Questions about paper "How closed is cosmology"

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  • #1
KleinMoretti
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TL;DR Summary
A new paper discusses how a closed system like the universe can exhibit features of open systems.
In the paper, the authors argue that a closed system can exhibit features of an open system one of the being the non-conservation of energy, my questions how can a closed system have non-conservation of energy. (I know in GR, conservation of energy is subtle issue but it doest seem like the authors are referring to the type of non-conservation of energy present In GR)
 
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  • #2
KleinMoretti said:
in GR, conservation of energy is subtle issue but it doest seem like the authors are referring to the type of non-conservation of energy present In GR
Yes, they are. They are not talking about "closed systems" in general. They are talking about a closed cosmology, i.e., a closed universe--where "closed" here means "spatially finite but unbounded". For example, an FRW universe containing only matter with density greater than the critical density. They are then simply choosing a definition of the global "energy" of such a universe that results in it not being conserved. Which is just an example of the subtle issue in GR with global conservation of energy.
 
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  • #3
the reason I said that is because they say that non conservation of energy is a feature of their model as oppose to a regular closed system where energy is conserved. "Throughout this work, we have investigated different inequivalent ways in which dynamical systems can be considered closed. These different notions include closure in the sense of conserved energy, conserved measure density and dynamical autonomy. While we found merits for each, no single notion of closure was completely adequate for all purposes. In particular, we found conven- tional notions of conserved energy and measure to be wanting when applied to the cosmological setting. In that context, we compared a closed (in the sense of preserved measure density and Hamiltonian) symplectic description of cosmology to an open contact formulation. We found that the latter should be taken to give a better complete description of the system.

Central to our argument was a requirement to treat as physical only those structures that are strictly necessary for maintaining empirical adequacy. The symplectic ‘closed’ descriptions violate this principle because they treat as distinct states that differ only by the overall scale of the universe (as determined by v), which is not empirically relevant. In contrast, the contact description does satisfy this principle as it excludes v. While this description does not conserve energy or measure density, it is nevertheless autonomous in the empirically sufficient variables, and is thus ‘closed’ in the third sense discussed above."
 
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  • #4
KleinMoretti said:
they say that non conservation of energy is a feature of their model as oppose to a regular closed system where energy is conserved
That's because they are choosing a very unusual definition of a "closed" system.

For example, they are defining a damped harmonic oscillator as "closed" on the grounds that they can define its dynamics to be "autonomous", by which they mean a self-contained set of equations. But that set of equations includes a damping constant, which they are treating as just a magical property of the system. In any actual oscillator, however, damping arises because of interactions with other systems (for example, friction), and those interactions exchange energy. The paper is simply ignoring this and pretending that they can still treat such as system as "closed". In ordinary physics terminology, such a damped oscillator would not be closed, and non-conservation of its energy would simply be a result of energy being dissipated to other systems through the damping interactions.
 
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yes I saw the their damping oscillator example and that I can understand, what im confused about is how they use that same logic in cosmology, in the oscillator example like you said there is a dissipation of energy due to damping interactions, but when talking about the universe where there is no interactions with an outside environment, what is the physical consequence of the non-conservation of energy present in their model.
 
  • #6
KleinMoretti said:
what is the physical consequence of the non-conservation of energy present in their model.
I'm not sure, and I'm not sure the authors of the paper have considered that question. The usual answer in GR is none--that if you find a definition of "total energy of the universe" that isn't conserved, that's just a consequence of the issues in GR that you referred to before, and it doesn't have any physical meaning.
 
