# GR and energy conservation

1. Jul 31, 2011

### TrickyDicky

I've just read the FAQ about this and IMO it is "not even wrong" to say that energy conservation doesn't apply to Cosmology. The fact is energy conservation is clearly stated in the EFE by the vanishing divergence of the stress-energy tensor and since GR is the theory we currently use in Cosmology, cerrtainly energy is conserved in cosmology.
There seems to be some silly confusion in that FAQ answer, the fact that currently the global energy can't be defined doesn't imply "energy is not conserved in cosmology", just like we don't say that since there is no "standard" way to define the total entropy of the universe it follows that the 2nd law of thermodynamics does't apply in cosmology.
It can be said that since we can't get out of the system called "universe", there is no easy way to define the universe energy unless we introduce a time-symmetry (Noether theorem). But that is a feature of the way we define energy. It doesn't have anything to do with GR.

2. Jul 31, 2011

### WannabeNewton

$\bigtriangledown _{\nu }T^{\mu \nu } = 0$ is only local though so how could it justify global energy conservation under the friedmann metric which doesn't have $\frac{\partial }{\partial t}$ as a killing field?

3. Jul 31, 2011

### pervect

Staff Emeritus
Where are the relativity FAQ's located? I thought the should be at https://www.physicsforums.com/forumdisplay.php?f=210 [Broken], but I don't see the FAQ in question (on energy conservation in GR)
there.

I'll defer detailed comments until I re-read the FAQ. I'm pretty sure I've read it before,and I doubt there is anything that a minor tweak wouldn't fix, but I'd like to re-read it again more carefully.

Last edited by a moderator: May 5, 2017
4. Jul 31, 2011

### WannabeNewton

Last edited by a moderator: May 5, 2017
5. Jul 31, 2011

### TrickyDicky

That $\bigtriangledown _{\nu }T^{\mu \nu } = 0$ is only local is debatable, chiefly when locally means as big a system as one can define, surely it assures local conservation, and by being in covariant form it opens the way to global conservation by introduction of symmetries.
I'm not trying to justify anything, my point was that energy conservation applies to cosmology if we strictly use the GR equations without further assumptions.

6. Jul 31, 2011

### TrickyDicky

Maybe it would be more correct if it specified that the lack of energy conservation is a feature of our current cosmological model rather than something intrinsic to the general relativity equations.

7. Jul 31, 2011

### pervect

Staff Emeritus
Let's compare it to the sci.physics.faq- which addresses a similar question.

I've always thought "It depends on what you mean by energy and what you mean by conserved" was a bit weasel-worded. The bit about the differential and integral formulations is very helpful to the advanced reader, but it's not so helpful to the less advanced reader.

Note that the sci.phsics FAQ is concerned with whether or not energy is conserved in general realtivity, while the FAQ in question is in the cosmology section and applies to cosmology.

While we might want to mention somewhere in the FAQ that we have definitions of energy that work in certain situations, it's accurate and IMO helpful to state right-up-front that none of these situations appear to apply to our universe - by which I mean the universe as a whole, not some infinitesimally small piece of it.

8. Jul 31, 2011

### WannabeNewton

Right ok, I think I see what you're getting at. So you're not disputing anything, your're just saying this isn't something that should be uniquely attributed to GR?

9. Jul 31, 2011

### TrickyDicky

I really thing it would pay off to clarify that we know from 1917 thanks to Noether theorem that energy conservation is just the result of time symmetry, and therefore the only reason we state energy is not conserved in the universe as a whole is the introduction of time asymmetry by the FRW metric, not something in the EFE or due to the way we define the total energy of the universe.

10. Jul 31, 2011

### TrickyDicky

Yes, and also that the phrase "energy conservation doesn't apply to cosmology" is misleading and should be rephrased.

11. Jul 31, 2011

### Q-reeus

Given the claim coe holds 'locally', are we talking about first or higher order curvature terms re 'global' departure? Is the lack of a gravitational contribution to the stress-energy tensor seen as the problem here? Shouldn't there be some relatively simple thought experiment capable of showing any violation if it exists? One would expect specific scenarios have been worked through over the last 95+ years, to leave no doubt! :zzz:

12. Jul 31, 2011

### Staff: Mentor

The CMBR is a good example that leaves no doubt. The CMBR photons that we receive now have lost a lot of energy from when they were last scattered.

13. Aug 1, 2011

### Q-reeus

No doubting the fact of enormous CMBR redshift and thus reduction in net radiant energy, but is that a sufficient proof? Why could that not be a case of energy transfer - from CMBR to expansion rate for instance (ie matter gets an added 'kick')? As many are aware the prevailing view amongst cosmologists is that the total energy of the universe (inclusive of radiation, matter, and 'dark energy') is an invariant zero; from beginning to end. As I recall it this assumption strictly relies on an overall zero 4-curvature (flat spacetime), which studies have apparently shown to either be true or a good approximation.
If on the other hand the claim of a global failure of coe is valid, this cannot magically only appear on the scale of the visible universe. One should be able to model some perfectly finite 'average' volume containing the requisite uniform distribution of radiation, matter, and maybe DE, and show that it's time evolution leads to an excess or deficit of total energy. Certainly not my province, but would be extremely surprised such has not been done. Anyone aware of such studies, and how that then tallies or not with the zero energy universe concept?

14. Aug 1, 2011

### Staff: Mentor

Do you have any reference for this? I was not aware that the FLRW spacetime admitted a globally conserved energy.

15. Aug 1, 2011

### TrickyDicky

Hi, Q-reeus.
AFAIK, that is not the prevailing view among cosmologists, might you be referring to zero spatial 3-curvature? Zero 4-curvature usually refers to the SR model.

16. Aug 1, 2011

### Q-reeus

Sur - here's one I had saved: http://arxiv.org/abs/astro-ph/0212574 I tend to look at the conclusions part.

17. Aug 1, 2011

### TrickyDicky

Ok, I had never heard of this, I'll take a look at it. However I still wouldn't say this is the prevailing view.

18. Aug 1, 2011

### Q-reeus

TrickyDicky - I may be taking a bit of liberty claiming it is for sure the majority view, but the flat spacetime bit is correct as the article linked in #16 explains. Lawrence Krauss makes a big thing of zero universe in an entertaining (~ 1 hr long) Youtube presentation:
http://www.freelecturevideos.com/ph...lawrence-krauss-aai-2009-video_243dcb1d9.html Here's another link re flat spacetime and zeu http://arxiv.org/abs/gr-qc/0605063

Last edited by a moderator: Apr 26, 2017
19. Aug 1, 2011

### TrickyDicky

I just read the paper and find it very interesting. And it further supports my criticism of the energy conservation FAQ, I really think that as it stands it is not only misleading but wrong and should be modified.

Last edited by a moderator: Apr 26, 2017
20. Aug 1, 2011