Dark energy and conservation of energy

[DoobleD]

From what I can read on the web, it seems poeple don't agree wether or not dark energy violates conservation of energy. For some, as dark energy density is constant and the Universe expands, the total energy grows. For others, that growing energy is compensated by a growing negative gravitational potential energy.

See here, or here for instance.

Is this really an open debate or is there a definitive answer ?

 

[Orodruin]

I don't see anyone in those links proposing that dark energy does not violate conservation of energy (in GR, it is not even necessarily true that total energy is a meaningful concept) apart from some viXra proponents. Hint: As a rule of thumb, do not trust things posted on viXra.

 

[DoobleD]

I don't see anyone in those links proposing that dark energy does not violate conservation of energy (in GR, it is not even necessarily true that total energy is a meaningful concept) apart from some viXra proponents. Hint: As a rule of thumb, do not trust things posted on viXra.

Thank you, I didin't know that. After looking it's story, it doesn't seem very reliable indeed. I also just found this article from Sean Carroll, which deals with my question.

 

[DoobleD]

Damn, now I read that Alan Guth says the growing energy of the Universe during inflation was compensated by negative potential energy. Seems to be the exact same reasoning than poeple who say the total energy of the universe is conserved even with dark energy. I'm not sure what to believe now.

It turns out that the energy of a gravitational field—any gravitational field—is negative. During inflation, as the universe gets bigger and bigger and more and more matter is created, the total energy of matter goes upward by an enormous amount. Meanwhile, however, the energy of gravity becomes more and more negative. The negative gravitational energy cancels the energy in matter, so the total energy of the system remains whatever it was when inflation started—presumably something very small. ...This capability for producing matter in the universe is one crucial difference between the inflationary model and the previous model.​

Source

 

[PeterDonis]

now I read that Alan Guth says the growing energy of the Universe during inflation was compensated by negative potential energy

He's just taking the alternate viewpoint described in Carroll's article, in particular in this paragraph:

...a lot of folks would want to say “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.”

I'm not sure what to believe now.

It's not a question of "what to believe". These two different descriptions (Carroll's and Guth's) are not two different possible ways the world could be, and we have to decide which one. They are two different descriptions of the same underlying reality--the same GR equations.

 

[kimbyd]

From what I can read on the web, it seems poeple don't agree wether or not dark energy violates conservation of energy. For some, as dark energy density is constant and the Universe expands, the total energy grows. For others, that growing energy is compensated by a growing negative gravitational potential energy.

See here, or here for instance.

Is this really an open debate or is there a definitive answer ?

There really isn't a significant debate about this. Energy isn't conserved in General Relativity. In an expanding universe, by the way, it isn't just dark energy that changes in energy per co-moving volume. Radiation does as well. In fact, any form of matter with non-zero pressure* does.

Here's one good explanation of this fact:
http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

* Pressure here is the pressure measured on cosmological scales. Normal matter doesn't experience pressure in this context because galaxies that aren't in contact don't exert pressure on one another, and because their speeds are non-relativistic relative to the background motion (galaxy speeds top out at a couple thousand km/s, as opposed to the speed of light at around 300,000 km/s).

 

[PeterDonis]

There really isn't a significant debate about this. Energy isn't conserved in General Relativity.

I don't think this is the right way to state it. I think a better way to state it would be: everybody agrees on the actual predictions of GR. But everybody does not agree on what ordinary language to use to describe those predictions to lay people. Some physicists want to say "energy is not conserved"; others want to say "energy is conserved, but you have to include energy stored in the gravitational field". But, as I said in my previous post, those are not two different ways the world could be; they are just two different ordinary language descriptions of the same physics. Everybody agrees on the physics, but "energy isn't conserved in General Relativity" isn't the only possible way to use ordinary language to describe the physics.

Here's one good explanation of this fact

Which has already been linked to by the poster you responded to (post #3). He's aware of Carroll's arguments; he's just also (understandably) confused by the fact that Guth seems to be saying something that contradicts Carroll, yet they're both talking about the same theory, GR. I don't think the best way to resolve that confusion is to just assert that Carroll is "right" and Guth is "wrong".

 

[kimbyd]

Damn, now I read that Alan Guth says the growing energy of the Universe during inflation was compensated by negative potential energy. Seems to be the exact same reasoning than poeple who say the total energy of the universe is conserved even with dark energy. I'm not sure what to believe now.

