Where did the energy in the CMB go to?

[moving finger]

This may seem like a silly question, but it has me puzzled.

Theory tells us that as space expands then photons (and I guess all form of energy?) in that space are red-shifted, ie their wavelength increases, ie they lose energy. The most obvious example of this is the CMB, which consists of maybe 10^88 photons (in the observable universe) "left-over" from the Big Bang. At the time of decoupling from matter (300,000 years after the Big Bang?) each of these photons was of very high energy (low wavelength), but as the universe (space) expanded each of these photons was red-shifted (lost energy), to end up as the microwave background that we see today.

If the first law of thermodynamics is to be obeyed (mass/energy must be conserved), what happened to the energy that these photons lost?

 

[Chronos]

Not lost, just stretched out by expansion. Does a rubber band lose mass when you stretch it? Of course not, it just has less mass [energy] per inch.

 

[Janitor]

Not lost, just stretched out by expansion. Does a rubber band lose mass when you stretch it? Of course not, it just has less mass [energy] per inch.

But if the number of CMB photons remains pretty much constant over time, and if typical photon wavelengths are increasing with time, then the product of number of photons and average energy per photon has to be decreasing, doesn't it?

At any rate, I find this a neat question!

 

[moving finger]

Not lost, just stretched out by expansion. Does a rubber band lose mass when you stretch it? Of course not, it just has less mass [energy] per inch.

sorry Chronos, your analogy doesn't apply in this case.

the total energy in a photon is proportional to its frequency E=hv. (the reason why your analogy does not apply is because the total mass of the rubber band is independent of how much the rubber band is stretched - this is not the case when we think of the relationship between energy and photon wavelengths)

as space expanded, the wavlength of each CMB photon was increased (frequency reduced).

hence the energy of each CMB photon was reduced.

the number of CMB photons has not changed much since decoupling with matter, hence the total energy locked up in the CMB has reduced over time.

this energy must have gone somewhere... but where?

 

[Chronos]

The energy is used to power expansion.

 

[moving finger]

The energy is used to power expansion.

what does that mean?

does that imply the expansion "needs energy" from the CMB in order to "power it" - in which case what happens if we have a universe with no CMB, does it stop expanding? i don't think so.

if anything, the CMB contributes to the total mass-energy of the universe and should slow down the expansion rather than "power it".

 

[Janitor]

The energy is used to power expansion.

Even when the expansion is the result of space itself being created? Maybe so, I don't know.

 

[SpaceTiger]

The energy is used to power expansion.

Although I'm not sure of this, I think that it does the opposite (slow the universe down). In a matter-dominated universe, the kinetic energy of the matter is gradually converted into potential energy, slowing the expansion. A radiation-dominated universe will decelerate, just like a matter-dominated one, but the light must move at the speed of light, so you can't take its kinetic energy. Instead, you reduce its frequency.

 

[moving finger]

Although I'm not sure of this, I think that it does the opposite (slow the universe down). In a matter-dominated universe, the kinetic energy of the matter is gradually converted into potential energy, slowing the expansion. A radiation-dominated universe will decelerate, just like a matter-dominated one, but the light must move at the speed of light, so you can't take its kinetic energy. Instead, you reduce its frequency.

Ahhh. OK, yes. The energy of the photons is converted into potential energy... because the expansion is pulling all the photons further apart hence (since they all attract each other gravitationally) the total gravitational potential energy must be increasing as the universe expands, and the energy of each CMB photon is reduced accordingly, so that everything remains balanced. Is that it?

 

[SpaceTiger]

... the total gravitational potential energy must be increasing as the universe expands, and the energy of each CMB photon is reduced accordingly, so that everything remains balanced. Is that it?

I think so. I've never directly worked with general relativity, so I'm not sure if my semi-classical understanding of the problem applies here.

 

[Garth]

I think so. I've never directly worked with general relativity, so I'm not sure if my semi-classical understanding of the problem applies here.

It doesn't!

It is important not to inconsistently mix up Newtonian and GR gravitational concepts as has happened in the above posts. GR does not in general conserve energy, in particular it does not do so in the cosmological solution of a non-static evolving universe.

The total energy of the CMB does decrease with time as the photon number (apart from the few absorbed by matter) is conserved.

Classically gravitational potential energy is that energy used in lifting a body against a gravitational force. In GR that force is replaced by curvature. In particular work has to be done to accelerate a body out of its freely falling inertial frame, and weight is the reaction to an inertial force. Therefore classical gravitational potential energy is radically re-interpreted in GR and should not be used to explain either cosmological or gravitational red shift.

