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Why does law of conservation of energy hold true?

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Law of conservation of energy says, energy can never be created or destroyed. It can only change its forms. Now what this statement says, let us understand it. read more

The equations $(17.7)$ and $(17.8)$ remain valid, but the conservation of energy is lost. This is excerpted from The Variational principles of Mechanics' Work function and generalised force by Cornelius Lanczos; the author asserts that for a $U$ which explicitly depends on time $t,$ the law of conservation of energy doesn't apply it is "lost". read more

In an isolated/closed system the law of conservation of energy still holds. But taken the whole universe into consideration - it goes out the window. Incidentally, the theory of general relativity does not need the energy to be conserved. Coming to black holes. They don't violate the law of conservation of energy. read more

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