What do we mean by Is the universe losing energy ?

[Robert100]

What do we mean by "Is the universe losing energy"?

In recent posts it has been proposed that, on a large scale, the law of conservation of energy just may not be true. Some analyses of the cosmic microwave background (CMB) are interrepted as meaning that energy has been lost over time. However, are all people using the same definitions for the same phrase?

The CMB photons 'cool' simply due to redshift, which is caused by expansion alone (ignoring the Reese-Sciama effect).

If I understand this correctlly, then are you saying that these photons have really not lost energy? In "Expanding Space: the Root of all Evil?", by Matthew J. Francis et. al., we read:

"The key is to make it clear that cosmological redshift is not, as is often implied, a gradual process caused by the stretching of the space a photon is traveling through. Rather cosmological redshift is caused by the photon being observed in a different frame to that which it is emitted. In this way it is not as dissimilar to a Doppler shift as is often implied. The difference between frames relates to a changing background metric rather than a differing velocity."​

On the surface, at least, this seems to contradict the brief discussion given here (http://www.gravityfromthegroundup.org/pdf/timeenergy.pdf ) in which the energy of the universe is said to decrease over time. But I may be mistaken. The way in which the author is considering energy to be lost over time may come from a different phenomenon? Anyone?

Also, this seems to contradict Marcus's analysis, which he comments on in post #27 in the thread "Is energy conserved in an expanding universe?"
https://www.physicsforums.com/showthread.php?t=179051&page=2

Marcus writes:

I calculated the energy lost by the redshifting of CMB photons starting out in some volume of space----as that space expanded (the calculation is simple and would be somewhere in PF archives I suppose)

I calculated the energy gained just by the expansion of that same volume of space, assuming a constant darkenergy density of 0.6 joules per cubic kilometer (the present measured value)

The amount lost and the amount gained were same order magnitude. Maybe they differed by a factor of 2. I don't recall. they didnt exactly match but they were same ballpark.

I have tried to find out what the consensus of the physics community is on this issue, only to get nowhere. There doesn't seem to be a consensus yet. If I understand correctly, the problem is worse: the total energy of the universe is being defined differently by different people.

Sound familiar? When people talked about "the expansion of space", it turned out that people used significantly different definitions for the same phrase, and worse, they were often unaware of this. It took years before someone finally wrote "The Root of all Evil" paper, in which this terminology mess was straightened out.

I think someone needs to write a similar paper for this issue. When talking about the energy of the universe, we need to look at the different ways that people have loosely used this term. We also need to look at all the analyses of the CMB, and analyses of the increase in volume of the universe, and subsequent contribution that is made by vacuum energy.

If there are any papers that do this, please let me know!

Robert

 

[Wallace]

I think you're on the right track when you suggest this is mainly an issue of definitions of energy, though there are some subtle issues.

Essentially 'energy' is a Newtonian 3D entity, and hence is not conserved in a full 4D space-time (though will be conserved 'locally'). This doesn't mean that the Universe is lawless, just that different conservation laws apply on Universe scales than we are used to in the Lab. The conservation laws for GR are known as the Bianchi Indentities.

So for the photon example, if you have a Universe filled only with photons then the total energy is the sum of the energy of each photon. As the Universe expands they redshift, losing energy and thus the total energy is decreased, however this interplay between the expansion rate and the energy loss is governed by physical laws, it is not arbitrary.

As a hand-waving explanation, the loss of energy from the photons alters the metric of space-time (if our test Universe contained only matter the metric and hence expansion rate would be different). Now, since acceleration in GR derives through derivatives of the metric then the metric is somewhat analogous to the Newtonian potential. Therefore this is a relativistic version of exchanging energy, just as a pendulum constantly converts between kinetic and potential energy. Now, the above is merely an analogy and is probably problematic on some level but I hope it helps in some way.

Vacuum energy works in a similar way except in that case the energy of the Universe increases with expansion, but the effect is the same in that there are physical laws including conservation laws applying, they just aren't (unsurprisingly really) the friendly neighborhood Newtonian laws we are more familiar with.

