Does Phantom Dark Energy Violate Conservation of Energy?

[KleinMoretti]

TL;DR Summary

phantom dark energy has negative kinetic energy, can an increase of phantom energy still be said to be compensated by negative energy of gravitational field

from Sean Carroll's blog " “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields”. This is an explanation that I have seen mentioned somewhat frequently, my question is in the case of phantom dark energy which has negative kinetic energy, does this explanation still hold?

 

[PeterDonis]

“there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields”. This is an explanation that I have seen mentioned somewhat frequently, my question is in the case of phantom dark energy which has negative kinetic energy, does this explanation still hold?

As a heuristic explanation, it holds for any solution of the Einstein Field Equation. However, it's only a heuristic explanation. As the blog post you reference will tell you if you read carefully, there is no localized energy density corresponding to "energy in the gravitational field". It's not a tensor quantity, and there are many physicists who would say that anything that isn't a tensor quantity has no physical meaning in GR.

 

[KleinMoretti]

As a heuristic explanation, it holds for any solution of the Einstein Field Equation. However, it's only a heuristic explanation. As the blog post you reference will tell you if you read carefully, there is no localized energy density corresponding to "energy in the gravitational field". It's not a tensor quantity, and there are many physicists who would say that anything that isn't a tensor quantity has no physical meaning in GR.

so it doesn't matter the type of dark energy?

 

[KleinMoretti]

As a heuristic explanation, it holds for any solution of the Einstein Field Equation. However, it's only a heuristic explanation. As the blog post you reference will tell you if you read carefully, there is no localized energy density corresponding to "energy in the gravitational field". It's not a tensor quantity, and there are many physicists who would say that anything that isn't a tensor quantity has no physical meaning in GR.

thx for the answer, my question has been answered so the thread can be closed if needed.

 

[PeterDonis]

so it doesn't matter the type of dark energy?

What I said is true for any type of energy, dark or otherwise.

 

[KleinMoretti]

What I said is true for any type of energy, dark or otherwise.

This is a comment by Phillip Gibbs "To define energy over a region including a black hole we need a space-like hypersurface that passes through it. It is a feature of ordinary black-holes that the singularity inside is in the future light cone so the hypersurface can easily be chosen to avoid it. Indeed the total energy of a black hole is given by the energy equivalent of its mass which is easily determined from outside.

There remains a question over how to deal with more complex space-times which can have naked singularities or wormholes through to disconnected regions of spacetime. Of course this does not invalidate energy conservation laws for any situations that are known to really exist."

My question is regarding the second paragraph, is he saying that in the spacetimes he describes, GR doesn't apply and by this I mean what you said in our private discussion where you explained how the local conservation of stress-energy is built into the theory and also what you said in #2

 

[PeterDonis]

This is a comment by Phillip Gibbs

From where? Please give a reference.

 

[PeterDonis]

is he saying that in the spacetimes he describes, GR doesn't apply

No, he's saying that the kinds of spacetimes he is describing, while they are mathematical solutions to the Einstein Field Equation, are not believed to describe anything that can actually exist.

 

[Vanadium 50]

Phillip Gibbs

Who?

The famous Gibbs is J. W. Gibbs. The only person with this name I found in the database hasn't written a published and cited paper since 1995.

 

[weirdoguy]

Who?

Someone who publishes on vixra. Namely, a crackpot.

@KleinMoretti you should change your sources.

 

[Vanadium 50]

Someone who publishes on vixra.

Jeepers.
That's too bad.

 

[KleinMoretti]

As a heuristic explanation, it holds for any solution of the Einstein Field Equation. However, it's only a heuristic explanation. As the blog post you reference will tell you if you read carefully, there is no localized energy density corresponding to "energy in the gravitational field". It's not a tensor quantity, and there are many physicists who would say that anything that isn't a tensor quantity has no physical meaning in GR.

I have a doubt, when Sean Carroll talks about dark energy increasing as the universe expands and then says “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” doesn't that still mean that new dark energy is being created out of nowhere thus violating the "can't be created or destroyed" part of the law of conservation of energy?

