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...it would be contraversial to suggest that, for example, the Hubble redshift is not mostly due to expansion.
The problem in discussing some of these subjects is that there are many ideas and very few experimental confirmations. Cosmology is like that.
Andrew, is the preferred frame of reference you refer to just one that removes our local motion from observation of the CMBR?
Isn't it to be expected that an expanding universe would result in the CMBR losing energy?
After all they started off very hot and are now rather cold. Or are you speaking of a new phenomenon?
Andrew, my intuition here was simply that the CMBR temperature fits with blackbody radiation assuming an expanding universe resulting in adiabatic cooling. I guess you are saying that the cooling is greater than this mechanism could predict (is that right?) so maybe this could be a result of the newly discovered accelerated expansion (??).
If so then you can't discount the effects of dark energy, though not affecting the CMBR directly, but being possibly the ultimate cause of greater cooling than expected.
Indeed, GR would have conservation of energy-momentum but energy can also said to be conserved. I think, rather as you observe in your post, this is a matter of interpretation. In flat (Minkowski space) energy is conserved. It could be argued that the FLRW metric this is not a bad approximation though has a few issues with boundary conditions.
Even then it could be said the energy is transformed into gravitational rather than not conserved. If you think of light emerging from a gravity well, the energy put in is in a different frame from when it is received. Observers in both frames will only agree on the total energy used if the gravitational effects are taken into account, including time dilation, and I don't think there will energy lost; it just depends on the frame. At least I think so.
To follow a discussion in another thread, do you know the formula for gravitational redshift from inside a massive sphere. i.e. that uses Gravitational potential as a function of radius. All the references I can find consider redshift outwards from the outside of a sphere and use field.
Andrew and the quote from Tommya are quite right about the effects of gravitational time dilation affecting the energy of a photon.
...The cosmological redshift effect can indeed be thought of consistently in this kind of way, as 'the photon continually climbing out of a gravitational field'...
I understand the need to do external work for adiabatic expansion of an ideal gas but this is not exactly the same as the universe though sometimes a convenient model. Could this not be effectively synthesised by the pressure reduction of matter condensing out? The energy is not lost in this case though it may appear so from just looking at em radiation in isolation.
I didn't understand why time assymmetry affects energy conservation or even why the FLRW metric results in this. Is this something to do with gravitational collapse? Can you explain or give a reference?
Can you give a clear example of energy conservation failure but where energy-momentum is conserved.
... IMHO this maintains energy conservation for those CMBR photons.
Quote from: graham.d on 31/05/2010 22:30:58I understand the need to do external work for adiabatic expansion of an ideal gas but this is not exactly the same as the universe though sometimes a convenient model. Could this not be effectively synthesised by the pressure reduction of matter condensing out? The energy is not lost in this case though it may appear so from just looking at em radiation in isolation.I'm not 100% sure I follow this. Are you talking about some sort of phase transition? It's not immediately clear to me that the Universe's expansion can be interpreted as an ongoing phase transition (and I've certainly not heard of anyone thinking of it in these terms), but I'd have to think about it.
As I stated in one of my earlier posts the conclusion you come to will depend to a large extent on how you choose to define 'energy' in a context where it's pushed beyond its normal bounds of usefulness.
So: it doesn't conserve energy in the sense that if you measure the total usable energy of a fixed number of CMBR photons at an early time, then again at a later time, the energy won't be the same.
But if you like to attribute that to a time-dependent 'potential energy', I suspect you can (with care) get a consistent description of redshift effects from these considerations. You're right that people don't often state it in these terms, and I suspect the reason is that it's because it's actually harder than thinking about it in the more standard way!
The reason we turn away from fixing up normal energy conservation using potentials (ala Newtonian mechanics) to the more general notion of energy-momentum conservation is because the latter is much more generally applicable (see for instance the dark energy example just above).