 

[Robert100]

What do we mean by "Is the universe losing energy"?

I think you're on the right track when you suggest this is mainly an issue of definitions of energy, though there are some subtle issues. Essentially 'energy' is a Newtonian 3D entity, and hence is not conserved in a full 4D space-time (though will be conserved 'locally'). This doesn't mean that the Universe is lawless, just that different conservation laws apply on Universe scales than we are used to in the Lab. The conservation laws for GR are known as the Bianchi Indentities.

This actually makes sense. I already know that the laws of conservation of energy, and conservation of momentum, are not ultimate laws. Rather, even in special relativity they combine into one law, conservation of the energy-momentum 4-vector (e.g. Taylor and Wheeler's Spacetime Physics.) So I am not surprised to hear that in general relativity a further generalization must be made.

I tried to read http://www.math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html, "Is Energy Conserved in General Relativity?" by Weiss and Baez, which helped, but your analogies helped further.

So for the photon example, if you have a Universe filled only with photons then the total energy is the sum of the energy of each photon. As the Universe expands they redshift, losing energy and thus the total energy is decreased, however this interplay between the expansion rate and the energy loss is governed by physical laws, it is not arbitrary.

Well, thanks a lot, spoilsport. There goes my last possible excuse for not paying my electric bill this month.

As a hand-waving explanation, the loss of energy from the photons alters the metric of space-time (if our test Universe contained only matter the metric and hence expansion rate would be different). Now, since acceleration in GR derives through derivatives of the metric then the metric is somewhat analogous to the Newtonian potential. Therefore this is a relativistic version of exchanging energy, just as a pendulum constantly converts between kinetic and potential energy. Now, the above is merely an analogy and is probably problematic on some level but I hope it helps in some way.

It certainly is good enough for me.

I do wonder, though, if detailed analyses of this phenomenon is consistent. Is there a good review paper on this subject? If not, then it might be time to prompt someone to start work on one. I have this nagging feeling that some papers might be comparing apples and oranges, and need a new "Root of all evil" paper to expose any inconsistent terminology.

Vacuum energy works in a similar way except in that case the energy of the Universe increases with expansion, but the effect is the same in that there are physical laws including conservation laws applying, they just aren't (unsurprisingly really) the friendly neighborhood Newtonian laws we are more familiar with.

Great. BTW, do you (or anyone reading this discussion) know of any papers that attempt to discuss both issues? Marcus is the only person I know brave enough to have done this (here on physicsforums), and I find it hard to believe that no connection exists.

That digression aside, thanks much for taking the time explain this.


Robert

 

[Wallace]

Try Mining Energy in an Expanding Universe by Ed Harrison. That and the references within should keep you busy for a while

 

[Chronos]

The 'Root of All Evil' assumes facts not in evidence. There is no observational evidence contradicting the laws of thermodynamics. As Wallace noted, the 'global' energy content of the universe is always preserved. Photons become 'diluted' as space expands.

 

[marcus]

The 'Root of All Evil' assumes facts not in evidence.

I didn't notice. Could you please quote the unjustified assumptions you found in the paper?

... As Wallace noted, the 'global' energy content of the universe is always preserved. Photons become 'diluted' as space expands.

Please clarify. Where did Wallace say the global energy content of the universe is preserved? Could you please quote?

Also what do you mean by photons, for instance CMB photons, becoming diluted. The individual photon could lose energy as lengths expand, or there could be fewer per unit volume, as volumes expand, or both. Which meaning or meanings did you have in mind?

 

[Wallace]

Photons become 'diluted' as space expands.

Photons become diluted, as in there number density drops with the inverse cube of the scale factor (or more simply with the inverse of the increase in volume) but in addition each photon losses energy via redshift, so the total energy of the Universe does change, the point is that there is nothing in that fact which is a problem for thermodynamics or anything else.