The lost energy of Cosmic Background Radiation

atyy

Quote by bcrowell

This is incorrect. You're comparing (1) a cosmological spacetime with (2) a system consisting of a box with photons inside. In case 1, energy isn't conserved (as explained in the FAQ linked to in #15). In case 2, energy is conserved.

It seems a not uncommon analogy:
http://books.google.com/books?id=kNx...page&q&f=false (p343)
http://www.astro.caltech.edu/~george...logy_notes.pdf
http://www2.ph.ed.ac.uk/teaching/cou...lCosmology.pdf

julcab12

Quote by Chalnoth

One way to understand why it has this effect is to consider a somewhat different scenario:

Imagine that we have an enclosed box, and within that box is a gas of photons (you can simply imagine the box as having some temperature, which causes it to be filled with radiation). That gas of photons exerts radiation pressure on each wall of the box equal to [itex]\rho/3[/itex].

Now, what happens if we cause this box to expand in size? Well, if the box expands by a factor of [itex]a[/itex], then the photon pressure on each side of the box exerts work on the box. Because the work is in the direction of the motion of the walls of the box, this amounts to a transfer of energy from the photon gas to the walls of the box. In fact, if you calculate the energy transfer, you exactly get the loss of energy of the photon gas that we see as a redshift.

As to why this pressure leads to a faster slowdown of the expansion, well, that's a bit harder to explain. But suffice it to say that pressure is sort of a kind of energy density, and gravity responds just as well to this sort of energy density as it responds to mass energy.

Good analogy but for noobies like me. It would be a good thing if you mention such limitations, conditions and a brief elaboration of each component first to avoid misconceptions.

Chalnoth

Quote by bcrowell

This is incorrect. You're comparing (1) a cosmological spacetime with (2) a system consisting of a box with photons inside. In case 1, energy isn't conserved (as explained in the FAQ linked to in #15). In case 2, energy is conserved.

It is a different system, but I think it is rather interesting that the math works out identically.

Chalnoth

Quote by julcab12

Good analogy but for noobies like me. It would be a good thing if you mention such limitations, conditions and a brief elaboration of each component first to avoid misconceptions.

It's not really an analogy. It's a slightly different system that behaves in the exact same way mathematically. This is at least suggestive that we can think of gravity as soaking up the lost energy in the expanding photon field.

atyy

In the Harrison textbook I linked to #18 there is an extensive discussion of the analogy (p349-350). He says it's ok for things that don't depend on spatial curvature. He contrasts two physicists, one doing the full GR calculation and one doing the box calculation. He does say that the GR physicist will be surprised that after evaluating all the difficult integrals, that he gets the same answer as the simple minded box physicist. He also says that energy is not conserved in the box. He does say that the analogy fails in that in the box, energy is still conserved in box + surroundings, whereas in the universe, energy is simply not conserved.

JuanCasado

The analogy described seems reasonable and clarifying to me. However, the ammount of ordinary matter within the observable universe results to be similar to the amount of energy lost by CBR since decoupling...
Just an accident by mere chance? or perhaps a kind of new coincidence problem in cosmology?

Chalnoth

Quote by JuanCasado

The analogy described seems reasonable and clarifying to me. However, the ammount of ordinary matter within the observable universe results to be similar to the amount of energy lost by CBR since decoupling...
Just an accident by mere chance? or perhaps a kind of new coincidence problem in cosmology?

I don't think there can be anything particularly special here, at least not anything pointing to new physics.

The issue is that the radiation energy density at decoupling is fixed by the fact that a hydrogen-helium plasma turns to a gas at around 2970K. The baryon energy density, on the other hand, was set by the amount of imbalance between normal matter and anti-matter in the very early universe, which was decided by physics at extremely high temperatures when the radiation energy density was vastly, vastly higher than the matter energy density.

Now, since the baryon asymmetry was determined in the very early universe, as the temperature dropped and various forms of matter became non-relativistic, they dumped their energy into photons. But the various times that occurred also happened at much higher temperatures when the photon and baryon energy densities were extremely different.

So no, I don't think there's anything particularly special here.

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JuanCasado	The analogy described seems reasonable and clarifying to me. However, the ammount of ordinary matter within the observable universe results to be similar to the amount of energy lost by CBR since decoupling... Just an accident by mere chance? or perhaps a kind of new coincidence problem in cosmology?