 

[Nugatory]

doesn't that still mean that new dark energy is being created out of nowhere thus violating the "can't be created or destroyed" part of the law of conservation of energy?

Conservation of energy in curved spacetime is more complicated than that simple "cannot be created or destroyed" soundbite. We have many older threads on this subject, and https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html is a good start as well.

 

[PeterDonis]

doesn't that still mean that new dark energy is being created out of nowhere

No. "Created out of nowhere" would violate the local conservation of stress-energy. Any viewpoint that says the "total energy contained in dark energy" is increasing has to make use of some global quantity that is not a tensor and has nothing to do with the local conservation law.

 

[Mordred]

In the FLRW metric there is an equation of state commonly applied for a scalar field

https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)
See the bottom equation on that link under scalar field modelling.

This equation will correlate to the potential energy terms and the kinetic energy terms. If the kinetic energy term exceeds the field potential energy terms you get the negative pressure term.

When w=-1 this equates to a constant negative pressure that we see for the cosmological constant.

I wouldn't be surprised if Sean Carroll is using this equation in his descriptives hope that helps.

 

[KleinMoretti]

Any viewpoint that says the "total energy contained in dark energy" is increasing has to make use of some global quantity that is not a tensor and has nothing to do with the local conservation law.

okay but from that "total energy contained in dark energy viewpoint" that Sean Carroll talks about, you said

No. "Created out of nowhere" would violate the local conservation of stress-energy.

so you are saying that “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” that this means that new dark energy is not actually being created?

Because to me it seems that saying that "the increase in dark energy is balanced by the negative gravitational energy so that energy is conserved" does not mean that dark energy is not being created out of nowhere, but you said this would violate local conservation so idk

 

[PeterDonis]

so you are saying that “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” that this means that new dark energy is not actually being created?

No. I'm saying that "energy being created" is a local concept--one that can't happen because it would violate the local conservation of stress-energy--whereas "there is energy in the gravitational field but it's negative so it exactly cancels the energy you think is being gained in the matter field" is a global concept and requires attributing physical meaning to non-tensorial global quantities. There is no local interpretation of "there is energy in the gravitational field but it's negative so it exactly cancels the energy you think is being gained in the matter field" at all. The global concepts of "energy" being used in that phrase have no local counterparts.

All this illustrates why physics is not done in ordinary language, it's done in math.

 

[KleinMoretti]

No. I'm saying that "energy being created" is a local concept--one that can't happen because it would violate the local conservation of stress-energy--whereas "there is energy in the gravitational field but it's negative so it exactly cancels the energy you think is being gained in the matter field" is a global concept and requires attributing physical meaning to non-tensorial global quantities. There is no local interpretation of "there is energy in the gravitational field but it's negative so it exactly cancels the energy you think is being gained in the matter field" at all. The global concepts of "energy" being used in that phrase have no local counterparts.

All this illustrates why physics is not done in ordinary language, it's done in math.

okay then, speaking only about global concepts like "increase in total dark energy" and "there is energy in the gravitational field but it's negative so it exactly cancels the energy you think is being gained in the matter field"
what about this:

Because to me it seems that saying that "the increase in dark energy is balanced by the negative gravitational energy so that energy is conserved" does not mean that dark energy is not being created out of nowhere.

 

[PeterDonis]

what about this

What about it?

 

[KleinMoretti]

when Carroll says energy can be said to be conserved because the increase in total dark energy is balanced by gravitational energy-which I understand are global concepts- is he saying then that dark energy is in fact not created out of nowhere?

 

[PeterDonis]

when Carroll says energy can be said to be conserved because the increase in total dark energy is balanced by gravitational energy-which I understand are global concepts- is he saying then that dark energy is in fact not created out of nowhere?

He's not saying anything about whether dark energy is "created out of nowhere". He is taking some global numbers and describing them in a particular way in ordinary language. But those global numbers are not tensorial quantities and many physicists would say they have no physical meaning. They let people like Carroll tell a comforting-sounding story. That's all.

