Cosmic Microwave Background and Its Temperature

[quantumkiko]

We know that the CMB has been decreasing in temperature since the big bang. This is due to the continuing expansion of the universe that results to an increase in the wavelengths of the CMB photons. Increased wavelength => less energy => less temperature. My question is why do the photons have to increase their wavelengths? Can't the wavelengths stay the same while the universe expands?

 

[Redbelly98]

I've often wondered this myself. I know that the CMB wavelengths get longer over time, but I'm puzzled about where does the energy go?

 

[gendou2]

The wavelength of a photon corresponds to it's energy.
Were the wavelength to be fixed, the energy of each photon would change to account for the changing spatial dimensions.
Due to conservation of energy, we can predict this is not what happened.

 

[marcus]

... My question is why do the photons have to increase their wavelengths? Can't the wavelengths stay the same while the universe expands?

The effect is not limited to CMB photons. It affects all photons traveling large distances
It is called the cosmological redshift.

The wavelength of any photon is increased, during its travel time, by the same factor that the universe's largescale distances expand during the time it has been traveling.

If the universe expands by a factor of TWO while the light is traveling, then when the light arrives here its wavelength will be TWICE what it was when the light was originally emitted and began its journey.

Now you ask some interesting questions. You ask how does the wavelength get stretched, in exactly the same amount as average intergalactic distances get stretched. By what mechanism?

And you ask where does the lost energy go?

===========================

But nobody has a satisfactory answer to where does the energy go, believe it or not! In fact it is not absolutely clear that global energy conservation law can be proven mathematically in the context of General Relativity. Any simple version of the law would be violated by "dark energy", since dark energy has a constant density of 0.6 joules per cubic kilometer. If your sample volume doubles the amount of energy in it doubles and no one can say where the extra came from.

That is tough. It is unintuitive. Energy conservation can be proven in the context of flat (uncurved) spacetime where you have a localized isolated system. Like something in a big imaginary box. Simple naive extensions of this idea to the whole expanding universe don't seem to work. People make special complicated definitions in the attempt to get something partially satisfactory. And some people will say that the energy lost by redshifted light goes into "gravitational energy". But how it goes into that form, and how you could harness it to do work, is not straightforward.

The CMB light has been redshifted by a factor of 1100. It has lost 1099/1100 of its energy. It has lost about 99.9 percent of its energy by the time it reaches us. The original light could have been harnessed to do work. Now if the microwaves were harnessed, they could do only 1/10 percent as much work. What could be harnessed to recoup the lost work? Frankly I don't think anybody has a clear idea.
=======================

The mechanism of redshift you asked about is simply Maxwell equations where space is expanding. Maxwell equations is just how electromag. waves propagate. The exansion is very gradual. Distances are now expanding at a rate of 1/140 percent every million years. That is very very slow expansion. But the waves are trying to travel thru this expanding space and distances between peaks are increasing. It gradually takes its toll. Each undulation is determined by the previous one. But by the time it is happening the previous one is just a tiny bit extended. The stretching builds up cumulatively. After 140 million years have gone by, the wavelength of the light is one percent longer.

We are used to visualizing waves traveling in space where distances are not expanding, so this is unintuitive. but you can try thinking of wave equations, or especially Maxwell (lightwave) equations, where distances are expanding.

Or you can explain it by thinking in terms of coordinate transformations, but I don't think that is any more intuitive or gives any more physical feel.

Good luck understanding this stuff!

 

[jonmtkisco]

Hi Redbelly,

I know that the CMB wavelengths get longer over time, but I'm puzzled about where does the energy go?

I have been bothered by this point as well. I now understand that the answer lies in the current explanation of cosmological redshift, which is that it is really best thought of as Doppler redshift plus gravitational redshift. At large distances the Doppler redshift dominates.

The CMB radiation is redshifted not because space is expanding between wavecrests (the former explanation for the phenomenon), but because the observer (us) is in a local inertial frame which is moving very rapidly away from the inertial frame of the source, and the source equally is moving very rapidly away from us.

Thus it's the same scenario as the whistle we hear from a receding train. The stationary observer detects a lower wavelength and therefore a loss of total energy; but the energy is not really lost, it's just a measurement frame phenomenon. If a second train follows the first train at a constant distance, it will not measure any wavelength change or energy loss.

