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No global conservation of energy?

Wangler

Master Poster
Joined
Feb 20, 2008
Messages
2,228
Hey,

I was reading Peebles, "Principles of Physical Cosmology", 1993.

On page 139, in a section talking about "Blackbody Radiation in an Expanding Universe" he says:

Peebles said:
The second confusing point is the nature of energy balance in the CBR............The resolution of this apparent paradox is that while energy conservation is a good local concept, as in equation (6.18), and can be defined more generally in the special case of an isolated system in asymptotically flat space, there is not a general global conservation law in general relativity theory.

What? No global energy conservation in general relativity?

How can that be? :confused:

Say it isn't so!

Can anyone clear this up, without me having to regurgitate the entire chapter here?
 
Hey,

I was reading Peebles, "Principles of Physical Cosmology", 1993.

On page 139, in a section talking about "Blackbody Radiation in an Expanding Universe" he says:



What? No global energy conservation in general relativity?

How can that be? :confused:

Say it isn't so!

Can anyone clear this up, without me having to regurgitate the entire chapter here?


equation 6.18 would help at the least.

However, I would hazard a guess that he's referring to the conversion of matter to energy and vice versa. It doesn't happen often on earth but is fairly common in the universe at large, see for example our Sun. However, he could be referring to a great number of things. eta: "asymptotically flat space" is not something I recall studying in physics so this may well be beyond me.
 
Last edited:
Hey,

I was reading Peebles, "Principles of Physical Cosmology", 1993.

On page 139, in a section talking about "Blackbody Radiation in an Expanding Universe" he says:

What? No global energy conservation in general relativity?

How can that be? :confused:

Say it isn't so!

Can anyone clear this up, without me having to regurgitate the entire chapter here?

I suggest the linked article on whether energy is conserved in General Relativity.
The answer is that there is no global proof that energy is conserved in GR but this depends on what you mean by "energy" and "conserved". Even in special relativity, energy is not conserved - it is the the energy-momentum 4-vector that is conserved.
 
Hey,

I was reading Peebles, "Principles of Physical Cosmology", 1993.

I don't like the way Peebles phrased that. Here's the deal - you pick any region of the universe, and I will prove for you that the total energy contained in that region at any time equals the total energy that started there plus (or minus) the energy that flowed in or out.

Normally, to obtain conservation of total energy, one extends that region to cover the entire space (so no energy can flow in or out, meaning the energy inside is constant, meaning total energy is conserved).

That is tricky to do in an infinite expanding cosmology - no matter how big you make the region, there is always a significant amount of flow (at least I think that's the problem - I haven't worked through the equations). I suspect this ISN'T an issue in closed cosmologied, but again, I'll need to check to be sure.
 
That is tricky to do in an infinite expanding cosmology - no matter how big you make the region, there is always a significant amount of flow (at least I think that's the problem - I haven't worked through the equations). I suspect this ISN'T an issue in closed cosmologied, but again, I'll need to check to be sure.

Sol,

What you say in your first sentance quoted above: this is my understanding of what Peebles is trying to say.
 
Is Energy Conserved in General Relativity? - this webpage by John Baez and Michael Weiss might be of some interest to readers of this thread ...

From what I can understand from this website, the problem arises partially from the calculation of the divergence across a bounding volume?

Is that correct?

I think that they kind of described this by explaining that Gauss' Law procedures are being extended from the expression of the flux across a boundary as a scalar, to a flux across a boundary expressed as a vector.

In other words, we are talking about the divergence of a vector on one hand, and a divergence of a tensor on the other hand.
 
I think he means to say that the total energy is constant, but that it is always spreading out more and more as the universe expands. Therefore, if you define any fixed space the amount of energy in that fixed space - no matter how big - will always be going downwards as energy expands into the growing parts that are beyond the fixed space.

It seems to me to be the same thing that Sol said.
 
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