Is energy conserved in an expanding universe?

  • Thread starter Robert100
  • Start date
  • #26
78
0
Trying to clarify my question yet again

Bingo. There is a problem with your question which makes your question invalid.

Given that GR offers us no definition for "the energy of the universe" (at least not a universe with a FRW metric), how can you possibly expect us to answer a question about what happens to said "energy of the universe" other than having us point out that it is not defined?
Thank you! This addresses at least half of my question. But, correct me if I am wrong, GR tells us nothing at all about quantum mechanics, or about the vacuum energy predicted by QM. Again, correct me if I am mistaken, but GR doesn't predict the Casimir effect (which reveals a type of vacuum energy).

So, in essence, I am asking a different question than the one that you are answering. I really am not asking about the implications of GR by itself, which everyone else here seems totally focused on. Rather, I am merely assuming that GR is more or less correct (unified field theories not yet being available), and asking a question that proceeds from this:

There is energy per cubic meter. QM teaches us this. And GR teaches us that the universe is getting larger in volume (at least for this epoch in cosmic history, and likely for a lot longer, maybe forever.) So with more and more volume filled with vacuum energy, doesn't this imply that the total energy of the universe is always increasing?

You also might want to think about how productive it is to criticize physicists for "not understanding your questions" when presumably it is the people you think of as "physicists" who are answering them?
I do appreciate that physicists have taken the time to answer me. But the problem is that physicists have not been answering my questions, but rather seem to have misunderstood them, or understood them in a much more limited way than was intended. Just re-read my initial and follow-up posts, and look at most of the answers. They misunderstood my question! You were the first one to address one of the imporant issues I was asking about (the problem with my question having hidden assumptions! Most questions do.)

I'm hoping that someone will think about QM, and address what I see as the core issue. There are many possible answers I can think of, such as:

(A) We postulate that the vacuum energy is entirely unrelated to anything in GR. GR thus really tells us nothing about the total energy of the universe, and this is one of its major limitations.

(B) We postulate that the vacuum energy is related to anything in GR. GR thus does tell us something about the total energy of the universe.

(B1) Perhaps this tells us that as the universe gets bigger, energy lost in some way due to expansion is gained as more vacuum energy. Total energy may thus be constant.

(B2) Perhaps this tells us that as the universe gets bigger, there really is more and more energy in the universe. Conservation of energy is thus being violated on a massive scale, all the time, but over regions so large that we don't observe this, and in a way that isn't useful to do work. (i.e. we can't use this to make a perpetual motion machine.)

(C) Something else I haven't thought of, which is much more likely.

Is my question more clear? I am not focusing on GR alone. This line of reasoning ends up being about the implications of QM. I have looked for papers on this subject, but so far have found none. I am sure that there is something in the literature out there, but I haven't been able to find a narrow enough search to let me find a paper that addresses my question.

Robert
 
  • #27
marcus
Science Advisor
Gold Member
Dearly Missed
24,738
785
I like both B1 and B2
(B1) Perhaps this tells us that as the universe gets bigger, energy lost in some way due to expansion is gained as more vacuum energy. Total energy may thus be constant.

(B2) Perhaps this tells us that as the universe gets bigger, there really is more and more energy in the universe. Conservation of energy is thus being violated on a massive scale, all the time, but over regions so large that we don't observe this, and in a way that isn't useful to do work. (i.e. we can't use this to make a perpetual motion machine.)
I'm sympathetic to B1 because I played around with it some here at PF in 2003 or thereabouts. I called it the "Marcus Conjecture" (just as a joke.)

I calculated the energy lost by the redshifting of CMB photons starting out in some volume of space----as that space expanded (the calculation is simple and would be somewhere in PF archives I suppose)

I calculated the energy gained just by the expansion of that same volume of space, assuming a constant darkenergy density of 0.6 joules per cubic kilometer (the present measured value)

The amount lost and the amount gained were same order magnitude. Maybe they differed by a factor of 2. I don't recall. they didnt exactly match but they were same ballpark.

Maybe some people were amused. Nobody I cared about their opinion was impressed. A few people made fun of me for calling it "Marcus Conjecture"

I had no MECHANISM I could propose for how the lost energy supplied the gained energy.

I figured that ultimately people would only find a mechanism like that if they mastered quantum gravity (the fundamental microscopic structure of space and how it interacts with matter). So I abandoned B1 (it is a nice question but one not ready to be answered by humans yet :smile: )
====================

I also like what you give here as B2. I think it is a good idea.

I suspect that to be a scientist is to have an intuitive sense of what questions can productively be address, and to avoid wasting too much time crying from the rooftops about questions that aren't ready to be answered yet. Patience is important. All in good time.
===================

I sympathize with both the ideas you express here, both B1 and B2. I don't blame you for asking them!

Maybe right now I slightly favor B2 over B1 (and B3 is an intelligent alternative too).