It turns out that the energy of a gravitational field—any gravitational field—is negative. During inflation, as the universe gets bigger and bigger and more and more matter is created, the total energy of matter goes upward by an enormous amount. Meanwhile, however, the energy of gravity becomes more and more negative. The negative gravitational energy cancels the energy in matter, so the total energy of the system remains whatever it was when inflation started—presumably something very small. ...This capability for producing matter in the universe is one crucial difference between the inflationary model and the previous model.​

Source

This is actually responded to in Carroll's article.

The basic context of this statement is that in some special cases, you can redefine your terms so that energy remains conserved in General Relativity, as long as you make it so that the gravitational field has negative energy. But you can't always do this. It just doesn't work in some other cases (in the context of an expanding universe, for instance, it only works for a closed universe, not an open universe).

Ultimately it comes down to this: you can't always write down the global energy of a system in General Relativity. If you can't write the value down, you can't conserve energy globally.

 

[haushofer]

Who says we may interpret the CC as an energy term in the first place? It determines the vacuum solution, but whether it can be interpreted as energy is part of the "geometry vs energy-momentum" discussion, or "is it on the left hand or right hgand side of the einstein eqns?"

 

[PAllen]

This is actually responded to in Carroll's article.

The basic context of this statement is that in some special cases, you can redefine your terms so that energy remains conserved in General Relativity, as long as you make it so that the gravitational field has negative energy. But you can't always do this. It just doesn't work in some other cases (in the context of an expanding universe, for instance, it only works for a closed universe, not an open universe).

Ultimately it comes down to this: you can't always write down the global energy of a system in General Relativity. If you can't write the value down, you can't conserve energy globally.

Well, actually you can. Carroll even refers to this ( the physicists who say total energy is exactly zero). The disagreement is on whether such universal approaches are physically meaningful. A substantial majority of physicists think they are not, in contrast to ADM energy which has a clear physical meaning when it is definable - so it is universally accepted ( but does not apply in cosmological solutions).

An example of a universal approach (that most would claim isn't meaningful - but not clearly wrong) is:

https://arxiv.org/abs/gr-qc/9701028

[note: in later work Gibbs has provided answers to the questions open in this early presentation, demonstrating complete generality. What he has not done is convince any significant number of physicists of the relevance of this work]

An older universally definable energy is the non covariant stress energy pseudo-tensor, which is always conserved by construction. Again, the main criticism of this is not wrongness, but lack of well defined meaning plus lack of covariance. There is a small school of physicists who argue that pseudotensor energy can be given well motivated physical meaning in harmonic coordinates, and this coordinate dependence is ok. This is clearly a minority opinion.

 

[kimbyd]

Well, actually you can. Carroll even refers to this ( the physicists who say total energy is exactly zero). The disagreement is on whether such universal approaches are physically meaningful. A substantial majority of physicists think they are not, in contrast to ADM energy which has a clear physical meaning when it is definable - so it is universally accepted ( but does not apply in cosmological solutions).

An example of a universal approach (that most would claim isn't meaningful - but not clearly wrong) is:

https://arxiv.org/abs/gr-qc/9701028

[note: in later work Gibbs has provided answers to the questions open in this early presentation, demonstrating complete generality. What he has not done is convince any significant number of physicists of the relevance of this work]

An older universally definable energy is the non covariant stress energy pseudo-tensor, which is always conserved by construction. Again, the main criticism of this is not wrongness, but lack of well defined meaning plus lack of covariance. There is a small school of physicists who argue that pseudotensor energy can be given well motivated physical meaning in harmonic coordinates, and this coordinate dependence is ok. This is clearly a minority opinion.

I don't understand your response. They only discuss energy conservation in the special case of a closed universe.

 

[PAllen]

I don't understand your response. They only discuss energy conservation in the special case of a closed universe.

No, they give an example of closed universe as a special case. The method presented before that application is not so restricted. I also explicitly mentioned other publications by Gibbs extended this line of work. These explicitly discuss open universes. Unfortunately, the most recent discussion is on vixra, which I would rather not link to, but it should be easy for you to find.

The whole second point about pseudotensors is inherently unrestricted to closed universes. In fact, when it was developed by Einstein and refined by Landau-Lifschitz, there was no expectation that the universe might be closed.

 

[kimbyd]

No, they give an example of closed universe as a special case. The method presented before that application is not so restricted. I also explicitly mentioned other publications by Gibbs extended this line of work. These explicitly discuss open universes. Unfortunately, the most recent discussion is on vixra, which I would rather not link to, but it should be easy for you to find.

