# How does cosmic microwave radiation lose energy?

## Main Question or Discussion Point

Can anyone explain how the cosmic microwave background radiation (CMBR) "cooled"...I'm supposing that about 300,000 years or so after the bang, when the universe became transparent, things were hotter than 2.7 degrees above absolute zero we observe today....

Wikipedia says:
The photons that existed at that time have been propagating ever since, though growing fainter and less energetic, since the exact same photons fill a larger and larger universe.
So an expanding universe redshifts light, and in doing so CMBR loses energy?? Does this mean the "new space" created by expansion would otherwise be at absolute zero but is being warmed by a finite amount of CMBR?? So if the universe were not expanding, would the CMBR be at the same temp as it was when the universe was about 300,000 years old.

marcus
Gold Member
Dearly Missed
... So if the universe were not expanding, would the CMBR be at the same temp as it was when the universe was about 300,000 years old.
Yes it would be the same temp.

The cosmic neutrino background is expected to have cooled by the same z+1 factor over the same time period, due to expansion.
Being massy, neutrinos lose energy by slowing down, while photons lose it by extending wavelength (redshift.)

When people model structure formation they model clouds of dark matter primarily because these eventually supply the strands and clusters that bring ordinary matter together---dark matter forms the skeleton or armature of visible structure. And in order for dark matter to be able to condense, it has to loose kinetic energy. Dark matter particles lose kinetic energy by the expansion of distance. Just like neutrinos do. Just like CMB photons do.

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The radiation temperature is proportional to 1 over the scale factor of the universe:

T -> 1 / S

So if we take the scale factor of the universe at the current time to be So = 1 and the current temperature to be To = 2.7K, we have

T = 2.7K / S

So when the universe was 1000 times closer together than now, the temperature was:

T = 2.7 X 1000 = 2700 K.

If you want to include time in this simple treatment, you could include the solution to the scale factor for a flat universe w/o cosmological constant:

S(t) = So (t / to)^2/3

and to ~ 13.2 billion years. So you could plug in 300,000 years and find the temperature at "decoupling."

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russ_watters
Mentor
So an expanding universe redshifts light, and in doing so CMBR loses energy??
Yes.
Does this mean the "new space" created by expansion would otherwise be at absolute zero but is being warmed by a finite amount of CMBR??
There is no "new space" and space itself is not a thing and doesn't have a temperature - it isn't being warmed by the CMB. The CMB travels though space and doesn't interact with sapce in the way you suggest.
So if the universe were not expanding, would the CMBR be at the same temp as it was when the universe was about 300,000 years old.
Yes, but since when the CMB light was emitted the universe was a hot, opaque plasma cloud, that's the state it would be in now if it didn't expand past that point.

There is no "new space" and space itself is not a thing and doesn't have a temperature - it isn't being warmed by the CMB. The CMB travels though space and doesn't interact with sapce(space) in the way you suggest.
Russ. I'm with you on everything except...
There is no "new space"...
Isn't the outward motion of galaxies a result of the expansion of space itself.....on cosmological distances?? I thought Hubble's observations showed the increase in separation distance between galaxies is proportional to the initial distance between them...that space is stretching/expanding??

Marcus posts:
And in order for dark matter to be able to condense, it has to loose kinetic energy. Dark matter particles lose kinetic energy by the expansion of distance.
Did not realize that...thanks....It's supposedly condensing from the big/initial bang??

russ_watters
Mentor
Isn't the outward motion of galaxies a result of the expansion of space itself.....on cosmological distances?? I thought Hubble's observations showed the increase in separation distance between galaxies is proportional to the initial distance between them...that space is stretching/expanding??
Yes, but space can only be measured via distance. It doesn't have any meaning to say that there is "new space" in between two objects as if the space is a "thing" that is being created.

Chalnoth
Yes it would be the same temp.
Actually, not quite. The cosmic neutrino background was emitted earlier, when the weak nuclear force "turned off" (that is, when the temperature dropped far enough below the masses of the mediators of the weak force that the weak force actually became, well, weak). After the cosmic neutrino background was emitted, a number of other particles cooled down and became non-relativistic: protons, neutrons, and electrons. When this happened, the matter and anti-matter components annihilated with one another en masse (leaving a small matter excess), dumping lots more energy into photons.

