Hi all, CMB photons are red-shifted due to Universe expansion -> this means that the whole CMB energy gets smaller... where does it go? pozdrawiam Jarek
On Mon, 23 Feb 2004, Jarek Rzepecki wrote:
Hi all, CMB photons are red-shifted due to Universe expansion -> this means that the whole CMB energy gets smaller... where does it go? pozdrawiam Jarek
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There's an FAQ on this but i'm not totally happy with it.
The photons that are observed in CMB observations have presumably been traveling through space undisturbed since sometime after the big bang. But thay have apparently lost energy in the process, as their wavelength has changed. Where did this energy go? Did it go into the gravitational field?
Submitted by jamont at visto.com 4/00
I'm surprised I haven't been asked this before, since it's such a good question!
There are several different ways of looking at this. One answer would be that the energy goes into the gravitational potential energy of the whole Universe.
Really this should be energy density, or energy within some fixed comoving volume.
Another answer is that it takes energy to expand the Universe, and that this "work" comes out of the contents which are expanding.
e.g. pp34, 35 Liddle 2000 polski
Yet another answer is that the cooling of the CMB as the Universe expands is part of a simple relativisitic solution which describes the entire Universe, using the theoretical basis of General Relativity, which is a well tested theory of gravity. And if part of that solution appears to violate energy conservation, then tough!
i would add the special relativistic point of view - energy is not an absolute quantity.
On scales where curvature is small (much less than a horizon radius), SR (STW) is valid.
The amount of energy depends on which reference frame you use.
If you stick to one inertial frame, you can think of photons *not* losing any energy.
E.g. Think of a UV photon which was emitted from a high redshift galaxy X when (in constant cosmological time) the first amoebae evolved on Earth and is today absorbed on the Earth. In the reference from of galaxy X, just using SR and not GR, the Earth is moving at extremely high velocity away from galaxy X.
So when the UV photon is absorbed, the calculation for what physically happens should be made between a UV photon moving at c, and a spectrometer moving at, e.g. 0.9c.
If we take an alternative inertial frame, where the Earth is at rest, then of course the energy of the photon in this frame is much lower - just standard SR.
boud
CMBR is almost perfectly well described by u(\ni) d\ni function - the plack function which is the spectral energy density described with the only parameter - temperature. Expansion changes the overall CMBR energy (as we see it) like (1+z)^4 which comes from 4'th power T relation when we integrate u(\ni) d(\ni) (to get Stefan boltzmann law) ( and there is stright relation between temperature of boson gaz with it's enery - alghough coefficients are different in classic and ultra relativistic regime).
Bosons are particles which participe positivly to universe's density and pressure thus they only make expansion slower, hence IMHO it's incorrect to say that "it takes some energy to expand the Universe..." nor that the expansion is derived by it's contents. In fact we don't know why BB happened. In fact we don't even know if it happened. (although the expansion rate is altered by the contents in various ways).
Recalling the energy density doesn't help much for the question since there still remains 1+z factor left to explain.
It's the question why photons suffer from redshift? And is the fact that different observers see, say two identical photons (each of them observes his own photon) as two different photons actually a manifestation of violation of energy conservation principle?
I've been thinking about this problem yesterday and what I concluded is... shocking simple. :)
IMHO The correct answer is: Nothing happened to that energy. It's still there (unless photons gets older or other crap like that), the only thing that changed is that we no longer see hot photons because, as we've been tought in high school, we're floating away from everything else according to the hubble law. (So the answer is essentialy in the question ;) The "doppler effect" which can easily be derived from SR transformaiton formulas causes that we see everythig red. The only difference from the situation described above with observers looking at identical photons (and yet seeing them in different colors) and complication I see here is that it is not possible to find a recerence frame in which we will see the whole CMB photons at different temperature - color etc. This is of course because it's the space that expands and there is nothing we can do about it, so changing reference frame won't help in understanding that it is just our obserwational effect not a true energy theft by some more less unidentified process. But still I belive that this reddening can be ballanced once when Universe start to collapse.
I hope that helps.
regards bartek
On Mon, 23 Feb 2004, Jarek Rzepecki wrote:
Hi all, CMB photons are red-shifted due to Universe expansion -> this means that the whole CMB energy gets smaller... where does it go? pozdrawiam Jarek
On Tue, 24 Feb 2004, Bartosz Lew wrote:
The correct answer is: Nothing happened to that energy. It's still there (unless photons gets older or other crap like that), the only thing that changed is that we no longer see hot photons because, as we've been tought in high school, we're floating away from everything else according to the hubble law. (So the answer is essentialy in the question ;) The "doppler effect" which can easily be derived from SR transformaiton formulas causes that we see everythig red. The only difference from the situation described above with observers looking at identical photons (and yet seeing them in different colors) and complication I see here is that it is not possible to find a recerence frame in which we will see the whole CMB photons at different temperature - color etc. This is of course because it's the space that expands and there is nothing we can do about it, so changing reference frame won't help in understanding that it is just our obserwational effect not a true energy theft by some more less unidentified process. But still I belive that this reddening can be ballanced once when Universe start to collapse.
Well I think that the problem is closer to the question: Why photons getting out of potential well suffer from red-shift - where their energy go in that case? then to the Doppler...
