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This leads me to my primary question: Why does the law of conservation of energy work the way it does?
Why does the law of conservation of energy work the way it does? Like, what does this law depend on to function as well as it does? I know it has something to do with time translation symmetry, but like, what the hack does that even mean? Why can't energy be created or destroyed? Is there a reason as to why the law works the way it does, or is it just a hard fact of life that we know exists, but can't explain with words, numbers and graphs?
Provided nothing chages about the physical processes between today and tomorrow then we could pump the water up to the high place today and expect to recover exactly the same amount energy tomorrow when we allow it run down hill. However, if something DOES change about the physical process then we don't expect energy to be conserved. For example if the water acquired extra mass for no apparent reason overnight, then we would be able to recover more energy when we let it run down hill tomorrow then we had to spend to pump it up there today. It would seem that we had generated extra energy from nothing. Similarly if the acceleration due to gravity increased overnight, then we are in the same position. When physical processes don't remain consistent through time translation, then we don't expect Energy to be conserved.
So... the law of conservation is a strict fact of life that arises from the laws of physics remaining the same throughout the flow of time, and although we humans can't violate it, it has the potential to just violate itself at a moments notice?
it has the potential to just violate itself at a moments notice?
Could they harness the positive energy of a quantum fluctuation and vent off the negative energy some place far away?
Do they simply draw power from another universe where time translation symmetry isn't a thing, and the laws of physics are impossible to define due to the fact that they're always changing?
I already knew about the whole light redshifting out of existence thing, but like, was energy REALLY destroyed by this, or did it just turn into a more useless form that's undetectable by our technology? Assuming this really does count as a violation of conservation of energy however, I don't suppose there exists any examples of the law being violated in the other direction (AKA energy coming from literally nowhere)?