Because of this, the CMB is actually quite a bit warmer than the CNB.

The cosmic neutrino background is expected to have cooled by the same z+1 factor over the same time period, due to expansion.
Being massy, neutrinos lose energy by slowing down, while photons lose it by extending wavelength (redshift.)
A bit of a pedantic point, but in terms of the quantum mechanics, they both lose mass through their wavelengths getting larger. But yes, it is only the neutrinos that actually slow down.

Chalnoth
Yes, but space can only be measured via distance. It doesn't have any meaning to say that there is "new space" in between two objects as if the space is a "thing" that is being created.
Why not? Space can carry momentum and energy (through gravity waves). How does that not make it a "thing"?

Chronos
Gold Member
I do not perceive CMB photons have lost energy. While much cooler than when emitted, they are also time dilated. Their energy is thus conserved over any fixed time interval. This interpretation appears consisitent with the laws of themodynamics.

Why not? Space can carry momentum and energy (through gravity waves). How does that not make it a "thing"?
I have a small question about this, and sorry to digress from the OP, but what is the consensus about space? Is it a thing? Does it have substance? When I hear people say that lensing is caused by stars warping the space around them, it makes it sound like space has substance. Einstein's analogy of mass bending space like a ball laying on a stretched piece of fabric sounds like there's a fabric to space. Don't waves need a medium to travel through? as in light waves, maybe that's an obsolete argument tho.

Chalnoth
I have a small question about this, and sorry to digress from the OP, but what is the consensus about space? Is it a thing? Does it have substance? When I hear people say that lensing is caused by stars warping the space around them, it makes it sound like space has substance. Einstein's analogy of mass bending space like a ball laying on a stretched piece of fabric sounds like there's a fabric to space. Don't waves need a medium to travel through? as in light waves, maybe that's an obsolete argument tho.
Well, no, waves don't need a medium to travel through. However, we frequently consider electromagnetic radiation (i.e. light) and electromagnetic fields as being "things" in a sense. Why not space-time?

Well, no, waves don't need a medium to travel through. However, we frequently consider electromagnetic radiation (i.e. light) and electromagnetic fields as being "things" in a sense. Why not space-time?
do you mean that things like gravity waves, electromagnetic radiation, and electromagnetic fields are all things that constitute space, or saying that space could have a substance of it's own, independent from all those things? Is considering space a thing an analogy to help us understand the concepts, or do we think space could really be a thing of its own?

Chalnoth
do you mean that things like gravity waves, electromagnetic radiation, and electromagnetic fields are all things that constitute space, or saying that space could have a substance of it's own, independent from all those things? Is considering space a thing an analogy to help us understand the concepts, or do we think space could really be a thing of its own?
Well, what I mean is that since we now think of gravity as the action of space-time interacting with matter, and since this geometry of space-time can carry energy and momentum in the same way that the electromagnetic field can, it seems a lot more like space-time can be thought of as very much analogous to the electro-magnetic field in many respects.

The primary difficulty here is that we don't yet know the full quantum behavior of space-time. If we did, we might have a clearer understanding how what makes it up.

ranrod: here are two discussions on the nature of space itself.

Is spacetime a physical entity?

"Is considering space a thing an analogy to help us understand the concepts, or do we think space could really be a thing of its own?"

Is space a physical entity? Is time a physical entity? Is spacetime a physical entity? There seems to be no consensus on this forum. The above threads provide multiple viewpoints....keeping an open mind is always wise. Stay tuned...

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Chronos posts:
I do not perceive CMB photons have lost energy. While much cooler than when emitted, they are also time dilated. Their energy is thus conserved over any fixed time interval. This interpretation appears consisitent with the laws of themodynamics.
So glad you posted that because it was my next question....Any further insights along these lines??

I'm not sure I understand how this relates to the above:

via Chalnoth's post:
When this happened, the matter and anti-matter components annihilated with one another en masse (leaving a small matter excess), dumping lots more energy into photons.
I guess I have never considered just how the energy in an electromagnetic wave (photons) in space "changes": gravity (time dilation), cosmic expansion/distance (frequency shift), and relative speed of the observer (also frequency shift)...How does an electromagnetic wave (photons) pick up energy from other entities? E = hf..seems like frequency change/wavelength/time is a mechanism...