But they are not RIPE. Wait a little. Maybe in your lifetime. (Maybe sooner than I expect---I got strong hints from Martin Reuter's talk at Loops 07 about this, he has a certain picture on page 17 or right before the section called "RG improved Cosmology". He is describing how a decrease in Lambda transfers energy to a test particle of matter. These things are preliminary, you have to avoid getting excited and let them develop.)
 
  • #28
78
0
Personally I don't expect it to be constant (or even well-defined, as Pervect points out.)...we had this sort of discussion back in 2003 not about the vacuum energy but about the CMB. the CMB has lost 999 percent of its energy since it was released (the redshift is about 1100, call it roughly 1000 so each one of those CMB photons only has 1/1000 of its original energy due to wavelength stretching). the same thing with "dark energy", which some people equate with vacuum energy. it appears to have a constant density, so making more cubic meters makes more energy (that nobody pays for).
Huzzah! So I'm not crazy, and someone else has also noticed this! Most people responding in this thread brought up good and interesting points, but they missed the precise thrust of my question (except you, and Prevect's helpful point about questions with hidden assumptions!)


the same thing with any inflation scenario that involves an "inflaton" field (as most inflation stories do). Inflatons egregiously violate energy conservation, because they have a near-constant energy density. and they cause very rapid expansion.

Some people have a dreadful time accepting that conservation of energy doesnt apply globally in cosmology. Several parts of the story involve stupendous gigantic humongous violations of the conservation "law". But I don't believe in such a general global "law". As Pervect points out you don't get one in the context of Gen Rel. Maybe in the future when we replace Gen Rel with something better....
This is a key point. As Gordon Kane writes in "The Particle Garden", all human created theories have an effective range. Outside of this range their predictions are, at best, incorrect, and often, totally off base. Einstein himself knew from day one that General Relativity (GR) had its own effective domain, so do we (see our "Beyond the Standard Model" forum.) Thus, should it really surprise us that on cosmic , conservation of energy within our universe could (just maybe) be violated?

If any of the theories about branes or multiple universes turn out to be correct (and we don't have to limit ourselves to anything related to superstring theories) then perhaps conservation of energy in our universe is violated, but not overall. That is, acceleration of our universe may be drawing off energy from a nearby universe/brane/flatworld, etc. So energy (in one form or another) in the overall bulk is conserved, but not within any one particular universe. (This reminds me Steinhardt's proposal that our universe began as a collision between two branes. )

http://wwwphy.princeton.edu/~steinh/

Robert
 
  • #29
Jorrie
Science Advisor
Insights Author
Gold Member
1,132
106
Cosmic energy loss/gain

I calculated the energy lost by the redshifting of CMB photons starting out in some volume of space----as that space expanded (the calculation is simple and would be somewhere in PF archives I suppose)

I calculated the energy gained just by the expansion of that same volume of space, assuming a constant darkenergy density of 0.6 joules per cubic kilometer (the present measured value).
Out of curiosity, I once calculated the (what I called) 'rest energy' of the observable universe over time since the end of inflation until well into the future. The expansion factor vs. time I got by the standard procedure of integrating the highly normalized Friedmann equation for a flat universe: [itex]\dot{a}^2 = H_0^2[\Omega_m/a+\Omega_r/a^2+\Omega_v a^2][/tex].

For every value a I then calculated the density of each energy component, using the standard 1/a^4 for radiation, 1/a^3 for matter and keeping [itex]\rho_v[/tex] constant. Adding up the energy densities and multiplying by the volume of the observable universe for that a, I got to the 'rest energy' at that time. The graph is attached.

Question: is this a valid method for obtaining the 'rest energy' of a piece of space in the Lambda-CDM scenario?

If so, it appears that the 'rest energy' only remained roughly constant during the matter dominated epoch, from some 1 million to some 5 billion years or so. Before that it was 'diluted' by the redshift and after that increased by the cosmological constant.
 

Attachments

  • #30
pervect
Staff Emeritus
Science Advisor
Insights Author
9,769
991
You've definitely computed some sort of number. The physical significance of this number is somewhat questionable. You might want to question why you consider this number to represent any sort of "energy".

Note that "rest energy" is not conserved in any event - consider blowing up an atomic bomb, for instance. "Rest energy" gets turned into kinetic energy, one cannot meaningfully separate out "rest energy" from kinetic energy without specifying some sort of favored coordinate system. If one does throw out all concepts of "kinetic energy" (by not including them in the sum) one doesn't expect the resulting quantity to be conserved, one knows that rest energy can be inter-converted to kinetic energy and that when such conversion happens kinetic energy must be included.

Another thing missing from your formula for "energy" would be any concept of "gravitational binding energy". For instance, the Newtonian gravitational binding energy of a sphere of mass M depends on its radius, R, by the formula

E = -G M^2 / r


So in essence you've computed a number to represent a quantity that you already know (or, should know, with a little thought) isn't conserved, and found that the universe as a whole doesn't conserve it.

