Here's a quote from Lawrence Krauss' book Fear of Physics:
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But the diehard inventor may say to me: How do I know for sure that energy is conserved? What makes this law so special that it cannot be violated? All existing experiments may support this idea, but maybe there is a way around it. They thought Einstein was crazy too!
There is some merit in this objection. We should not take anything on faith. So all these books tell undergraduates that Energy Is Conserved (they even capitalize it). And it is claimed that this is a universal law of nature, true for energy in all its forms. But while this is a very useful property of nature, the important issue is Why? Emmy Noether gave us the answer, and it disappoints me that many physics texts dont bother going this far. If you dont explain why such a wonderous quality exists, it encourages the notion that physics is based on some set of mystical rules laid down on high, which must be memorized and to which only the initiated have access.
So why is energy conserved? Noethers theorem tells us that it must be related to some symmetry of nature. And I remind you that a symmetry of nature tells us that if we make some transformation, everything still looks the same. Energy conservation is, in fact, related to the very symmetry that makes physics possible. We believe the laws of nature will be the same tomorrow as they are today. If they werent, we would have to have a different physics text for every day of the week.
So we believe, and this is to some extent an assumptionbut, as I shall show, a testable onethat all the laws of nature are invariant, that is, they remained unchanged, under time translation. This is a fancy way of saying that they are the same no matter when you measure them. But if we accept this for the moment, then we can show rigorously (that is, mathematically) that there must exist a quantity, which we can call energy, that is constant over time. Thus, as new laws of nature are discovered, we do not have to worry at each stage whether they will lead to some violation of the law of conservation of energy. All we have to assume is that the underlying physical principles dont change with time.
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