Do Maxwell's equations offer insights??

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Chalnoth
I guess I have never considered just how the energy in an electromagnetic wave (photons) in space "changes": gravity (time dilation), cosmic expansion/distance (frequency shift), and relative speed of the observer (frequency shift)...How does an electromagnetic wave (photons) pick up energy from other entities? E = hf..seems like frequency change/wavelength/time is a mechanism...
Well, in this situation it's a pretty simple process, at least for electrons: electron and positron collide, emit a pair of high-energy gamma rays. Those high-energy gamma rays smack into lots of other things, spreading their energy around to everything they can interact with. The same basic thing went on with the proton/anti-proton and neutron/anti-neutron interactions (though those are more complex, the principle remains the same).

In the end, after this happens, you end up with about the same amount of energy as before (neglecting the effects of expansion for a moment), but that same energy is spread among fewer particles. So the particles that remain get a boost in energy.

The neutrinos, however, couldn't participate in this interaction as they were basically non-interacting when all this was going on, and so couldn't take a piece of that extra energy per particle.

marcus
Gold Member
Dearly Missed
...How does an electromagnetic wave (photons) pick up energy from other entities?...
That's a generally phrased question. I won't try to give an encyclopedic answer (if I even could).

but you should know about something very nice. Compton scattering and inverse Compton scattering. Look it up on (the not always reliable but nevertheless often very useful) wikipedia.

Cosmic rays are highspeed protons. They can actually give some or most of their energy to the photons of the microwavebackground (which form such a thick soup in space that a cosmicray proton is eventually almost certain to hit one. This is an example of what you asked about. The microwave photon ( a millimeter wavelength photon, which means it has miniscule energy) actually can "pick up" a rather large energy from another "entity" namely the cosmicray photon, by interacting with it. It's really nice. It is inverse Compton interaction. And the highspeed proton actually sees the background photon as doppler blued to quite high energy! Because the proton thinks he is sitting still and he sees the millimeter wave as a gammaray photon coming at him.

Arthur Holly Compton studied the scattering of Xray by electrons in the 1920s. This was a very good thing to have done in the 1920s, and he has something called the "Compton wavelength" named after him. I picture you as a serious learner, which people who live on boats sometimes are, so if you get interested in Compton and inverse Compton scattering you could find or start a thread about it. I think it's neat.

There's also the integrated Sachs-Wolfe effect by which a photon can actually pick up some energy in a universe with accelerating expansion (you'd think that any expansion would always dull a photon down, but there is a trick that lets the opposite happen.) This is a pure gravity (active geometry) effect. No particle scattering involved. The photon picks up energy as it passes through an unstable grouping of galaxies, or some other gravitationally unstable structure. The effect is observed and is part of the evidence for dark energy/positive cosmo constant.

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Chalnoth, Marcus..sorry for my sloppily worded question: I am trying to figure how electromagnetic waves/ photons change energy without interactions with matter since I infer that most CMBR hasn't been scattered....is that approximately correct??

I think of Compton (electron) scattering as a photon being absorbed and another being emitted, typically of different energy....that's fascinating enough, but my question is how EM or photons change energy without particle interactions.

Chalnoth's comment:
but that same energy is spread among fewer particles. So the particles that remain get a boost in energy.
and Marcus'
And the highspeed proton actually sees the background photon as doppler blued to quite high energy!
seems to be about the same dichotomy that confused me in my post #16....have to think some more...got to check on an auto repair...back later....

As I wrote this I suddenly though of double slit experiments where waves interact but individual photons do not....I think that's what I was having trouble articulating....

Chalnoth
Okay, perhaps I've confused you a bit. The photons do have lots and lots of interactions with matter. Up until the time that the CMB is emitted. Then they basically stream freely. But before the CMB was emitted, our universe was a plasma: the protons and electrons were separated from one another, instead of combined into neutral atoms, which meant that photons didn't have very far to go before they would slam into some charged particle or another.

