# Would non-conservation of energy imply no science?

1. Apr 8, 2015

### DaPi

(I throw myself on your mercy - I'm sure my language needs tightening up.)

Let's start with Noether's theorem stated as: invariance under displacement in time implies conservation of energy.

The converse is: non-conservation of energy implies non-invariance under displacement in time.
Which would mean experiments would not be repeatable, and we wouldn't be able to do science as normally accepted.

Is this wrong, trivial or profound?

Does it place us in a similar position as the anthropic principle does - in this case, having chosen the scientific method we can't observe a violation of conservation of energy?

2. Apr 8, 2015

### jitu16

Yes we demand it, if it's not the case it's not much of a physics anymore. But even if law of physics changes(energy not conserved anymore) it changes slowly. The apple has not gone to heaven as far as civilization can remember :p

3. Apr 8, 2015

### Staff: Mentor

Yes, that's true. And our universe is not invariant under displacement in time (because it is expanding, so you can tell "what time it is" by how much the universe has expanded), and therefore does not conserve energy. See this article by Sean Carroll:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

No, that's not correct. Experiments only have to be "repeatable" if all the conditions that can affect the outcome are held constant. If the universe is not invariant under displacement in time because it's expanding, then whenever you do an experiment measuring energy conservation, the "size of the universe" becomes a condition that can affect the outcome; so the only way to truly "repeat" an experiment would be to go back in a time machine and do it again at exactly the same universe size (which of course we can't actually do). In practice, of course, the expansion of the universe is slow enough, relative to our ordinary experience, that we can treat energy as conserved. But if we're talking about fundamentals, we have to take all factors into account, and the expansion of the universe is one of them.

What is really going on here is that you are confusing the properties that the laws of physics, themselves, must have, with the properties that particular solutions to those laws must have. The laws of physics are invariant under time translations. However, our particular universe, which is one solution to those laws, is not, because the invariance under time translations is a property of the whole set of possible solutions, not of any particular solution by itself. So if one solution to the laws describes an expanding universe, there will also be a corresponding solution that describes a contracting universe with all other parameters the same. We know we're in the first solution (expanding) and not the second (contracting) through observation.

Also, it's important to point out, as Carroll does in his article, that when we say energy is not conserved in the universe as a whole, we are not saying that "anything goes". All we are saying is that spacetime obeys a somewhat different law than you thought it did. You thought the law was "spacetime has to be time translation invariant, so energy is always conserved". The actual law is more like "the change in spacetime when you do a time translation has to be related to the change in the matter and energy under the same time translation, in a particular way". (The equation that governs this is called the "Einstein Field Equation". The relativity forum is the place to go if you want to discuss this in more detail.) One important consequence of this is that locally, energy is conserved, in the sense that matter and energy cannot be created or destroyed. So you still can't build a perpetual motion machine, even though the universe as a whole is not time translation invariant.

4. Apr 8, 2015

### Staff: Mentor

I'd take a step broader and say that the error is confusing the scientific method with the laws of the universe it investigates.

Indeed, Aristotle essentially believed in a different formulation of conservation of energy, where objects continuously lose energy and thus must get a constant energy input to remain in constant speed motion. If the universe really worked that way, the scientific method could have proved him correct.

5. Apr 9, 2015

### DaPi

Gentlemen, thanks very much for your replies - especially Peter who has taken so much time.

I'm reminded of being 16-17 bedazzled by symmetry and sure that a symmetrical problem MUST have symmetrical solutions. Luckily I was introduced to the "sombrero hat" potential before I made too much of a fool of myself

I will depart and cogitate upon all this. I may return.

Thanks again - DaPi

6. Apr 11, 2015