The whole second point about pseudotensors is inherently unrestricted to closed universes. In fact, when it was developed by Einstein and refined by Landau-Lifschitz, there was no expectation that the universe might be closed.

My understanding is that this method doesn't give a sensible answer for a flat or open universe.

 

[PAllen]

My understanding is that this method doesn't give a sensible answer for a flat or open universe.

That's the point. What is sensible to some is not to others. But the minority who find one or another general approach to energy conservation GR sensible get the same answer for any observable predictions for GR as those who don't. It boils down to the following disagreement:

1) If you require total energy on large scales have certain sensibility properties, then it can only be defined for some special cases, so conservation is out of the question.

2) It is ok for total energy on large scales in GR to fail to have some expected properties.It follows a formal conservation law in all cases but has generally accepted properties of energy only in special cases.

 

[kimbyd]

That's the point. What is sensible to some is not to others.

What I meant is that the total energy in those cases is either divergent or undefined, so there's no way to say that it's conserved. What I mean by sensible is not the colloquial definition. I mean you can't mathematically write down the concept of conservation of energy in these situations.

 

[PAllen]

What I meant is that the total energy in those cases is either divergent or undefined, so there's no way to say that it's conserved. What I mean by sensible is not the colloquial definition. I mean you can't mathematically write down the concept of conservation of energy in these situations.

Yes you can. The canonic form of conservation of energy is that the change in energy in a volume, however large, is equal to its flux across the boundary. No one says Newtonian physics violates conservation of energy even though total energy for an infinite universe of nonzero average energy density is undefined.

Both Gibbs formalism, as well as the Einstein or Landau-Lifschitz formalism write down a conservation law of the mathematically correct formalism as just described, in full generality. Then, the reason why most physicists (myself included, though I am not a physicist, just an amateur) are skeptical of these is that the energy so defined lacks connection to any in principle measurements (except in the special cases like ADM energy or Komar energy), while in the Newtonian case there is connection to measurements. The pseudotensor formalisms are also subject to the critique that they are not covariant objects (though Einstein and Landau-Lifschitz thought this was ok in order to preserve conservation of energy).

 

[kimbyd]

Yes you can. The canonic form of conservation of energy is that the change in energy in a volume, however large, is equal to its flux across the boundary. No one says Newtonian physics violates conservation of energy even though total energy for an infinite universe of nonzero average energy density is undefined.

Right, but in an expanding space-time in the standard formulation, the change in energy in a volume is not simply the change in flux across a boundary. It's the change in flux across the boundary plus an additional geometric term that comes from the space-time curvature.

If you want to, you can try to define that additional geometric term as a change in potential energy. But I just don't think it's been demonstrated that works in a consistent way in all cases.

 

[PAllen]

Right, but in an expanding space-time in the standard formulation, the change in energy in a volume is not simply the change in flux across a boundary. It's the change in flux across the boundary plus an additional geometric term that comes from the space-time curvature.

If you want to, you can try to define that additional geometric term as a change in potential energy. But I just don't think it's been demonstrated that works in a consistent way in all cases.

It works in a mathematically consistent way in all cases. For example just check as old a source as Bermann's 1942 text on GR. A complete derivation is given that applies to any pseudorienannian manifold whatsoever. The point is that any conserved energy approach in GR includes curvature propagation (except Komar mass because it only applies to stationary space times). The problem with universal approaches is not consistency, it is physical interpretation.

 

[kimbyd]

It works in a mathematically consistent way in all cases. For example just check as old a source as Bermann's 1942 text on GR. A complete derivation is given that applies to any pseudorienannian manifold whatsoever. The point is that any conserved energy approach in GR includes curvature propagation (except Komar mass because it only applies to stationary space times). The problem with universal approaches is not consistency, it is physical interpretation.

But if it includes curvature propagation, it's not simply conservation of energy. It's a statement that energy changes in a well-defined way because space-time changes.

 

[PeterDonis]

if it includes curvature propagation, it's not simply conservation of energy. It's a statement that energy changes in a well-defined way because space-time changes.

This is a matter of language, not physics. Questions about what ordinary language is the "right" language to use to describe a piece of physics cannot be resolved by experiment; they are a matter of preference and judgment. So they're not really on topic here.

 

[PeterDonis]

The OP question has been sufficiently answered. Thread closed.