Conservation of energy in quantum gravity

[KleinMoretti]

TL;DR Summary

is conservation of energy present in our current theories of gravity?

This is what I found regarding LQG
https://www.hindawi.com/journals/ahep/2009/905705/

is conservation of energy present in our current theories of gravity? more specifically string theory and loop quantum gravity?

 

[PeterDonis]

is conservation of energy present in our current theories of gravity? more specifically string theory and loop quantum gravity?

String theory and loop quantum gravity are not "our current theories of gravity". They are speculations about a possible quantum theory of gravity.

As such, I am moving this thread to the Beyond the Standard Models forum.

 

[KleinMoretti]

String theory and loop quantum gravity are not "our current theories of gravity". They are speculations about a possible quantum theory of gravity.

okay fair point, but still my question still stands

 

[pines-demon]

TL;DR Summary: is conservation of energy present in our current theories of gravity?

This is what I found regarding LQG
https://www.hindawi.com/journals/ahep/2009/905705/

is conservation of energy present in our current theories of gravity? more specifically string theory and loop quantum gravity?

I do not know about string theory or LQG, but in general relativity the usual concept of energy conservation is complex. Some would even say it is not locally conserved depending on the definition. Other would argue that Einstein's equation are a sort of energy conservation. However the point is that the usual notion of energy conservation is more complex in GR and needs to be discussed in more precise terms when handling non-pertubative gravity.

 

[KleinMoretti]

I do not know about string theory of LQG, but in general relativity the usual concept of energy conservation is complex in general relativity. Some would even say it is not locally conserved depending on the definition. Other would argue that Einstein's equation are a sort of energy conservation. However the point is that the usual notion of energy conservation is more complex in GR and needs to be discussed in more precise terms when handling non-pertubative gravity.

yes I know that in GR conservation of energy is more subtle, I also know that in QFT there isn't as much trouble with it which is why it made me curious about string theory and LQG

 

[PeterDonis]

I also know that in QFT there isn't as much trouble with it

In QFT in flat spacetime there isn't. But QFT in flat spacetime means QFT ignoring gravity.

 

[KleinMoretti]

In QFT in flat spacetime there isn't. But QFT in flat spacetime means QFT ignoring gravity.

And what about string theory and LQG

 

[PeterDonis]

And what about string theory and LQG

Since they both claim to be theories of gravity, I would expect them to have the same issues as General Relativity has with conservation of energy. But I'm not knowledgeable enough about the details to say how specifically those issues appear.

 

[KleinMoretti]

Since they both claim to be theories of gravity, I would expect them to have the same issues as General Relativity has with conservation of energy. But I'm not knowledgeable enough about the details to say how specifically those issues appear.

But I thought quantum gravity would solve those problems

 

[pines-demon]

But I thought quantum gravity would solve those problems

Why? These are not "problems" but features of the theory.

 

[PeterDonis]

But I thought quantum gravity would solve those problems

Why would you think that? Why do you think they are "problems" to begin with?

 

[KleinMoretti]

Why would you think that? Why do you think they are "problems" to begin with?

I was referring to the issues that you mentioned general relativity has with energy I didn’t mean to imply that it was a problem of the theory, I thought that a theory of gravity would help with those issues.

 

[PeterDonis]

I was referring to the issues that you mentioned general relativity has with energy

Yes, I know.

I didn’t mean to imply that it was a problem of the theory

Ok.

I thought that a theory of gravity would help with those issues.

I take it you mean a theory of quantum gravity. But if there isn't a problem, why would any help be needed?

 

[KleinMoretti]

Yes, I know.


Ok.


I take it you mean a theory of quantum gravity. But if there isn't a problem, why would any help be needed?

I though that the main issue GR has with energy conservation is that gravitational energy is a non-local quantity, you can't express gravitational energy as a local density. I was under the impression that a theory of quantum gravity would deal with this problem.

 

[PeterDonis]

I though that the main issue GR has with energy conservation is that gravitational energy is a non-local quantity, you can't express gravitational energy as a local density.

That's true.

I was under the impression that a theory of quantum gravity would deal with this problem.

Again, why do you think it's a problem?

 

[KleinMoretti]

That's true.


Again, why do you think it's a problem?

