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My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed. Why is that? Is there a theory or scientific evidence that proves his statement true or false? I apologize for the elementary question, but I sometimes tend to over-think things, and this is one of those times. :)

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"...but I sometimes tend to over-think things, and this is one of those times." You should study physics then. – NikolajK Jan 7 '12 at 13:15
Possible duplicate of Is energy really conserved? and links therein. – Qmechanic Feb 1 '12 at 20:37
up vote 47 down vote accepted
  • At the physics 101 level, you pretty much just have to accept this as an experimental fact.

  • At the upper division or early grad school level, you'll be introduced to Noether's Theorem, and we can talk about the invariance of physical law under displacements in time. Really this just replaces one experimental fact (energy is conserved) with another (the character of physical law is independent of time), but at least it seems like a deeper understanding.

  • When you study general relativity and/or cosmology in depth, you may encounter claims that under the right circumstances it is hard to define a unique time to use for "invariance under translation in time", leaving energy conservation in question. Even on Physics.SE you'll find rather a lot of disagreement on the matter. It is far enough beyond my understanding that I won't venture an opinion.

    This may (or may not) overturn what you've been told, but not in a way that you care about.

An education in physics is often like that. People tell you about firm, unbreakable rules and then later they say "well, that was just an approximation valid when such and such conditions are met and the real rule is this other thing". Then eventually you more or less catch up with some part of the leading edge of science and you get to participate in learning the new rules.

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Lol. Thanks for the help! I've wondered this for a while. – Dustin L. Jan 7 '12 at 6:05
What advantage do we get by recasting the question in terms of time translational invariance? – Revo Jan 7 '12 at 14:28
@Revo: You're able to understand this rule as one of a class of conservation principles that arise from symmetries so you feel a whole lot smarter. – dmckee Jan 7 '12 at 16:33
@dmckee So it is all psychological then ?:) – Revo Jan 7 '12 at 16:39
@Revo if you're dealing with something new and don't know what the expression for energy looks like, or want to know if there's some other conserved quantity, symmetry methods will let you figure that stuff out from the rest of the theory. – Robert Mastragostino Feb 3 '14 at 0:02

We can't create noting from something and we can't create something from nothing. Nothing or nonexistence doesn't exist, it is it's definition. The only thing that exist is energy in different forms. So energy exists and cannot become nonexistent, as there is no such thing as nonexistence. Energy can neither come into existence because it has nowhere to come from which is not existence as everything is existence.

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1) Time is homogeneous. Spectroscopy tells us that stuff happens (spectroscopic transitions) universally locally at the same rate.
2) Noether's theorems then link that continuous symmetry to a conserved current (mass-energy conservation) and vice-versa.
3) However, we live at the bottom of a gravitational well (and gravitational potential), so time is NOT LOCALLY homogeneous (re GPS on-board clock general relativity correction).
4) Gobsmack your physics instructor.

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I actually learned WHY it was true in Vector Calculus. There's a proof under conservative fields with line integrals you may want to look at

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Isn't that just another axiom? What's the proof that vector calculus models the real world? – Keith Thompson Jan 8 '12 at 23:41
@KeithThompson There is no proof of anything, only mathematical consistency between theories, and consistency between theory and observation, until new observations contradict it. AFAIK, there is no proof that you exist, but some observations make it a credible hypothesis. – babou Jul 2 '13 at 9:36

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