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Dan Brumleve
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Why is global conservation of energy not considered a tautology?

This question is in reference to my downvoted answer to this active physics.SE question. More than one user has indicated that it is simply wrong and I am having trouble understanding why. My point of view is that the fact that energy is conserved is essentially part of its definition. In particular I don't understand why it is necessary to invoke Noether's theorem, GR, or BB in order to "prove" the conservation of energy. I can't see how a universe without conservation of energy is even possible in principle.

A thought experiment (of a sociological nature) to illustrate my point: suppose a perpetual motion machine were discovered or invented that seems to create energy continuously from nothing in defiance of all known physical theories. So we create a new theory to explain it by saying that the energy comes from "somewhere else", i.e. a "different universe". But now we have expanded our concept of "universe" to include this other place; isn't it still fair to believe that energy is globally conserved within this newly-defined larger universe? I know that numerous discoveries have been made on the basis of missing energy, e.g. the existence of the neutrino, but seems like it is always preferable to violate Occam's razor by postulating new entities than it is to question the law of conservation of energy.

Can someone help clear this up for me? I am not so much interested in knowing the mathematics as I am in getting my scientific intuition straightened out. How is a universe without conservation of energy even possible in principle? If energy is not globally conserved as some users have suggested in response to the linked question, does this mean that some sort of cosmological-scale perpetual motion device is actually possible? If so, why not just define it away as I have done in my thought experiment?

Dan Brumleve
  • 478
  • 1
  • 4
  • 19