Jon

 

[yuiop]

Hi Redbelly,

I have been bothered by this point as well. I now understand that the answer lies in the current explanation of cosmological redshift, which is that it is really best thought of as Doppler redshift plus gravitational redshift. At large distances the Doppler redshift dominates.

The CMB radiation is redshifted not because space is expanding between wavecrests (the former explanation for the phenomenon), but because the observer (us) is in a local inertial frame which is moving very rapidly away from the inertial frame of the source, and the source equally is moving very rapidly away from us...

Jon

As far as I know, the current explanation is the "space itself expanding" version which stretches the distance between wavecrests. This was discussed in another thread and it seems to me the cause of CMB redshift in the comoving expanding space cosmology, is a combination of classic doppler shift plus stretching due to expansion of space during the travel time of the photons plus a lesser amount due to gravitational redshift. The old explanation was originally that all the redshift was due to classic doppler shift, which later evolved to the relativistic doppler shift idea and then finally to the current expanding space version. Personally I do not like the expanding space idea. One difficulty with the space itself expanding idea is that there appears to be no satisfactory answer for what exactly is meant by "space itself". Is the vacuum expanding? If so, is the vacuum a substance like the aether, but we don't call it that in polite circles? Is spacetime expanding? Apparently that is not possible according to mejennifer. So we are left with no answer.

If I recall correctly, one of the original ideas for the CMB temperature redshift was based on the ideal gas law relationship PV=nRT so that a temperature of about 3000 degrees kelvin at the time of recoupling and the CMB temperature we see now of about 3 degrees kelvin indicates the volume of the universe is roughly 1000 times larger now than it was then, depending on how you measure the pressure of the universe. If the universe as a whole is obeying the ideal gas laws then there is no energy problem. Put a balloon of hot gas in a vacuum and it will expand according to the laws of thermodynamics, without violating any energy conservations laws. However, this idea is not mentioned much these days because the cosmological principle requires the universe to have no center which requires the universe to be infinite now and infinite at the time of the big bang. Considering the universe to be infinite at the start does not sit comfortably with the idea of cooling due to increase of volume because an initially infinite volume can not increase in volume.

It is interesting to consider the universe from a thermodynamic point of view. It is certainly an adiabatic process as no heat is lost from the system. Whether it is a reversible process or not (which would determine whether the universe can recollapse or not) depends on whether you consider the expansion to be isenthalpic or isentropic. If you consider the process to be isenthalpic which is the unrestrained expansion of a gas that does no work, then the process is irreversable and the universe can not collapse without violating the laws of thermodynics. If you consider the process to be isentropic due to work done overcoming gravity, then it is possible for the entropy of the universe as a whole to remain constant as the universe expands and that allows the process to be reversible and allows bouncing type models of the universe that can cycle through expansion and collapse indefinitely.

 

[Chronos]

How does a 'bounce' solve the problem?

 

[yuiop]

How does a 'bounce' solve the problem?

I am not sure I claimed a bounce would solve any problem and I am not sure what you think "the problem" is.

Some cosmologies predict a bouncing universe alternately going though a big crunch and starting all over again. I was simply pointing out the thermodynamics does not necessarily exclude a bouncing model even though on first inspection it is easy to imagine that the expanding universe represents an increasing entropy and therefore an irreversable process excluding a big crunch scenario, whatever the matter density of the universe.

If the problem is "where does the lost energy of CMB photons go?" then there is no problem. The loss of thermal energy of a expanding gas is equivalent to the work done in expanding the volume. It is a bit like the potential energy of a falling object being converted into kinetic energy. There is no loss of energy from the system as a whole. Energy is simply converted from one form into another.

 

[yuiop]

How does a 'bounce' solve the problem?

I guess a bouncing model solves the problem of where the matter and the energy of the universe came from, because a bouncing model says it was always there and no creation of everything from nothing is required. Philosophically it is probably just as hard to imagine something that was always there without a beginning or an end as it to imagine everything being created from nothing.

 

[Redbelly98]

If the problem is "where does the lost energy of CMB photons go?" then there is no problem. The loss of thermal energy of a expanding gas is equivalent to the work done in expanding the volume. It is a bit like the potential energy of a falling object being converted into kinetic energy. There is no loss of energy from the system as a whole. Energy is simply converted from one form into another.