The question of “Where does the energy of a CMB photon go?” is similar to the question of “Where does the energy of a gravitationally red shifted photon go?” The GR answer is, "into the field", whatever that means.

GR just loses the CMB energy into the cosmological field with no mechanism to explain how that happens or where it might be re-located.

Remember GR does not in general conserve energy, it conserves energy-momentum instead and that is different. It is the curvature of space-time that violates the conservation of energy, which is why the energy of a system can only be properly defined in GR in the absence of curvature, where the space-time is asymptotically flat.

Garth

 

[Chronos]

Interesting. You have pointed out a problem in both models.

 

[chronon]

Sorry, but the redshifting of CMB photons has nothing to do with gravity. You get the same redshifting in the Milne universe where the effects of gravity are ignored.

Of course if you ignore the idea of space stretching and say that the photons are redshifted because their source was moving rapidly away from us then there isn't a problem.

 

[Garth]

chronon you have to be consistent, in this case with the principles of GR.

Sorry, but the redshifting of CMB photons has nothing to do with gravity. You get the same redshifting in the Milne universe where the effects of gravity are ignored.

According to the principles of GR what is 'gravity' except the effect of 'curvature', and what is cosmological expansion except the effect of 'curvature'? The Milne universe may not have matter but it still has 'curvature', that is if you want to remain consistent to GR. Empty space has 'gravity', i.e. 'curvature'!

Of course if you ignore the idea of space stretching and say that the photons are redshifted because their source was moving rapidly away from us then there isn't a problem.

According to the principles of GR are the sources moving through space-time producing a Doppler effect, or is it space-time itself that is 'stretching'?

Garth

 

[chronon]

chronon you have to be consistent, in this case with the principles of GR.According to the principles of GR what is 'gravity' except the effect of 'curvature', and what is cosmological expansion except the effect of 'curvature'? The Milne universe may not have matter but it still has 'curvature', that is if you want to remain consistent to GR. Empty space has 'gravity', i.e. 'curvature'!

Gravity is the curvature of space-time. The space-time of the Milne universe is flat. You might consider the space to be curved, but that depends on the choice of the coordinate system.

According to the principles of GR are the sources moving through space-time producing a Doppler effect, or is it space-time itself that is 'stretching'? Garth

Sources don't move through space-time. Space-time doesn't stretch. These are time-based verbs.

 

[marcus]

I agree with Garth. No one, to my knowledge, has ever explained where the lost CMB energy went. there is no energy-conservation law in GR, but GR is currently the prevailing largescale theory of spacetime and other theories just apply locally or approximately. So as far as anyone knows ENERGY CONSERVATION IS NOT TRUE except in some restricted local or approximate sense.

The CMB is an excellent example to show that energy conservation is not true, since no one can find the lost energy.

The concept of energy is a growing, evolving idea. Feynman's "dennis the menace" story illustrates this (I don't have a link). So one can conjecture that someday the concept of energy will be extended to something we don't know about, that we can measure, and people will measure it and say ahah THAT is where the missing CMB energy went, so they will have "found" the missing energy and conservation will be vindicated.

but that is only a conjecture. there would need to be an improved theory of spacetime, to replace GR. Because in GR the CMB energy when the photons get stretched out just goes away. It is a wellknown fact that GR does not support the energy conservation law.

So moving finger question is not at all silly. It seems very sensible to be puzzled. I've quoted several posts, including Garth's to keep track of the main points in the thread.

This may seem like a silly question, but it has me puzzled.

Theory tells us that as space expands then photons (and I guess all form of energy?) in that space are red-shifted, ie their wavelength increases, ie they lose energy. The most obvious example of this is the CMB, which consists of maybe 10^88 photons (in the observable universe) "left-over" from the Big Bang. At the time of decoupling from matter (300,000 years after the Big Bang?) each of these photons was of very high energy (low wavelength), but as the universe (space) expanded each of these photons was red-shifted (lost energy), to end up as the microwave background that we see today.

If the first law of thermodynamics is to be obeyed (mass/energy must be conserved), what happened to the energy that these photons lost?

... I've never directly worked with general relativity, so I'm not sure if my semi-classical understanding of the problem applies here.

It doesn't!

It is important not to inconsistently mix up Newtonian and GR gravitational concepts as has happened in the above posts. GR does not in general conserve energy, in particular it does not do so in the cosmological solution of a non-static evolving universe.

The total energy of the CMB does decrease with time as the photon number (apart from the few absorbed by matter) is conserved.

