# Problem with an infinite universe

1. Apr 2, 2007

### phil ess

if the universe is infinite in size, then wouldnt it have infinite energy contained within it?

if so, wouldnt it be possible to create/destroy matter or energy without violating conservation? if + 10 = then we can create energy without having more of it?

2. Apr 2, 2007

### EL

Yes, if it's homogeneous (as all measurements indicate). However, note that the "observable universe", which is all we really can speak of, is finite.

3. Apr 2, 2007

### marcus

even if the universe were spatial infinite, I think an energy conservation law would be stated in terms of some localized region

you would put an imaginary box or "plastic baggie" around some system and suppose no energy passes in or out thru the baggie
and then just talking about that system you would say that energy in that system is conserved.

that statement of energy conservation would apply regardless of whether space is finite or infinite.
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"the total energy in the universe" is quite possibly not even a well-defined quantity, and if it is not operationally defined then the conservation law wouldn't apply.

i dont think your problem gives the conservation law any trouble. Also it does not give the possibility of infiniteness of the universe any trouble.

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however there are reasons to suspect that the universe is spatially finite----for example the official series of papers from WMAP that came out last year (March 2006, I think) had one called "WMAP three year data: implications for cosmology" by Spergel et al. and Ned Wright was one of the co-authors. there was stuff in Spergel et al, and also a later paper of Ned Wright, that suggested one should take seriously the possibility of a spatial closed universe. It might be infinite flat, but it also might be "nearly flat" but with some average positive curvature, and of large but finite extent.

Last edited: Apr 2, 2007
4. Apr 2, 2007

### phil ess

didnt see that line :)

Last edited: Apr 2, 2007
5. Apr 2, 2007

### marcus

excuse me if this is a dumb question, what line?
this thread has gone so rapidly I may have missed something

Oh, I bet you mean that funny line by Bush

6. Apr 2, 2007

### phil ess

i was referring to the two paragraphs you added shortly after your initial response (the ones below the =====)

i had a question that you answered in those sections, and i edited out the query with "didnt see that line"

i meant "those lines"

sorry for the confusion

7. Apr 2, 2007

### marcus

cosmology topics are exciting and sometimes I get excited and think of more to say.

but also you could still ask it! even if I respond one way other people with different viewpoints might like a shot.
in a forum like this, the more question the more energy.
you seem to be new. welcome to PF cosmology sector!

8. Apr 2, 2007

### phil ess

well i was going to ask, would you take conservation of energy to mean that "matter cannot be created or destroyed", or that the "total energy of the system will stay the same".

if you take the latter, then i guess in an infinite energy universe you can create/destroy energy. not so in the former. im just thinking out loud here

yeah im new, thanks :)

9. Apr 2, 2007

### marcus

personally I take it as the latter (total energy of the system conserved)
You know, personally I don't know about that. I wish some other people of this forum would respond so it isnt just me.
I would ask WHERE do you imagine the energy being created/destroyed?

If it is all happening inside some baggie, then the familiar local law of energy conservation would forbid it.

It wouldnt matter whether the U was finite or infinite.

I'm going to hold off pursuing this with you for a while in the hopes that we could get somebody else to put in a word.

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EDIT retroactive reply to next post: that is a really interesting perspective. In fact the CMB photons have lost about 999/1000 of their energy and nobody seems to know where it went to :surprised

Mother nature is not running a tight ship, it seems. something funny in the bookkeeping.

or more exactly the CMB lost 1100/1101 of its energy but why quibble.

Last edited: Apr 2, 2007
10. Apr 2, 2007

### Wallace

Here's an interesting thought, there is no energy conservation in GR, since energy as the rest of physics uses it is a 3D quantity. Imagine an expanding universe that contains only photons. As it expands the photons redshift due to the rule

$$\frac{\lambda}{\lambda_0} = \frac{a}{a_0}$$

So the universe contains the same number of photons but each now has less energy since

$$E = h\nu$$

for photons.

So, energy has not been conserved! However, what has happened is that the metric has changed. Since the analog of Newtonian gravitational acceleration in GR depends on derivatives of the metric it is somewhat reasonable to think of the metric is a kind of potential in some sense. Therefore can think that the lost energy has 'gone into the metric' is some sense. This is by no means a rigorous argument, just waving my hands really, but the point is that energy is not conserved in GR.

A comment on the OP though, your idea that

$$\infty + 10 = \infty$$

is not quite accurate since you can't do that with infinity. Even if the universe is infinite in extent it has a finite energy density, and the evolution of that density is bound by physical laws, so just because the total energy may be infinite dosn't mean that all bets are off and anything goes!

btw there is an interesting idea that the total energy of the universe is zero since if you add up all the positive energy that exists to the negative gravitational potentials is is sometimes argued that you get zero. I don't have a reference handy for any rigorous work on this idea but I think it was studied a fair bit a few decades ago.

Last edited: Apr 2, 2007
11. Apr 2, 2007

### phil ess

Thanks for that energy density tidbit i overlooked, i guess i got too excited at my crafty formula.

When you say that the "evolution of that density is bound", do you mean it is a constant? or that the "evolution" is constrained in that it only manifests under specific conditions?

12. Apr 2, 2007

### Wallace

Neither really, the energy density most certainly evolves and depends on the equation of state $$w = \frac{P}{\rho}$$ of the energy component.

Specifically the energy density goes as

$$\rho(a) = \rho_0 a^{-3(1+w)}$$

where a is the scale factor of the Universe.

so for matter (w=0) we have $$\rho(a) = \rho_0 a^{-3}$$

for radiation (w=1/3) we have $$\rho(a) = \rho_0 a^{-4}$$

and for a cosmological constant w=-1 so you just get $$\rho = \rho$$

From these is should become clear why the very early universe we radiation dominated, then there was a matter domination phase followed by the current phase dominated by something with $$w \sim -1$$.