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I am reading Landau and Lifshitz’s Mechanics, where they explain how the conservation of momentum and angular momentum follow from the homogeneity and isotropy of space, respectively. They also show how the conservation of energy follows from the homogeneity of time. This makes me wonder if there is a similar conservation law that follows from the isotropy of time?

Qmechanic
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Manish Kumar Singh
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1 Answers1

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Since time is only one dimensional, the only possible "isotropy" would be symmetry under time reversal. But that is a discrete symmetry and Noether's theorem only works for continuous symmetries. So there is no conservation law associated with isotropy of time.

Tarik
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