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First of all, it stems from a large number of observations. No violation of the law of conservation of energy has been found, despite the fact that thousands of scientists have dedicate many years to study energy-related phenomena.

Currently, however, the law of conservation of energy is usually derived to Noether's Theorem, which relates conservation laws with symmetry laws. In the case of conservation of energy, according to Emmy Nöther, this is related to the fact that physical laws are the same today as they were yesterday. In other words, if conservation of energy would be violated, that would be equivalent to physical laws changing over time! Since this involves some pretty advanced math which I don't understand, and you probably don't understand either, I won't go into details; but if you are interested in the details, read the encyclopedia article on Noether's Theorem.

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