystems and states of effect subsystems, correlations resulting from the fact that states of subsystems are determined by the states of the whole system. Then the concepts of equivalence relation and equivalence class are presented. Scientific laws as expressions of causal relations. Such laws must ignore certain aspects of states of physical systems. That introduces equivalence relations in the sets of states of systems, from which follows the equivalence principle: Equivalent states of a cause → equivalent states of its effect. From the equivalence principle is derived the symmetry principle: A symmetry transformation of the cause is also a symmetry transformation of the effect. Equivalently: The symmetry group of the cause is a subgroup of the symmetry group of the effect. Alternatively: The effect is at least as symmetric as the cause. What the symmetry principle means is that any symmetry of a cause must appear in its effect, while the effect may possess symmetry that is not symmetry of the cause. Causes and effects in quantum systems are discussed.
KeywordsEquivalence Class Equivalence Relation Quantum System Symmetry Group Causal Relation
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