I understand how photons can change wavelength via gravitational redshifting, but that doesn't seem to be what's going on with the CMB radiation. I've heard it explained as happening because of the expanding universe, but I'm thinking that would have to imply that as the universe expands, lower wavelengths have higher energy, so to conserve energy, the CMB would have to redshift. Is that the case, or is something else going on?
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Why do you think energy is conserved on cosmological scales? The universe is certainly not time-translation invariant. – ACuriousMind Aug 11 '14 at 20:05
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Similar to this question. Note that the accepted answer is actually wrong. You can see a simple explanation of what's going on here in my answer just below the accepted one. – ticster Aug 11 '14 at 20:20
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@ticster: I am getting the feeling that you have an absolute belief in the universal validity of general relativity. The question where the energy goes is an experimental question, not a question for a theory, that has, so far, not been tested experimentally with regards to this question. – CuriousOne Aug 12 '14 at 18:24
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Possible duplicates: http://physics.stackexchange.com/q/7060/2451 and links therein. – Qmechanic Mar 31 '15 at 20:17
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The energy goes nowhere. It needs to go nowhere, since energy conservation only holds for systems which are time translation invariant, and conversation of energy then follows by Noether's theorem.
But the universe, as a whole, is not a time-translation invariant system (or in GR terms, there is no guarantee that we always have the right time-like Killing vectors, see also this old question. You should not expect energy to be in any form conserved on cosmological scales (though in SR, and in suitable subsystems, it is).
ACuriousMind
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Correct me if I am wrong, but doesn't Noether's theorem only apply for Hamiltonian systems? GR does not describe a Hamiltonian system, neither is there a global time coordinate which one could plug into it to break time-translation invariance, so it seems a bit far fetched to make an argument that GR plus Noether can decide the physical question if the total energy of the universe is conserved or not. I would love to be proven wrong with a citation, though. – CuriousOne Aug 11 '14 at 20:39
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1The old question you mentioned has an answer saying that the total energy in the universe is increasing. Is that answer correct? If so, and photons are decreasing in energy, what's causing the increase in energy in the universe? – B T Aug 11 '14 at 20:40
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@CuriousOne: That's why my parenthesis mentions the Killing vectors. GR conserved quantities have associated Killing vectors, and for an energy-like quantity, it would have to be a time-like Killing vector, which we cannot guarantee for arbitrary spacetimes. – ACuriousMind Aug 11 '14 at 20:42
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@BT: I've honestly no idea whether the energy of the universe grows, especially since some say that term is ill-defined. Due to the 8 upvotes I'd guess there's some merit to it, though. – ACuriousMind Aug 11 '14 at 20:44
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@CuriousOne: I got that. We may simply be asking two different questions. One is what GR has to say about the conservation of energy, while I am more interested in what nature has to say about it? Is that a fair characterization? – CuriousOne Aug 11 '14 at 20:44
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@CuriousOne: Do you have a definition of energy other than "That which is conserved under time translation" or "That which is the value of the Hamiltonian"? – ACuriousMind Aug 11 '14 at 20:45
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@ACuriousMind: Energy is that which can perform work. As cosmological time goes by, CMB photons can perform less and less work. It is a valid question whether there is something beyond the description of GR on which these photons are performing work in such a way, that the total work performed by CMB photons, plus the ability of the photons to perform additional work is constant. I don't have an experimental answer to that, and I don't think that GR can supply a conclusive theoretical one, either. I would simply call this one as being outside of the real of any established theory. – CuriousOne Aug 11 '14 at 20:55
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CMB photons are redshifted, because the space trough which they travel gets "stretched". You are correct, that this implies, that the accessible universe is "losing" energy in the sense, that one could extract less and less energy from the CMB as more and more cosmological time goes by. It is instructive to imagine a giant "solar array" soaking up all the CMB photons.
Where does this energy go? Assuming that the universe as a whole is energy conserving (that's an assumption for which we lack sufficient experimental evidence, so far), the energy of the photons get converted into an energy term that has to increase the total energy of the "field" that creates spacetime to begin with. We don't have a valid theoretical description for what that "field" is, but energy conservation would tell us something about the time evolution of its energy density and total energy, IF it applies.
CuriousOne
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Energy conservation is a mathematical guarantee for time translation invariant systems. The fact that we don't think energy is conserved on cosmological scales has nothing to do with lack of experimental evidence. If anything, it's due to the observationally confirmed process of expansion which breaks time translation invariance. This is a known property of General Relativity and of most (if not all) other metric theories. – ticster Aug 11 '14 at 20:24
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The question where the energy goes is a physical question, not a question about GR. That GR is not a complete theory is a known fact, which means that it does not have to answer the question where the energy goes correctly. That's why I said that IF we assume that energy conservation holds, then there has to be a component of spacetime that is not described by GR, which, of course, could be some form of field theory. – CuriousOne Aug 11 '14 at 20:29
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"The question where the energy goes is a physical question, not a question about GR." :/ I'm curious, what exactly do you think GR is ? You seem to think it's somehow unphysical. – ticster Aug 11 '14 at 20:31
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I think this end of this article describes something like what CuriousOne is talking about - it mentions how another interpretation is that "energy" is "conserved" if you include the energy of gravitational fields: http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/#.U-koR_ldWao . I have no idea how accurate that is tho. – B T Aug 11 '14 at 20:39
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@ticster: GR is a theory which describes SOME aspects of the universe properly. Like all theories it does not (and does not have to) describe all aspects of the universe. GR does, for instance, not mention photons, at all, neither is there "matter" with structure in it. Both are constructs that are external to it and which are properly described by other theories that are equally valid in their realm. My point is, that this question may not be answered correctly by GR any more than it can answer what the spectrum of hydrogen looks like. – CuriousOne Aug 11 '14 at 20:48
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GR is a metric theory that breaks time translation invariance. As such, it is the quintessential theory to be considered when addressing this question. Energy is most certainly not an "external" construct to GR. You may want to look into the right hand side of the Einstein Equations. – ticster Aug 12 '14 at 07:05
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@ticster: In physics theory only has one function: to describe the experimental data that we see. I know that it is fashionable to blow the role of theory out of proportion, but that's a deviation from the scientific method: observe first, describe later. It has never been the other way around and it is still not the other way around. Just because GR breaks your notion of time translation invariance, does not mean that energy conservation is violated in the actual universe. It only means that GR may have a flaw. If we want to check energy conservation, we have to come up with an experiment. – CuriousOne Aug 12 '14 at 18:17