Where Does the Energy of Redshifted Light Go?

[Chalnoth]

from the perspective of any given observer, the redshifted photons will persist over a long periond of time. the total energy will be preserved.

That's just not the case though. Not unless you use the Hamiltonian formalism which includes gravitational potential energy, that is. Just a simple example shows this is so: the energy density in photons now is non-zero (though pretty small compared to matter). Fast forward to the asymptotic future assuming the universe continues to expand, and the total energy in photons any volume you pick will be zero.

 

[JuanCasado]

Well, I was not referring to hot plasma among galaxies within a cluster, but to very cold matter in the voids among the clusters...

 

[sylas]

Well, I was not referring to hot plasma among galaxies within a cluster, but to very cold matter in the voids among the clusters...

I understand that; and specifically allowed for it in my explanation for why it can't explain the CBR. Repeating what I said before:

... The same thing would occur in reverse with compton cooling of radiation, which is why we cannot get a cold blackbody spectrum by cooling hot radiation using interactions with cold matter.

In interactions with matter, a blackbody spectrum is not preserved. The CMB has a fantastically accurate blackbody spectrum. Therefore the CBR is not some originally hotter radiation that has been cooled (redshifted) by comptomization -- which is what you are asking about.

It is all the same process; energy transfer between radiation and matter, when there is a temperature difference. It's known and studied. The process of "compton cooling" and "compton heating" are the same physical process, and it does distort a blackbody spectrum. You are proposing "compton heating" (which means hotter matter and a cooler radiation temperature). It's a neat idea, but it can't work for explaining the CBR.

Cheers -- Sylas

 

[Chronos]

I perceive a misunderstanding of general relativity. Do you have any particular math in mind, Chalnoth? I do.

 

[Chalnoth]

Well, I was not referring to hot plasma among galaxies within a cluster, but to very cold matter in the voids among the clusters...

But why would you think that matter is very cold? Certainly it's not as absurdly hot as the matter within clusters, as that matter has been heated up by falling into the large gravitational potential wells. But it still tends to be ionized due to starlight.

 

[Chalnoth]

I perceive a misunderstanding of general relativity. Do you have any particular math in mind, Chalnoth? I do.

You do realize that energy is not always conserved in General Relativity, right?

 

[Chalnoth]

Good. So, could CMB photons be (conversely) red shifted, i.e. "cooled down", due to interactions with very cold intergalactic media?

Only if that medium were colder than the CMB, which isn't the case.

 

[JuanCasado]

Only if that medium were colder than the CMB, which isn't the case.

What is the temperature of that medium?

 

[JuanCasado]

In interactions with matter, a blackbody spectrum is not preserved. The CMB has a fantastically accurate blackbody spectrum. Therefore the CBR is not some originally hotter radiation that has been cooled (redshifted) by comptomization -- which is what you are asking about.

It is all the same process; energy transfer between radiation and matter, when there is a temperature difference. It's known and studied. The process of "compton cooling" and "compton heating" are the same physical process, and it does distort a blackbody spectrum. You are proposing "compton heating" (which means hotter matter and a cooler radiation temperature). It's a neat idea, but it can't work for explaining the CBR.

Cheers -- Sylas

Thanks for the details. In fact I was proposing cooler matter and hotter radiation. Any references supporting the "distortion" you mention?

 

[sylas]

Thanks for the details. In fact I was proposing cooler matter and hotter radiation. Any references supporting the "distortion" you mention?

What I mean is that you are proposing radiation that gets colder, and matter that gets hotter, as a result of the interaction.

I've already given you the key terms to look for, though unfortunately they are only for the case where cold radiation is made hotter. Here's a page on the Sunyaev-Zel'dovich Effect which includes a diagram illustrating the distortion for this case. Here's the diagram:

The rightward shift is the heating effect on the radiation; the distortion is the small change in shape you can see. It diverges from the blackbody spectrum.

What you are proposing is the same physical process, but in reverse, with cold matter. And I don't know of a corresponding diagram, nor even of a case where it is measured. It may be that at such cold temperatures the effect becomes less, well, effective. I'm not sure. It would have to be very cold indeed, because the CMBR is only about 2.7 degrees above absolute zero.

Cheers -- Sylas

 

[JuanCasado]

What I mean is that you are proposing radiation that gets colder, and matter that gets hotter, as a result of the interaction.

I've already given you the key terms to look for, though unfortunately they are only for the case where cold radiation is made hotter. Here's a page on the Sunyaev-Zel'dovich Effect which includes a diagram illustrating the distortion for this case. Here's the diagram:

The rightward shift is the heating effect on the radiation; the distortion is the small change in shape you can see. It diverges from the blackbody spectrum.

What you are proposing is the same physical process, but in reverse, with cold matter. And I don't know of a corresponding diagram, nor even of a case where it is measured. It may be that at such cold temperatures the effect becomes less, well, effective. I'm not sure. It would have to be very cold indeed, because the CMBR is only about 2.7 degrees above absolute zero.

Cheers -- Sylas

Do you realize that in the figure quoted "the SZE distortion shown is for a fictional cluster 1000 times more massive than a typical massive galaxy cluster", so that the effect I am proposing will be practically null and would yield an spectrum undiscernible from a blackbody spectrum?
Regards

 

[sylas]

Do you realize that in the figure quoted "the SZE distortion shown is for a fictional cluster 1000 times more massive than a typical massive galaxy cluster", so that the effect I am proposing will be practically null and would yield an spectrum undiscernible from a blackbody spectrum?
Regards

Of course I do realize the SZE effect is small.

But no, the effect you are proposing is NOT nearly null. You are proposing a very large effect indeed! That's another tremendous physical difficulty with invoking matter interactions. The problem is to explain a very cool background radiation, showing the spectrum of a thermodynamic blackbody at a fantastically cold 2.7 degrees above absolute zero.

The conventional explanation is that cosmic microwave background radiation is from a source that is at about 3000K; but redshifted by a factor of about 1100 from the cosmological redshift -- the same process that gives a redshift to distant galaxies. This works, because redshift from an increase in the scale factor does preserve a Planck spectrum. This can therefore account for the large shifts needed to give a very cold CMBR.

You have suggested an alternative; that it comes from some hot source, and has been cooled, not by processes connected with velocity or gravitation or scale factor, but by interactions with matter. The effect has to be very large, because the radiation is very cold.

Interactions with matter will distort a Planck spectrum. If there is any significant level of cooling in the radiation, there will necessarily be a correspondingly significant distortion of the spectrum.

You've actually hit here upon another reason to think interactions with matter won't work. As you note, interactions with matter tend to have a very small effect indeed. That only makes it harder to find sufficient time and matter to cool hot radiation down by the large amounts you require. In fact, this might be a better way to help you see why interactions with matter are physically not able to account for the CMBR.

Cheers -- Sylas

 

[Chalnoth]

What is the temperature of that medium?

It's not well-described by a single temperature, as it's not in thermal equilibrium (as I said, it's ionized by stars).

Oh, and by the way, the result of this cooling wouldn't be a thermal spectrum either. The CMB has an almost perfect blackbody spectrum.