On Tue, 24 Feb 2004, Jarek Rzepecki wrote:
On Tue, 24 Feb 2004, Bartosz Lew wrote:
The correct answer is: Nothing happened to that energy. It's still there (unless photons gets older or other crap like that), the only thing that changed is that we no longer see hot photons because, as we've been tought in high school, we're floating away from everything else according to the hubble law. (So the answer is essentialy in the question ;) The "doppler effect" which can easily be derived from SR transformaiton formulas causes that we see everythig red. The only difference from the situation described above with observers looking at identical photons (and yet seeing them in different colors) and complication I see here is that it is not possible to find a recerence frame in which we will see the whole CMB photons at different temperature - color etc. This is of course because it's the space that expands and there is nothing we can do about it, so changing reference frame won't help in understanding that it is just our obserwational effect not a true energy theft by some more less unidentified process. But still I belive that this reddening can be ballanced once when Universe start to collapse.
Well I think that the problem is closer to the question: Why photons getting out of potential well suffer from red-shift - where their energy go in that case? then to the Doppler...
well, your question, as I understood it, was about what's with the energy that seems to be missing because of the redshift. So I disagree. The cosmological redshift isn't caused by gravitational effects - i.e. gravitational reddening, but by combined effect of time dilatation and lenght change which comes from transformation from one reference frame to another - and together we call it "a doppler effect". Sahs Wolfe effect is a minor one here, and fully understood in terms of GR predisitons.
However I do realise that my explanation is a bit outstretched, because SR do not allow space to change in time, or at least doesn't say anything about that. But on the other hand a single photon, or any other particle (eg. proton, neutrino) can't (or can ? - I think not :) feel it travels trough space that is actually expanding. If it did, we all would grow in time, atoms would have become greater etc. So eventually it makes no difference weather space is expandind or observer is receeding, except the problem I said before >>
******************************************************************************* Bartosz Lew e-mail: blew@astri.uni.torun.pl blew@astro.uni.torun.pl Centrum Astronomii UMK TORUN, POLAND www: http://adjani.astro.uni.torun.pl/~blew *******************************************************************************
Bartosz Lew wrote:
On Tue, 24 Feb 2004, Jarek Rzepecki wrote:
On Tue, 24 Feb 2004, Bartosz Lew wrote:
The correct answer is: Nothing happened to that energy.
That is not the correct answer. A single photon loses its energy.
It's still there (unless photons gets older or other crap like that), the only thing that changed is that we no longer see hot photons because, as we've been tought in high school, we're floating away from everything else according to the hubble law. (So the answer is essentialy in the question ;) The "doppler effect" which can easily be derived from SR transformaiton formulas causes that we see everythig red.
SR do not apply to cosmology in this case as I believe.
The only difference from the situation described above with observers looking at identical photons (and yet seeing them in different colors) and complication I see here is that it is not possible to find a recerence frame in which we will see the whole CMB photons at different temperature - color etc. This is of course because it's the space that expands and there is nothing we can do about it, so changing reference frame won't help in understanding that it is just our obserwational effect not a true energy theft by some more less unidentified process. But still I belive that this reddening can be ballanced once when Universe start to collapse.
well, your question, as I understood it, was about what's with the energy that seems to be missing because of the redshift. So I disagree. The cosmological redshift isn't caused by gravitational effects - i.e. gravitational reddening, but by combined effect of time dilatation and lenght change which comes from transformation from one reference frame to another - and together we call it "a doppler effect".
O really? I always thought calling photon reddening a "doppler effect" is the most naive one. A agree it comes from the transformation..... but it is far more complicated.
If fact the problem as I see it is: photon field energy + energy of the gravitational field is conserved (when only those 2 fields are present). Have you never solved Friedmann's equations? Come back to the source, to the lagrangian density for the tensor grav. theory (Riemann tensors etc.) - I believe a conservation rule can be obtained at this level. As I remember the energy of the photon field (as well as any other form of the energy) is (depending on its equation of state) transfered between the grav. field and this particular field.
Why do you think photon field is trying to slow down the expansion??? Because of this interaction.
My answer is: do not treat photons as separate objects for the photon field is not an isolated system - the photon field interacts with the grav. field. If GR does not give you the answer - that would be a problem.
Sahs Wolfe effect is a minor one here, and fully understood in terms of GR predisitons.
However I do realise that my explanation is a bit outstretched, because SR do not allow space to change in time, or at least doesn't say anything about that.
Forget about SR in cosmology!!!!!!!!!!!!!!!!!!!
But on the other hand a single photon, or any other particle (eg. proton, neutrino) can't (or can ? - I think not :) feel it travels trough space that is actually expanding.
have you attended prof Rudak's lectures on cosmology?
If it did, we all would grow in time, atoms would have become greater etc. So eventually it makes no difference weather space is expandind or observer is receeding, except the problem I said before >>
we do not grow in time because subatomic, atomic (electromagnetic) and even gravitational interaction on small scales are MUCH STRONGER than the effect of space expansion.
GR is not a "perfect" and "final" theory. But for sure all the modern cosmology (Friedmann's cosmology) is based on it. Search for the answer in GR.
regards - michal
On Tue, 24 Feb 2004, Jarek Rzepecki wrote:
Well I think that the problem is closer to the question: Why photons getting out of potential well suffer from red-shift - where their energy go in that case? then to the Doppler...
When you throw a frictionless ball up in the air at initial vertical velocity v_0, it starts off with kinetic energy 0.5 m v_0^2 .
So why does the ball lose (kinetic) energy as it goes up? Why does 0.5 m v^2 get smaller? Where does the energy go?
When you throw a frictionless ball up in the air at initial vertical velocity v_0, it starts off with kinetic energy 0.5 m v_0^2 .
So why does the ball lose (kinetic) energy as it goes up? Why does 0.5 m v^2 get smaller? Where does the energy go?
Well, sure but how can one definne potential energy for a photon?
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Bartosz Lew -
Boud Roukema -
Jarek Rzepecki -
Michal Frackowiak