For each symmetry that a theory possesses, there is a corresponding law of conservation that must hold in the world it describes. A conservation law is one that states that some quantity can be neither created nor destroyed. If a particular theory is symmetric under space translation—that is, if its equations remain unchanged when the spatial perspective is shifted—that implies the law of conservation of momentum. Similarly, if the theory is symmetric under time translation, that implies the law of conservation of energy. Symmetry under shifts in orientation implies the law of conservation of
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