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tionis
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The CMB used to be gamma rays, right? And now it's microwaves - more redder energy: so where did the rest of the energy go?
In GR, global total energy can only be defined asymptotically flat spacetimes. Cosmological solutions do not have this property, and total energy is undefined for them. It is better to think of 'conservation of total energy of the universe' as undefined rather than violated. This is because there are ways to look at any individual CMB photon and say there is no change in energy - it is no different than a gamma ray emitted from a source at rest in one frame, and absorbed by a detector moving near c away from the source (arbitrary redshift possible). However, there is still no way to get from here to globally conserved energy - you just have that the 'loss of energy' for any specific photon is a coordinate dependent statement.
A related nice read: http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
A related nice read: http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
I feel hardly qualified to question Sean Carroll, but I wonder about some statements made here.
He seems to suggest there is some well formulated energy that is not conserved (rather than not definable for Cosmology, like the ADM energy). Does anyone have any idea what he is referring to?
- It can't be Bondi energy as that ignores the energy of light and also requires asymptotic infinity assumptions which do not apply to our universe.
- It can't be Komar mass, because the universe is not static.
So what is it? Some pseudo-tensor integrated in comoving coordinates, taken as a meaningful physical quantity?
Since he doesn't reference, even by footnote, any more technical discussion, I can't guess what he is referring to.
Does anyone perhaps familiar with his body work or opinions have any idea?
PAllen, hi!
I corresponded with Prof. Carroll this morning and this is what he said about your questions:
''Just the integral of the energy density over a Robertson-Walker spacelike hypersurface (with the factor \sqrt{-g} = a^3 to account for the expansion of the universe). That's what people think of when they say "the energy of the universe" in a cosmological context, and my point was simply that it's not conserved, there's no reason to expect it to be conserved, and there's no way to fix it up to make it conserved. (Except, of course, to take the true Hamiltonian, which will be identically zero in cosmology and doesn't really reflect what people are thinking about when they worry over conservation of energy.) -Sean''
That's not the point. You can introduce the cosmological constant into the field equations w/o relating it to energy at all. Locally you will still have a covariantly conserved energy-momentum tensor. The point is that you cannot define the concept "energy" as a volume integral in general, therefore energy is not even defined (and it's pointless to discuss whether something that is not defined can be conserved)Dark energy seems to account for 70% of the universe's current rate of expansion. Most notable, since it is not diluted by expansion, then every moment the volume of the universe increases, the dark energy increases with it. Not even a hint of energy conservation there. The energy of the universe is growing exponentially.
An article by Michael Weiss and John Baez might help.
http://cybermax.tripod.com/Energy.html
Another one by Philip E. Gibbs
http://www.prespacetime.com/index.php/pst/article/viewFile/89/85
Gibb's presents an interesting argument that you can, that is not yet accepted.
One interesting consequence that appears to me to follow from his final formulation for the conserved Noether current (the one that is simplified by using the EFE) is that, if you can find a coordinate chart on a spacetime such that the timelike basis vector is independent of *all* the coordinates (i.e., its partial derivative with respect to all four coordinates is zero), then the total energy of that spacetime, by his definition, is zero. (This follows immediately from the formula I mentioned since it includes a multiplicative factor that depends on the partial derivatives.) An equivalent way of formulating the condition is that there must be a chart in which the metric coefficient ##g_{00}## is constant.
One obvious case that satisfies the above condition is any FRW spacetime in the standard FRW chart--i.e., not just the closed FRW spacetime that Gibbs specifically mentions in his paper, but *any* of the FRW spacetimes, since the metric in all of them obviously meets the condition of constant ##g_{00}##.
Some physicists have claimed that energy conservation is violated when you look at the cosmic background radiation. This radiation consists of photons that are redshifted as the universe expands. The total number of photons remains constant but their individual energy decreases because it is proportional to their frequency ( E = hf ) and the frequency decreases due to redshift. This implies that the total energy in the radiation field decreases, but if energy is conserved, where does it go? The answer is that it goes into the gravitational field, but to make this answer convincing we need some equations.
....As the universe expands, the inflation field gains energy from gravity [negative pressure]
....Self-creation cosmology (SCC) theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology..
"The scalar field is a source for the matter-energy field if and only if the matter-energy field is a source for the scalar field."
As the source for the scalar field is the trace of the stress-energy tensor, the PMI is delivered by coupling this trace to the divergence of the stress-energy tensor.
Since no one has replied, I will. I read this
An article by Michael Weiss and John Baez ....
http://cybermax.tripod.com/Energy.html
And it probably gives as good a set of explanations as any.