Classically gravitational potential energy is that energy used in lifting a body against a gravitational force. In GR that force is replaced by curvature. In particular work has to be done to accelerate a body out of its freely falling inertial frame, and weight is the reaction to an inertial force. Therefore classical gravitational potential energy is radically re-interpreted in GR and should not be used to explain either cosmological or gravitational red shift.

The question of “Where does the energy of a CMB photon go?” is similar to the question of “Where does the energy of a gravitationally red shifted photon go?” The GR answer is, "into the field", whatever that means.

GR just loses the CMB energy into the cosmological field with no mechanism to explain how that happens or where it might be re-located.

Remember GR does not in general conserve energy, it conserves energy-momentum instead and that is different. It is the curvature of space-time that violates the conservation of energy, which is why the energy of a system can only be properly defined in GR in the absence of curvature, where the space-time is asymptotically flat.

Garth

 

[marcus]

It is fun to calculate how much the lost energy is. I did this a couple of years ago and found that (unless I made a mistake) the lost CMB energy is within a factor of ten or so of the estimated "dark energy" density.

that is, if you take a cubic kilometer it has estimated about 0.6 joules of "dark energy" in it, according to astronomers.

but if you look at all the CMB photons in that cubic kilometer and add up their energy it is something roughly on the order of 1/10000 of that, like
on order of 0.00006 joules.

now each one of those photons has lost 999/1000 of his energy by being stretched out by the expansion of space

so therefore, if you gave each photon, in that cubic kilometer, BACK the energy that he has lost by redshifting, then within a factor of ten or so there would be about the same CMB energy in the cubic kilometer as there is supposed to be dark energy.

but there is no theory that allows lost CMB energy to reappear as dark energy. indeed I am skeptical that dark energy exists. it is not proved.
also one can be skeptical of the estimate of how much dark energy there is, assuming it exists----the 0.6 joule per cubic km.

I will recalculate the energy per cubic kilometer of the CMB and see how it compares, however. this is just for fun and not serious.

 

[marcus]

calculation in natural units:
WMAP estimate of dark energy density is 0.85E-120
current CMB temperature 0.96E-31
current CMB energy density is (pi²/15) (0.96E-31)⁴

order of magnitude about E-124

but redshift of CMB is 1100, so each photon started life 1100 times more energetic, so if you gave them back their lost energy the density would be E-121

so about a tenth of "dark energy" density

... comparable anyway, same ballpark

 

[SpaceTiger]

so about a tenth of "dark energy" density

... comparable anyway, same ballpark

Actually, I think this is a natural consequence of the standard model (sort of). In order for the universe to remain flat, the total energy density must be critical. In the standard model, the currently dominant form of energy is dark energy, while in the past it was matter and radiation, respectively. During its era, of course, radiation had an energy density comparable to critical, but since then the comoving energy density has dropped due to the redshift. If it weren't for that redshift, the radiation would still have an energy density comparable to critical density and, therefore, the dark energy density.

Now, it's no coincidence that the matter-radiation transition and decoupling occur at about the same time (within a factor of a few), because recombination is related to the fact that matter is becoming the dominant constituent. Thus, the comoving energy density lost since decoupling is roughly equivalent to that lost since matter-radiation equality which, by definition, is equivalent to that lost by redshift of photons. In light of this, your calculation is perhaps a bit less surprising.

That said, however, we have no idea what the dark energy is, so it's possible that you're right (redshift -> dark energy). I doubt it, though.

 

[Garth]

Gravity is the curvature of space-time. The space-time of the Milne universe is flat.

The Milne universe is hyperbolic, k = -1, to my knowledge that means it isn't flat or even conformally flat! In the cosmological solution to Einsteins field equation the space-time of an empty universe has curvature.

You might consider the space to be curved, but that depends on the choice of the coordinate system.
Sources don't move through space-time. Space-time doesn't stretch. These are time-based verbs.

True, I was reflecting your own choice of words back to you, again, be consistent!

However from our frame of reference and our temporal "time-based" existence we can ask whether these sources are moving away from us and cosmological red shift is doppler in nature or whether space-time "stretches", i.e. the world lines of distant observers co-moving with the cosmological frame of reference in which the universe (CMB) is globally isotropic and homogeneous diverge from each other.

Garth

 

[meteor]

marcus must remember "the marcus conjecture"
https://www.physicsforums.com/archive/topic/t-2220_The_Marcus_Conjecture.html
that is, the energy of the CMB photons being transformed into dark energy

But we can also consider the inverse mechanism: vacuum energy (a candidate to dark energy) decaying into CMB photons
http://arxiv.org/abs/astro-ph/0409451

So, perhaps this is like the water cycle here in Earth, water from the sea evaporating, then falling like rain, and being channeled again to the sea by streams and rivers.