I have a problem with the expanding gas analogy.

In an expanding gas, gas molecules collide with the receding wall of the container, and lose energy in those collisions. It's this interaction where the energy is lost.

My understanding (which could be wrong) is that CMB photons have not interacted (scattered, collided, been absorbed/re-emitted) with anything since they were emitted at ____ years after the Big Bang (whenever that was).

Regards,

Mark

 

[Redbelly98]

Hi Redbelly,
The CMB radiation is redshifted not because space is expanding between wavecrests (the former explanation for the phenomenon), but because the observer (us) is in a local inertial frame which is moving very rapidly away from the inertial frame of the source, and the source equally is moving very rapidly away from us.

This I can understand and accept. If that's the reason, it would mean the presently observed CMB was emitted by sources that were moving faster (relative to us) than the sources that emitted CMB that was observed yesterday, or last year, or billions of years ago. It would mean the radiation itself is not increasing in wavelength, we are just observing radiation of longer-wavelengths than the radiation we observed in the past.

But never having taken a class in cosmology or GR, there is always this doubt in my mind that the "real answer" requires me learning and then following some tensor calculus or other tedious mathematical derivation. I have to balance my desire to understand this with my willingness to spend a lot of time on it (rather than spending time on entertainment, taking care of the house, paying bills, etc.)

 

[jonmtkisco]

Hi Redbelly,

If that's the reason, it would mean the presently observed CMB was emitted by sources that were moving faster (relative to us) than the sources that emitted CMB that was observed yesterday, or last year, or billions of years ago.

Yes your deduction is correct, but it's a bit difficult to demonstrate in a universe that has no apparent center and appears to go on forever. As Wallace has consistently counselled, galaxies are moving apart now simply because the were moving apart previously. Individual galaxies must have a conserved Hubble flow momentum; mere expansion does not mean they are gaining momentum, in fact they are constantly losing momentum from the original expansion (inflation or whatever) due to gravitation. (However, the late-times acceleration of expansion due to dark energy or the cosmological constant does cause them to gain momentum.)

Therefore, distant galaxies recede from us very rapidly in part (ignoring dark energy) because they were always receding from us very rapidly. Nearby galaxies recede from us slowly because they were always receding from us slowly.

If your other obligations permit you to read more about cosmic redshift being a combination of Doppler redshift and gravitational redshift, here is a good http://arxiv.org/abs/astro-ph/0404095" "The expansion of space: free particle motion and the cosmological redshift" by Alan B. Whiting, 4/04.

Jon

 

[jonmtkisco]

Hi Redbelly,

If that's the reason, it would mean the presently observed CMB was emitted by sources that were moving faster (relative to us) than the sources that emitted CMB that was observed yesterday, or last year, or billions of years ago.

Yes your deduction is correct, but it's a bit difficult to demonstrate in a universe that has no apparent center and appears to go on forever. As Wallace has consistently counselled, galaxies are moving apart now simply because the were moving apart previously. Individual galaxies must have a conserved Hubble flow momentum; mere expansion does not mean they are gaining momentum, in fact they are constantly losing momentum from the original expansion (inflation or whatever) due to gravitation. (However, the late-times acceleration of expansion due to dark energy or the cosmological constant does cause them to gain momentum.)

Therefore, distant galaxies recede from us very rapidly in part (ignoring dark energy) because they were always receding from us very rapidly. Nearby galaxies recede from us slowly because they were always receding from us slowly. CMB photons we see this year were last scattered from a surface that was receeding from us faster at the time of last scattering, than was the case for the CMB photons we saw last year. With each passing year we see further into the past and therefore we see things that were receding from us faster at the time the radiation was emitted. (Again ignoring the effects of dark energy).

If your other obligations permit you to read more about cosmic redshift being a combination of Doppler redshift and gravitational redshift, here is a good http://arxiv.org/abs/astro-ph/0404095" "The expansion of space: free particle motion and the cosmological redshift" by Alan B. Whiting, 4/04.

Jon

 

[Redbelly98]

Hi Redbelly,
If your other obligations permit you to read more about cosmic redshift being a combination of Doppler redshift and gravitational redshift, here is a good http://arxiv.org/abs/astro-ph/0404095" "The expansion of space: free particle motion and the cosmological redshift" by Alan B. Whiting, 4/04.

