# Is an accelerating universe consistent with the conservation of energy

1. Aug 13, 2013

### Bobcent

Hi,

Is the fact that the expansion of the universe accelerates consistent with the conservation of energy? If so, how?

Grateful for response!

2. Aug 13, 2013

### phinds

Conservation of energy is local. It does not apply over cosmological distances.

3. Aug 13, 2013

### Bobcent

Okay, that is very interesting! I thought energy never can be created, no matter how small or large the system is, thats what I was taught in school.

So would it theoretically be possible to convert this energy into work?

4. Aug 13, 2013

### nst.john

Isn't the acceleration of the universe caused by dark energy?

5. Aug 13, 2013

### phinds

"Dark energy" is just a name meaning "we don't know WHAT is going on". That is, we CALL it an "energy" but we don't actually know that it is. It SEEMS to be because it has an effect that seems to require energy, but that's not definitive.

The issue is that conservation of energy is a classical concept and the universe is governed by General Relativity, which is not classical, and does not define "conservation of energy".

6. Aug 13, 2013

### phinds

What energy are you talking about?

7. Aug 13, 2013

### Bobcent

Say that you would connect our galaxy to a distant one with a leash, and connect the leash to a generator. Say that you generate equally much electricity (converted from kinetic energy of the galaxies) from the galaxies as they would otherwise "speed up" due to the accelerated expansion of the universe.

Is this theoretically possible? If not, why? If yes, where did the energy come from?

8. Aug 13, 2013

### WannabeNewton

Energy is very complicated in general relativity. It does not work like in force based Newtonian mechanics. Read this: https://www.physicsforums.com/showthread.php?t=506985 and the references therein. The more math you know, the easier this stuff is to understand.

9. Aug 13, 2013

### marcus

Good questions. I think maybe WBN and others answered as well as one briefly can. Papers have been written about the "tethered galaxy problem". That is, professional researchers have wondered about this kind of thing, various versions of the type of question you are asking---even before acceleration of distance growth was discovered. You already had this kind of puzzle with ordinary expansion. So you aren't alone and incidentally congratulations on insightfulness of the question.

Sean Carroll is a cosmologist at Caltech, with a decent reputation and publication track record. He blogs as well. He has a wide-audience blog essay called "energy is not conserved in an expanding universe". Besides doing what WBN said you could also google "carroll energy not conserved expanding" and have a look.
It doesn't depend on "acceleration" or on hypothetical "dark energy"---it's more basic and general.
(A math theorem discovered by one Fräulein Emmy Noether around 1915-1918 in Berlin. It's a beautiful theorem, one for which Einstein had high praise, and gets at the basis for WHY energy is a conserved quantity in certain situations and not others.) Anyway, Sean Carroll gives a popular account of that business. There's also John Baez account, he's a good explainer. You could google "baez noether theorem".

Last edited: Aug 13, 2013
10. Aug 13, 2013

### marcus

The short answer is "no". Conservation of energy is inconsistent with the basic fact of expansion. And this doesn't depend on "acceleration". Already conservation of energy is negated by the simple fact of expansion without acceleration.
Expansion is because of the GR equationwhich is more basic than the conservation law.

The conservation law is CONTINGENT on having a certain condition on geometry hold. GR guarantees that condition to hold approximately at small scale but it allows geometry to be dynamic and not satisfy the condition at large scale. So the conservation law is contingent, depending on favorable geometric conditions, and is "at the mercy of geometry" so to speak. GR guarantees the conservation law is good, with negligible error, at small scale but does not guarantee it at large.

They really should mention that when they teach energy and momentum conservation in school.

That's kind of a crude answer. For more nuanced answers you can check out the PF FAQ or the John Baez or Sean Carroll discussion.

I like the question about the "leash" spinning the electric generator very much. My sister's dog, that I take for walks where there are deer and wild turkeys, has a leash with spring loaded reel and is often excited and difficult to manage. I could generate electricity with that dog when she sees a turkey.

For some concrete numbers, go here:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
If you put 10 in the upper limit box
and 0.1 in the lower limit box
and put in 10 for the number of steps, and then press "calculate" you will get this table that shows recession speeds for galaxies in our past and future light cones.

Vnow is the speed the distance is growing when we receive or send a signal flash of light.
Vthen is their recession speed when they send, or receive, the flash.
By hovering over blue dots you can find definitions of other quantities, the actual webpage is more interactive than this printout:

$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.000&0.5454&0.8196&30.684&3.068&4.717&2.13&3.74\\ \hline 0.158&6.310&1.0886&1.6308&26.444&4.191&6.804&1.84&2.57\\ \hline 0.251&3.981&2.1646&3.2127&21.143&5.311&9.452&1.47&1.65\\ \hline 0.398&2.512&4.2500&6.1052&14.651&5.833&12.396&1.02&0.96\\ \hline 0.631&1.585&8.0151&10.4035&7.226&4.559&14.962&0.50&0.44\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 1.585&0.631&20.9561&16.4103&5.731&9.083&17.047&0.40&0.55\\ \hline 2.512&0.398&28.6942&17.0630&9.638&24.210&17.204&0.67&1.42\\ \hline 3.981&0.251&36.6015&17.2395&12.160&48.409&17.240&0.84&2.81\\ \hline 6.310&0.158&44.5532&17.2847&13.760&86.821&17.285&0.96&5.02\\ \hline 10.000&0.100&52.5163&17.2961&14.772&147.715&17.296&1.03&8.54\\ \hline \end{array}}$$

S is the factor by which distances are smaller in the past (or reciprocally larger in future). It is one plus the redshift. A galaxy we see with redshift 9 is at the epoch S=10 back when distances were 1/10 present size. S=1 is the present.
For more blue dots, click on "column definition and selection". It's remarkably informative.

Last edited: Aug 13, 2013
11. Aug 13, 2013

### phinds

Marcus, here's a product idea for you: Have the leash spring thingy generate electricity as you suggested and then have the electricity generate a mild shock to the dog. It becomes a self-regulating system of leash/dog => DON'T CHASE TURKEYS

12. Aug 13, 2013

### Bobcent

Hi Marcus, and thanks for a thorough reply! I find this very interesting, even if I don't understand relativity more than really fundamentally.

I will look into Sean Carroll and John Baez, sounds really good.

About the leash - We could always just connect it to the moon if its too hard to get to a distant galaxy :tongue: Probably unlimited kinetic energy to be extracted there, compared to our consumption, no need for space expansion Just have to wait till graphene, or carbon nanotubes become really really cheap! Would be nice with a bigger moon on the sky aswell.

Also gonna check out the FAQ that WbN linked.