I mean there is a reason why we have pseudotensors, isn’t it because some people think that this is problematic enough that it deserves a solution

 

[pines-demon]

I though that the main issue GR has with energy conservation is that gravitational energy is a non-local quantity, you can't express gravitational energy as a local density. I was under the impression that a theory of quantum gravity would deal with this problem.

I do not think any current program of quantum gravity is actively trying to make a new definition of conservation of energy in curved spacetime. Again the subtlety of energy in GR is related to how curved space-time needs to be described, but this feature is inherent to relativity and definitely not an issue. Quantum gravity is more focused on other problems like quantizing gravity in a formalism comparable or at least compatible with quantum electrodynamics or chromodynamics. Other problems are related to how to deal with singularities in extreme gravitational fields like those found near black holes or the beginnings of the Universe.

 

[KleinMoretti]

I do not think any current program of quantum gravity is actively trying to make a new definition of conservation of energy in curved spacetime. Again the subtlety of energy in GR is related to how curved space-time needs to be described, but this feature is inherent to relativity and definitely not an issue. Quantum gravity is more focused on other problems like quantizing gravity in a formalism comparable or at least compatible with quantum electrodynamics or chromodynamics. Other problems are related to how to deal with singularities in extreme gravitational fields like those found near black holes or the beginnings of the Universe.

So are you saying conservation of energy in quantum gravity is the same as in GR, with the same subtleties?(e.g. depending on the definitions energy is/isn’t conserved)

 

[pines-demon]

So are you saying conservation of energy in quantum gravity is the same as in GR, with the same subtleties?(e.g. depending on the definitions energy is/isn’t conserved)

We do not have a valid theory of quantum gravity so I can't tell, but it would be very conflicting if GR and QG do not have a limit in which both agree.

 

[KleinMoretti]

We do not have a valid theory of quantum gravity so I can't tell, but it would be very conflicting if GR and QG do not have a limit in which both agree.

I guess I should have specified, is conservation of energy treated the same in string theory and LGQ as in GR?

 

[PeterDonis]

I mean there is a reason why we have pseudotensors, isn’t it because some people think that this is problematic enough that it deserves a solution

But the pseudotensors do not solve the problem you described earlier: they don't give a way to localize "gravitational energy". They only give a way to define a global energy in spacetimes which are not asymptotically flat or stationary, so the recognized global energies for those particular cases do not exist. And all the pseudotensor definitions are frame-dependent, so whether they actually provide a valid global energy is itself questionable.

 

[KleinMoretti]

And you saying that this should also be the same for string theory and LGQ or any theory that deals with gravity no?

 

[PeterDonis]

And you saying that this should also be the same for string theory and LGQ or any theory that deals with gravity no?

I have already said all I can usefully say about string theory and LQG in post #8.

 

[KleinMoretti]

I have already said all I can usefully say about string theory and LQG in post #8.

Okay, thanks for your input.

 

[OlderWannabeNewton]

Not to bring up an older thread, but this is an interesting topic. Most of the conceptual subtleties around conservation of energy in quantum gravity are already contained in classical GR. If you have a spacetime with an asymptotic null/timelike boundary, then energy can be defined at infinity and has conservation laws associated to it. What this actually defines is a Hamiltonian at infinity which generates time evolution. In canonical quantum gravity this boundary Hamiltonian can be quantized, with all the usual subtleties (but nothing specific to conservation of energy).

In the bulk of the spacetime we just have the Hamiltonian constraint. This basically says there's no gauge-invariant bulk notion of energy/time. It is famously difficult to construct a Hilbert space of states which satisfies the Hamiltonian constraint in higher dimensions, but again nothing really related to the conceptual issues surrounding conservation of energy.

In classical GR, one way to get a meaningful notion of bulk energy is via the covariant phase space formalism applied to finite boundaries in the bulk. For example you can treat the event horizon as a boundary of the exterior and define quasi-local charges on cuts of the horizon associated to bulk diffeomorphisms. This essentially acts as a Hamiltonian for exterior degrees of freedom. This will satisfy conservation laws as usual. But this is much trickier to achieve in quantum gravity, where the bulk spacetime fluctuates (and can even have topological changes), hence making it difficult to precisely defined a finite boundary in the bulk spacetime, though it can be done via constraints. Once again, nothing about quantum gravity adds conceptual depth to the notion of energy in gravity. It's already quite deep in GR.