Only a mad thought. Possibly the reality of what happens is very different

 

[chronon]

Again I'll try to emphasise the difference between space and spacetime. General relativity tells us about the intrinsic curvature of spacetime. It allows considerable freedom of how we coordinatise spacetime. What we think of as space depends upon our choice of coordinate system.

The Milne universe is hyperbolic, k = -1, to my knowledge that means it isn't flat or even conformally flat! In the cosmological solution to Einsteins field equation the space-time of an empty universe has curvature.

The space in the Milne universe is hyperbolic in the usual coordinate system. The spacetime is flat. The case which is usually referred to as 'flat', k=0, has curved spacetime, flat space (in the usual coordinate system)

True, I was reflecting your own choice of words back to you, again, be consistent!

When I talk about movement or stretching, this is with respect to space, not spacetime

 

[wolram]

marcus must remember "the marcus conjecture"
Its as good as any i have seen, if one wants to go beyond "established",
models, yea bring out your dead, least they rot and infect ye.

 

[Chronos]

An observer on an oil rig counts 10 coast bound waves per minute passing by the rig. An observer passing by the rig on a coast bound vessel counts 2 waves per minute passing by his vessel. Is there a missing energy problem here?

 

[floped perfect]

Yes I'd have to go with the doppler effect on that one. Maybe we just see them as red but if you looked at them from the opposite side they would be violet or something.

 

[marcus]

Yes I'd have to go with the doppler effect on that one...

be careful though, it is possible you are mistaken.
something taught in first few weeks of a cosmology course is
the generally accepted idea that the cosmological redshift is not a
doppler effect.

that is, the redshift is not due to the motion of the source at the time of emission, and it is not due to to our motion at the time we receive the signal. (there are small doppler effects due to motion that are superimposed on the main redshift)

the usual story is that the redshift is chiefly caused by the expansion of space during the time that the light is in transit.

there are some cosmology lecture notes available online that probably cover this---by Ned Wright or by Eric Linder. I have to go, can't supply links at the moment.

anyway caution is advisable. attributing redshift to doppler puts you in
a kind of marginal or minority place AFAIK, you could be right but it would involve a major overhaul of the current agreed on model of the universe to make you right

 

[chronon]

Here are a couple of links, and some quotes from their faq's.

Ned Wright's cosmology tutorial
http://www.astro.ucla.edu/~wright/cosmo_01.htm

Are galaxies really moving away from us or is space just expanding?
This depends on how you measure things, or your choice of coordinates.

Eric Linder
http://supernova.lbl.gov/~evlinder/umass/fpoc.html

It turns out, however, in the specific case of flat spacetime (called a Milne universe)...

 

[hellfire]

Are galaxies really moving away from us or is space just expanding?
This depends on how you measure things, or your choice of coordinates.

This seams reasonable, but there is one aspect I do not understand. If we consider that space is expanding, then to compute the (aparent) recession speed from redshift one should make use of a formula derived from the Friedmann equation and the Hubble law (redshift -> comoving distance from the Friedmann equation -> recession speed from Hubble's law). But If we consider that the galaxies are really moving away from us, then the recession speed can be directly derived making use of the Doppler effect. This second method leads to a very different result (no superluminal recession speeds are possible with the Doppler effect formula). Inserting then the obtained speed into Hubble's law, one would obtain a very different comoving distance than the one obtained making use of the first method. Since distances might be independently measured with other methods, doesn't this mean that both descriptions are not equivalent?

 

[Chronos]

But that is just wrong. Space is expanding and there is no way to get around that. You can apply a doppler interpretation to redshift, but guess what? You get a totally unrealistic age for the universe. Something has to give. I chose the concordant version.

 

[marcus]

Are galaxies really moving away from us or is space just expanding?
This depends on how you measure things, or your choice of coordinates.

This seams reasonable, but there is one aspect I do not understand. If we consider that space is expanding, then to compute the (aparent) recession speed from redshift one should make use of a formula derived from the Friedmann equation and the Hubble law (redshift -> comoving distance from the Friedmann equation -> recession speed from Hubble's law). But If we consider that the galaxies are really moving away from us, then the recession speed can be directly derived making use of the Doppler effect. This second method leads to a very different result (no superluminal recession speeds are possible with the Doppler effect formula). Inserting then the obtained speed into Hubble's law, one would obtain a very different comoving distance than the one obtained making use of the first method. Since distances might be independently measured with other methods, doesn't this mean that both descriptions are not equivalent?

I agree it sounds reasonable that you can change coordinates but I wouldn't know how to translate that into a redshift.