 

[KleinMoretti]

He's not saying anything about whether dark energy is "created out of nowhere". He is taking some global numbers and describing them in a particular way in ordinary language. But those global numbers are not tensorial quantities and many physicists would say they have no physical meaning. They let people like Carroll tell a comforting-sounding story. That's all.

I see, thanks for your responses and time.

 

[KleinMoretti]

@PeterDonis hey on this same topic, I came across this 2 threads, (second thread) that discuss this paper where is argued that energy can be "mined" from the expansion of the universe, is this "energy extracted" the same as the increased dark energy in an expanding universe that we talked about in this thread? I asked this because the answers on those threads were not that clear to me,
for example you said:

"Given the fact that he says this hypothetical network of strings "has the same effect as the cosmological term or as a negative-pressure fluid", the "internal energy" he is referring to is functionally equivalent to dark energy. Since the energy density of dark energy is constant, as the universe expands you can view the total energy due to dark energy in some comoving volume (i.e., the dark energy times the spatial volume of some set of comoving worldlines at some instant of cosmological time) as being an "internal energy" of that comoving volume, which will then increase with time due to expansion (since the spatial volume increases and the energy density is constant).

His working out of the dynamics bears this out, since what he obtains are well known equations for a universe dominated by dark energy.

None of this is a mystery or is controversial. Nor is it a mystery or controversial to say that energy is not conserved in an expanding universe. Sean Carroll has a blog post often referenced here at PF that says the same thing and explains what that statement corresponds to in the math. Another way of saying the same thing is that, except in some special classes of spacetimes (asymptotically flat spacetimes and stationary spacetimes), there is no well-defined "total energy" in any volume; more precisely, there is no invariant that corresponds to any such thing. The "total energy" defined in this paper, which I described above, is coordinate-dependent, not an invariant; the "spatial volume" is the volume in comoving coordinates."

Since in your answer you linked Sean carroll's post, im thinking that this extracted/mined/created energy is what carroll is referring in his article about how "energy increases as the universe expands but is compensated by negative gravitational energy"

See also this answer here, that says "So, just from knowing that some energy conservation law in the cosmological setting exists we must conclude that universe expansion is not a magical source of free energy but rather a reservoir from which we can extract energy (yes!), but this reservoir would be finite either on a fundamental level (e.g. imposed by cosmological horizon) or on a practical one"

 

[PeterDonis]

is this "energy extracted" the same as the increased dark energy in an expanding universe that we talked about in this thread?

No.

 

[KleinMoretti]

also this paper, says

No.

then is the mechanism discussed in the paper an actual perpetual motion machine?
This other paper that mentions the original "Mining energy" paper says:

"As Edward Harrison emphasized: 'The conclusion, whether we like it or not, is obvious: energy in the universe is not conserved' (Harrison, 1981 [13], p.276).
The same conclusion was reached by Peebles (1993) [23] when he considered the energy loss inside a comoving ball of the photon gas (see our Eq.28). On page 139 he wrote 'The resolution of this apparent paradox is that while energy conservation is a good local concept, ... there is not a general global energy conservation in general relativity.'
In fact, only for dust (p = 0) one may speak about energy conservation in expanding universe. But for any matter with p ̸= 0 within any local comoving volume energy is not conserved. This is because in GR there is no EMT of gravity field."
According to that paper the reason why energy can be said to extracted from the expansion of the universe is "This is because in GR there is no EMT of gravity field." which is kind of what Sean carroll says no?

 

[PeterDonis]

then is the mechanism discussed in the paper an actual perpetual motion machine?

No. Perpetual motion is impossible. It would require violation of local conservation of stress-energy.

You keep giving quotes that use vague ordinary language instead of math, from papers you don't fully understand, out of context. That's not a good way to learn physics. If you really want to understand the issues involved here, you need to take the time to work through actual examples, with math, as was done in one of the threads you linked to, and think carefully about what is going on in those examples.

This thread is closed.