 

[KleinMoretti]

Not to bring up an older thread, but this is an interesting topic. Most of the conceptual subtleties around conservation of energy in quantum gravity are already contained in classical GR. If you have a spacetime with an asymptotic null/timelike boundary, then energy can be defined at infinity and has conservation laws associated to it. What this actually defines is a Hamiltonian at infinity which generates time evolution. In canonical quantum gravity this boundary Hamiltonian can be quantized, with all the usual subtleties (but nothing specific to conservation of energy).

In the bulk of the spacetime we just have the Hamiltonian constraint. This basically says there's no gauge-invariant bulk notion of energy/time. It is famously difficult to construct a Hilbert space of states which satisfies the Hamiltonian constraint in higher dimensions, but again nothing really related to the conceptual issues surrounding conservation of energy.

In classical GR, one way to get a meaningful notion of bulk energy is via the covariant phase space formalism applied to finite boundaries in the bulk. For example you can treat the event horizon as a boundary of the exterior and define quasi-local charges on cuts of the horizon associated to bulk diffeomorphisms. This essentially acts as a Hamiltonian for exterior degrees of freedom. This will satisfy conservation laws as usual. But this is much trickier to achieve in quantum gravity, where the bulk spacetime fluctuates (and can even have topological changes), hence making it difficult to precisely defined a finite boundary in the bulk spacetime, though it can be done via constraints. Once again, nothing about quantum gravity adds conceptual depth to the notion of energy in gravity. It's already quite deep in GR.

@PeterDonis I know you said that right now we dont have a theory of quantum gravity so its hard to make general statements, but I came across this old paper that does since to make a general statement about unitarity and conservation of energy in quantum gravity, more specifically it says
"
dρ/dt = 0(7.7)

This proposal that we make is not without its difficulties, however, these difficulties are also present in any unitary theory as well. Namely, if we believe that quantum mechanics is fully consistent and applies to the universe as a whole, then Equation (7.7) will hold, and one will need to find an internal observable to act as a clock. Likewise, if we believe that Hawking radiation can be explained by a unitary theory of quantum gravity, then the Wheeler deWitt Equation akin to (7.7) holds. In other words if we are trying to decide whether our fundamental evolution laws are unitary or non-unitary, then both options suffer from the same problems when it comes to energy conservation and time.
In a unitary theory one encounters various issues of time and energy conservation, usually studied in the context of attempts to apply canonical quantization to gravity. In particular, although it will be possible to find an observable τ which is at least approximately conjugate to some Πτ , if it is not perfectly conjugate, then there is some (arguably small) probability that the clock will run backwards[28]. There is however, a lot of freedom in how we decompose H into Ho and Πτ . Not only can we choose it so that τ acts as a good clock, but we can also choose it so that the energy exchange between the clock and system is as small as possible. This provides an interesting new criteria for decomposing closed systems, for example, in quantum cosmology."

 

[PeterDonis]

I know you said that right now we dont have a theory of quantum gravity so its hard to make general statements, but I came across this old paper that does

No, the paper is not making a general statement, it's proposing a speculative model.

to make a general statement about unitarity and conservation of energy in quantum gravity, more specifically it says
"
dρ/dt = 0(7.7)

Again, that's not a general statement, it's a speculative proposal. An obvious problem with it is that it assumes time translation invariance, but an expanding universe is not time translation invariant.

 

[ohwilleke]

And you saying that this should also be the same for string theory and LGQ or any theory that deals with gravity no?

There is no a priori reason that conservation of the energy should be the same in string theory (which uses gravitons and branes to address GR), LGQ which quantizes space-time, and GR which is GR.

Intuitively, string theory ought to be localizing gravity mass-energy looking mechanistically at how it gets the job of gravity done. Maybe there is some reason that is beyond me that it doesn't, but what "feels" like non-conservation of energy, non-localization of energy in GR could arise from off brane activity in versions of string theory where non-gravitational activity and matter are confined to branes that don't similarly confine gravitons.

I honestly have no real idea how either dark energy phenomena or conservation and localization of energy works in LQG, which is struggling to establish GR as its classical limit at all.