  • #7
PeterDonis said:
I'm not sure, and I'm not sure the authors of the paper have considered that question. The usual answer in GR is none--that if you find a definition of "total energy of the universe" that isn't conserved, that's just a consequence of the issues in GR that you referred to before, and it doesn't have any physical meaning.
another confusing thing is the supposed reason why their model is better, "Note that the Hamiltonian is constraint and must be zero — a fact that follows from the time reparametrization invariance of
general relativity. From the existence of these structures it is easy to verify that the ‘energy’ (the Hamiltonian) and the measure Ω = ω1+n where n is the number of scalar fields, are conserved over time. Furthermore, from Hamilton’s equations we can find an equations of motion of each of the phase-space variables written in terms of itself and the other phase-space variables. Our system is therefore autonomous. It would hence seem apparent that cosmology is a closed system following all three notions that we have discussed.
There is, however, a catch: The algebra generated by the set of variables just described is strictly larger than what is needed for empirical adequacy. In particular, the volume v can be set to any value by re-scaling its initial condition without affecting any empirical predictions of the theory. This is because such predictions only ever rely on the value of v relative to some reference value (usually taken to be an initial or final condition).
It is clear from these that the dynamical algebra closes in terms of the φ and H without ever needing to refer to v. We should therefore seek a description of our system that never makes reference to v in the first place."

it seems that to me that the presence of non-conservation in their model is intentional.
"In contrast, the contact description does satisfy this principle as it excludes v. While this description does not conserve energy or measure density, it is nevertheless autonomous in the empirically sufficient variables, and is thus ‘closed’"
 
  • #8
PeterDonis said:
Yes, they are. They are not talking about "closed systems" in general. They are talking about a closed cosmology, i.e., a closed universe--where "closed" here means "spatially finite but unbounded". For example, an FRW universe containing only matter with density greater than the critical density. They are then simply choosing a definition of the global "energy" of such a universe that results in it not being conserved. Which is just an example of the subtle issue in GR with global conservation of energy.
I don't understand this claim. if it's spatially finite then it should be bounded, if it's unbounded then it cannot be spatially finite.
Do you physicists also think logically?
Sorry if I offended anyone by this question.
 
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  • #9
billtodd said:
if it's spatially finite then it should be bounded, if it's unbounded then it cannot be spatially finite.
No. A 3-sphere is spatially finite but unbounded.

billtodd said:
Do you physicists also think logically?
Sorry if I offended anyone by this question.
The question is not offensive, but it does show that you should be really, really hesitant about making such remarks, since any lack of logic in this case is on your side.
 
  • #11
Bandersnatch said:
Finite but >without a boundary<.
Yes, that would be the precise term.
 
  • #12
PeterDonis said:
No. A 3-sphere is spatially finite but unbounded.


The question is not offensive, but it does show that you should be really, really hesitant about making such remarks, since any lack of logic in this case is on your side.
Well the sphere is bounded by the fact that it's the boundary between the interior of a 4-d ball and the outside of the ball.

But the universe if it's a closed system then it's all what there is if it's finite in space or infinite we cannot really know.
 
  • #14
billtodd said:
Well the sphere is bounded by the fact that it's the boundary between the interior of a 4-d ball and the outside of the ball.
...but by making this argument you are presupposing a 5-or-more dimensional background in which the universe is embedded, just as the 3d surface of the Earth is embedded in a 3d space in which we are free to move. That is not the model under discussion, which is one where the 4d universe (closed or otherwise) is all there is. There is no "inwards" or "outwards" direction, so no boundary.
 
  • #15
billtodd said:
Well the sphere is bounded by the fact that it's the boundary between the interior of a 4-d ball and the outside of the ball.
First, that's not the sense in which I was using the term "bounded". I was using to mean "without boundary", which @Bandersnatch correctly pointed out is the more precise term.

Second, as @Ibix pointed out, our best current model of our universe does not include an embedding in any higher dimensional space, and we have no evidence for any such embedding, so to our best current knowledge there is no "4-d ball" or "outside".

billtodd said:
But the universe if it's a closed system then it's all what there is if it's finite in space or infinite we cannot really know.
Our best current model says that our universe is spatially infinite. However, it is still possible (though considered unlikely) that it is spatially finite but very much larger than our observable universe.
 

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