Quote: a physical system is symmetric with respect to an operation if the operation commutes with the passage of time

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quantum mechanics

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Thinking of the hydrogen ion [this equation] says that: … is the same as "waiting a while and … These should be the same so long as … [the passage of time] doesn't change … [the physics] … [This is really an equation about [operators] … We can then define "symmetry" in the following … .U_hat., the operation of the passage of time. … [p. 17-4] Now it is clear that if it … some time, say t=0, it is true forever. … [p. 17-4] So with certain symmetries something which is … That's the basis of all the conservation laws … [p. 17-8] Symmetry with respect to displacements in time … implies the conservation … of momentum. Symmetry with respect to rotations … implies the conservation of … angular momentum. Symmetry with respect to reflection implies … of something we don't have a name for, …   Google-1   Google-2

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Quote: symmetries are the basis of all conservation laws of quantum mechanics; e.g., conservation of energy, momentum, angular momentum, parity

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