Thanks for that link! After a quick skim, the math doesn't appear too daunting.

Direct link to .pdf version of Whiting article:
http://arxiv.org/PS_cache/astro-ph/pdf/0404/0404095v1.pdf

Edit added:

... your deduction is correct, but it's a bit difficult to demonstrate in a universe that has no apparent center and appears to go on forever ...

I think we can do a thought experiment to demonstrate the effect.

CMB radiation is traveling through space; some is impinging on the Earth and our detectors, and some of it is going right pass the Earth and continuing on.

We measure a certain blackbody spectrum for the radiation that is measured in our detectors. As for the radiation that misses our planet, it continues to propagate onward. Perhaps some billions of years hence, some of that CMB radiation will be detected in a galaxy billions of light-years away.

What spectrum is measured in this other galaxy, billions of years into the future? Remember that such a galaxy is receding away from ours, in the very direction that this radiation of interest is travelling. So they will measure a CMB spectrum that is red-shifted relative to what we measure here, today. It's a simple Doppler shift, with perhaps some gravitational red shift factored in as well.

Finally, since there are no exceptional differences between our and other galaxies, it stands to reason that a few billion years from now a red-shifted CMB would be measured in our galaxy, or anywhere else, as well.

 

[yuiop]

I have a problem with the expanding gas analogy.

In an expanding gas, gas molecules collide with the receding wall of the container, and lose energy in those collisions. It's this interaction where the energy is lost.

My understanding (which could be wrong) is that CMB photons have not interacted (scattered, collided, been absorbed/re-emitted) with anything since they were emitted at ____ years after the Big Bang (whenever that was).

Regards,

Mark

I agree that the universe has no container walls. In thermodynamics, a gas released in a vacuum is generally not a reversible process because no work is done. If the gas is allowed to expand in a cylinder with a piston that is resisted by external pressure or a spring then the process can in principle be reversible because work is done and entropy does not increase. The expanding universe appears to be the case where no work is done, but I believe work IS done overcoming gravitational attraction.

 

[Redbelly98]

The expanding universe appears to be the case where no work is done, but I believe work IS done overcoming gravitational attraction.

I'm sure there is some gravitational effect, but what is the average gravitational field in intergalactic space? I would think gravity plays a small role compared to ordinary Doppler redshifting.

Mark

 

[yuiop]

I'm sure there is some gravitational effect, but what is the average gravitational field in intergalactic space? I would think gravity plays a small role compared to ordinary Doppler redshifting.

Mark

I tend to agree that redshifting of the CMB is mostly a doppler effect and I think I have mentioned that in other posts. I was just making the observation that there appears to an interesting correlation between the change in the CMB temperature and the ideal gas law PV=T where pressure can be considered as energy density of the universe and temperature is proportional to the spectrum of an ideal black body.

 

[Redbelly98]

Got it.

My understanding of CMB has now gone up a notch thanks to you, jonmtkisco, and others. Hopefully the OP has benefited as well.

Best regards.

 

[jonmtkisco]

Hi Kev,
The problem I have with the pressure analogy (beyond the fact that the pressure here isn't doing true "work") is that the I can't convince myself that the CMB photons are what has been causing the universe to expand. It's an interesting philosophical question exactly which particles have been driving the expansion of the universe, assuming that "the universe as a whole" expands in any meaningful sense through the motion of its particles.

One would be tempted to think that the very first particles to "push the frontiers" of the early universe would be the "pioneers" actually driving the so-called "expansion", paving the way for hordes of "settlers" that follow later. In that sense, any radiation that escaped from inflation before the quark-gluon plasma formed, and thereby evaded the Thompson scattering phase, should be the pioneers. They are always the furthest from their initial starting point, whether that starting point was a single point or "everywhere in the tiny initial universe". Then CMB Photons that later escaped at the end of the Thompson Scattering could be thought of as the first wave of settlers. And then the slow, ponderous, nonrelativistic matter particles followed far behind as city-slicker settlers, never venturing into virgin, unscouted territory, or even anywhere near the then-current frontier, at any stage.

I know all of this sounds a bit silly, but SOME particle had to be the first one to scout out each region of space, claiming the virgin territory in the name of the expanding universal "empire". Or actually "creating new space" as the particle proceeded, if one prefers to think in such terms (I don't.)

Jon