After the emission of the CMB, those photons don't interact much at all with matter any more. They just stream freely. After that, the only change in energy that they experience stems from their stretching due to the expansion.

Chalnoth...your post #20 is crystal clear and exactly my understanding...thanks for the clarification.....

Two possible views on CMBR energy loss:

(1) If the CMBR loses energy, where has it gone?? That's why originally I was asking if "new space" emerges at absolute zero....and can be "heated" ...yet as soon as I pose that, I realize its a relativistic question since observer velocity is reflected in the measured frequency (energy)#.....

(2) and Chronos posted:
I do not perceive CMB photons have lost energy. While much cooler than when emitted, they are also time dilated. Their energy is thus conserved over any fixed time interval.
That's a new idea to me...but seems plausible....so which view makes more sense and why??

# I have a different view of space(time) itself than russwaters (He does not thing space is a "thing") but his post got me thinking he is right because I know of no mechanism for electromagnetic heating of empty space....unless the presence of electromagnetic waves (energy) causes further bending of spacetime and maybe such gravitational effects would be reflected as "heat"?? but that's speculation on my part....so maybe I'm wondering here if otherwise "empty" space with gravitational waves present can be at absolute zero....

Chalnoth
Well, there are multiple ways to look at it. The first thing to keep in mind is that conservation of energy isn't required in General Relativity. The reason is simple: conservation of energy requires that certain properties of the theory are independent of time, but the time coordinate is largely arbitrary in General Relativity, so even if you have energy conservation in one set of coordinates, you can just rewrite it with a different set and end up with no energy conservation!

Instead, General Relativity conserves a different entity: the stress-energy tensor. This combines energy, pressure, and stresses into one structure. Precisely how this entity is conserved depends upon the properties of the matter in question. If the matter has pressure (as photons do), then conservation of the stress-energy tensor forces energy to not be conserved: there is sort of a trade off between pressure and energy so that the stress-energy tensor as a whole remains conserved.

So, from the traditional perspective of General Relativity, photons are forced to not conserve energy in curved space-time, because they have pressure.

But there are other ways to look at the same thing. Unfortunately, things can be a little bit confusing with General Relativity, and whether or not energy is conserved depends entirely upon what you mean by "energy" and what you mean by "conserved". If you want to read more on the subject, this is a good essay:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Thanks for the Baez reference!!!!....I HAVE seen it before......I even found this in my own notes on a related subject from that same source :

The Cosmic Background Radiation (CBR) has red-shifted over billions of years. Each photon gets redder and redder. What happens to this energy? Cosmologists model the expanding universe with Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding balloon speckled with galaxies" belongs to this class of models.) The FRW spacetimes are neither static nor asymptotically flat. Those who harbor no qualms about pseudo-tensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost.
No wonder I could not figure it out on my own....thanks again....

Marcus post #10 says:

There's also the integrated Sachs-Wolfe effect (ISW) by which a photon can actually pick up some energy in a universe with accelerating expansion (you'd think that any expansion would always dull a photon down, but there is a trick that lets the opposite happen.) ... No particle scattering involved. The photon picks up energy as it passes through an unstable grouping of galaxies, or some other gravitationally unstable structure. ...
I finally got around to following up and that....never heard of it...Wikipedia does have some insight which seems consistent:

Accelerated expansion due to dark energy causes even strong large-scale potential wells (Supercluster) and hills (Voids) to decay over the time it takes a photon to travel through them. A photon gets a kick of energy going into a potential well (a supercluster), and it keeps some of that energy after it exits, after the well has been stretched out and shallowed. Similarly, a photon has to expend energy entering a supervoid, but will not get all of it back upon exiting the slightly squashed potential hill.
http://en.wikipedia.org/wiki/Sachs-Wolfe_effect#Late-time_integrated_Sachs.E2.80.93Wolfe_effect

Sounds similar to the slingshot effect utilized for some space probes.....

Marcus: I especially appreciate your comment because one of the things I was wondering and did not posts is how CMBR interacts with varying gravitational strengths as it passes through the cosmos...I had assumed they all averaged out due to large scale cosmological smoothness.....but ISW offers a fascinating insight....THANKS!!