Just for illustration sake, I put the CMB redshift z = 1100 into Morgan's calculator and got

1. then (when light was emitted from the Last Scattering Surface)
LSS distance from us was 40 million LY
LSS recession speed was 57c

2. now (when we receive the microwaves)
LSS distance from us is 45.5 billion LY
LSS recession speed is currently 3.3c

So I can see how you might construct coordinates so that the atoms that emitted a particular CMB photon are actually moving away at 57 times speed of light when they emit
and are now moving away (when we get the light) at 3.3 times the speed of light. And all this time space does not expand. that is reasonable I guess.
It is just substituting the atoms motion thru space for the usual expansion picture.

But I do NOT see how one could translate that motion into a DOPPLER effect. The relativistic doppler formula that i know applies only to speeds less than c. But the recession speeds we are dealing with are all the time greater than c. So what doppler formula would one use?

Maybe I am missing something and someone will explain. But it seems much easier to understand the redshift as a non-doppler effect of the expansion of space. And AFAIK this is the usual way people teach it and talk about it.

It seems reasonable that one could introduce new coordinates so all the expansion is represented as motion, but then (like hellfire was asking maybe) how do the Friedmann equations work? What do they even look like? We are told that expansion started off very fast and was slowing down for the first 10 billion years or so and is now speeding up. This can be explained in the Friedmann equation model as due to changing matter and dark energy density, or the cosmological constant. But I do not see how, if one throws the Friedmann model out and the Friedmann-Robertson-Walker coordinates one gets anything except some rather artificial construct in which the changing expansion rate is either impossible to represent or else has to be put in by hand. Must confess that I haven't thought about that kind of coordinate change so several people here are probably in better position to clarify this.

 

[marcus]

But that is just wrong. Space is expanding and there is no way to get around that. You can apply a doppler interpretation to redshift, but guess what? You get a totally unrealistic age for the universe. Something has to give. I chose the concordant version.

I'm suspect Chronos is right about this. (notwithstanding I do not fully understand how one would re-coordinatize so that one would represent the recession of galaxies as motion and interpret the redshift as doppler.)

 

[chronon]

General relativity determines the shape of spacetime, but doesn't specify how you coordinatise it. The usual choice is to take a time coordinate corresponding to the proper time of comoving objects. My feeling is that this is just going back to the idea of absolute time, and it is better to use a coordinate system in which the speed of light is taken to be constant. Then nothing travels faster than light. I've written some ideas on how this could be done at: http://www.chronon.org/Articles/milne_cosmology.html

It is important to distinguish between the actual physics of the situation and the effects of the choice of coordinates. The trouble with the proper time system is that it leads to effects which people interpret as physical, such as stretching space. (I don't think that the slowing down from 57c to 3.3c is physical either). The constant speed of light system has some strange properties as well, but these are the more familiar puzzles of special relativity.

The best way to distinguish between the physical effects of gravity in GR, and the artifacts of the coordinate system is to consider the Milne universe, where there is no gravity. Take a look at Matt McIrvin's page on the subject: http://world.std.com/~mmcirvin/milne.html

 

[hellfire]

But I do NOT see how one could translate that motion into a DOPPLER effect. The relativistic doppler formula that i know applies only to speeds less than c. But the recession speeds we are dealing with are all the time greater than c. So what doppler formula would one use?

I agree with you marcus, and I want to add the following for clarification. In my understanding, the only fact that one obtains different recession speeds with both methods is not the problem, since relating redshift to recession speed may be a matter of definition (how to infer about recession speeds without measuring redshifts?). But, as long as (1.) it exists a relation between speed and distance (Hubble's law) and (2.) there exist independent methods to determine distances, then both interpretations of the Hubble flow cannot be equivalent.

 

[turbo]

General relativity determines the shape of spacetime, but doesn't specify how you coordinatise it. The usual choice is to take a time coordinate corresponding to the proper time of comoving objects. My feeling is that this is just going back to the idea of absolute time, and it is better to use a coordinate system in which the speed of light is taken to be constant. Then nothing travels faster than light. I've written some ideas on how this could be done at: http://www.chronon.org/Articles/milne_cosmology.html

Thank you for the link to your page. I've got to spend some time tracking down Milne.

Well I hope I've shown you that the usual way of looking at the universe isn't the only one, and one can use SR coordinates without disagreeing with general relativity. Next time you hear of something strange going on in cosmology remember to think 'Is this just because of the choice of coordinate system?'.

 

[Chronos]

Pardon me for being impolite. Chronon is espousing a bunch of crap.