If your goal is to come up with a conserved energy of the universe, these flaws unfortunately can't be repaired unless you find a way around Noether's theorem.

For some past discussions on some similar issues, including some added material on a related topic known as quasi-local energy, you might try the old PF thread:

https://www.physicsforums.com/showthread.php?t=142298

I haven't seen Garth around here for a while, he has a published theory that is NOT GR with a well-defined energy. The theory incorporates a scalar field that gives the theory a "preferred frame", which is what allows it to get around Noether's theorem. Unfortunately, last I heard it appeared very likely that this theory will be falsified by GP-B.
 
Last edited:
  • #31
Jorrie
Science Advisor
Insights Author
Gold Member
1,132
106
Cosmic static and binding energies?

Thanks pervect.

You've definitely computed some sort of number. The physical significance of this number is somewhat questionable. You might want to question why you consider this number to represent any sort of "energy".
I understand that 'rest energy' in this context is problematic but why I considered 'this number to represent any sort of "energy"' is probably not so problematic. Since we know the co-moving size and the critical energy density of the observable universe, we can easily calculate a present 'static' energy component of 2.62E+71 Joule for the observable universe. Is it not reasonable to say that this number represents some valid component of the total energy?

OK, the frame dependence remains, but it may be valid in our 'observational frame', whatever that means. Anyway, the next step could be to calculate the negative gravitational binding energy from this value. You said:

Another thing missing from your formula for "energy" would be any concept of "gravitational binding energy". For instance, the Newtonian gravitational binding energy of a sphere of mass M depends on its radius, R, by the formula

E = -G M^2 / r
Based on this and the 2.62E+71 Joule (or 2.92E+54 kg) 'static energy' of the observable universe and taking the co-moving radius as 46 Gly, or 4.35E+26 m, I get a present binding energy of -1.30E+72 Joule.

If this is correct, can one then conclude that the positive energy of expansion (the 'kinetic' energy?) is 1.30E+72 Joule, so that the total (binding + expansion) energy of the observable universe is zero for the Omega=1 case?

If all the above make any sense, (which I doubt somehow) one can calculate the variable static and expansion energies over the history of the universe as per the attached graph. This is an "engineering approach", which I hope is not considered too "agricultural"!:wink:
 

Attachments

  • #32
pervect
Staff Emeritus
Science Advisor
Insights Author
9,769
991
OK, the frame dependence remains, but it may be valid in our 'observational frame', whatever that means. Anyway, the next step could be to calculate the negative gravitational binding energy from this value. You said:

If this is correct, can one then conclude that the positive energy of expansion (the 'kinetic' energy?) is 1.30E+72 Joule, so that the total (binding + expansion) energy of the observable universe is zero for the Omega=1 case?

If all the above make any sense, (which I doubt somehow) one can calculate the variable static and expansion energies over the history of the universe as per the attached graph. This is an "engineering approach", which I hope is not considered too "agricultural"!:wink:
How to put this: I would not recommend trying to get the above analysis published in a peer-reviewed journal :wink:

Note that the formula I gave for binding energy was a Newtonian formula - not a GR formula. As I have been trying to explain, a GR formula just doesn't exist, at least not for the case of the universe - there are many situations in which GR does define an energy, the universe as a whole happens not to be one of them.

So you're (slightly) better off not including the binding energy rather than applying a Newtonian formula in an area where you know it won't give the right answer. (It would be best if this were a conscious omission). But basically the whole approach is so badly flawed as to be not worth very much, and if you talk to anyone knowledgeable about GR about the "energy of the universe" you shouldn't be too surprised if you get negative reactions or "funny looks".
 
  • #33
Jorrie
Science Advisor
Insights Author
Gold Member
1,132
106
So you're (slightly) better off not including the binding energy rather than applying a Newtonian formula in an area where you know it won't give the right answer. (It would be best if this were a conscious omission). But basically the whole approach is so badly flawed as to be not worth very much, and if you talk to anyone knowledgeable about GR about the "energy of the universe" you shouldn't be too surprised if you get negative reactions or "funny looks".
OK, thanks again, I expected something to this effect.

One final question: if I drop the 'observable universe' as a basis and just consider a large, finite region that is fairly homogeneous, would the [edit: 'evolution over time of the'] 'static energy' (including all forms) still be fundamentally flawed as a concept?
 
Last edited:

Related Threads on Is energy conserved in an expanding universe?

Replies
21
Views
572
Replies
12
Views
528
Replies
36
Views
13K
Replies
3
Views
557
Replies
2
Views
2K
Replies
46
Views
3K
Replies
5
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
20
Views
3K
  • Last Post
Replies
16
Views
3K
Top