Where does the light energy lost due to expansion go?

[mister i]

TL;DR Summary

If light changes its frequency during a long time of travel in space (vacuum?) for all observers (redshift) and therefore its energy decreases (E=hf), what "entity" absorbs this energy?

Sorry for my questions as an amateur interested in physics: If light changes its frequency during a long time of travel in space (vacuum?) for all observers (redshift) and therefore its energy decreases (E=hf), what "entity" absorbs this energy? I suppose the answer will be that the wavelength is lengthened due to the expansion of space, but wouldn't this mean that its lost energy is distributed in the created space?

 

[Ibix]

Global conservation of energy cannot be defined in non-stationary spacetimes such as the cosmological models. So the energy doesn't go anywhere, it is just lost.

If you don't like that you aren't alone, but there are no convincing solutions to the problem (or not one that convinces anywhere near a majority).

I remind you that space isn't being created in this process. You are just looking at different slices of spacetime where the spatial scale factor is different.

 

[PeroK]

TL;DR Summary: If light changes its frequency during a long time of travel in space

The frequency of light is dependent on the relationship between the source and the receiver. Light doesn't inherently change its frequency as it travels.

Over large cosmological distances, the source and receiver are separated by expanding space. The receiver measures a lower frequency than would have been measured by the source. This is redshift.

There is also redshift between a source and a receiver moving away from the source. You could also ask where the energy goes in that case.

 

[phinds]

Sean Carroll on "Energy is not conserved"
http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[Vanadium 50]

There are hand-wavy ways to explain this (Rocky Kolb taught me an excellent one) but none of them are without their downsides, and these downsides are hard to explain at B-level. About the best that can be done is that conservation of energy is related to an insensitivity of our measurements on the time in whcih tehy are performed, and this is not valid if the universe itself is expanding.

 

[jbriggs444]

There are hand-wavy ways to explain this (Rocky Kolb taught me an excellent one) but none of them are without their downsides, and these downsides are hard to explain at B-level. About the best that can be done is that conservation of energy is related to an insensitivity of our measurements on the time in whcih tehy are performed, and this is not valid if the universe itself is expanding.

I'd never heard Noether's theorem expressed that way.

 

[Vanadium 50]

I'd never heard Noether's theorem expressed that way.

Um...thanks? I guess. Is that a good thing?

 

[PAllen]

I'll add my standard mini-rant that I don't like the terminology "energy is not conserved" because it implies there is some notion of energy that is definable that is not conserved. The IMO more correct statement is that without special conditions (stationary spacetime, asymptotically flat, etc.), large scale energy cannot be defined; thus you never get to ask about conservation.

In particular, I hate when someone integrates some notion of energy, finding that it changes with time (violating energy conservation) - when the integral used fails to define conserved energy in the cases where it is well defined and conserved. This to me, is not just sloppy but wrong. I will refrain from naming some big names who have done this.

 

[PeterDonis]

I don't like the terminology "energy is not conserved" because it implies there is some notion of energy that is definable that is not conserved.

It's true that Carroll's article doesn't address this issue: he assumes without argument that "energy density times volume" gives a meaningful notion of "total energy". But in our best current model of our universe, which is spatially infinite, that calculation gives an infinite total energy, so at the very least there is some more explaining to do to justify the argument that, for example, "total energy is increasing" as the universe expands. In a spatially finite universe one could do this calculation and get a finite answer, but it's still not clear what it would mean physically (see further comments below).

the notion of adding up locally measured energy with no other compensation for gravity is wrong.

Not only that, in a spacetime that isn't stationary or asymptotically flat, it's not even clear what "compensation for gravity" would mean, since there is no meaningful notion of "gravitational potential energy". The various "pseudo-tensors" in the literature are attempts (IMO not successful) to try to define such a notion for cases like the universe as a whole. And for extra fun, for the case of a spatially closed universe (at least with zero cosmological constant--I'm not sure how a nonzero CC would affect this), the "obvious" way of defining "gravitational potential energy" makes the total energy zero. (IIRC this is actually a special case of the general fact that the "Hamiltonian constraint" in GR, which seems like an "obvious" way of defining total energy, is identically zero.)

 

[PAllen]

While the following is popular presentation, it is by Tamara Davis of Davis and Lineweaver fame. I think it has a good discussion of the the real issues in conservation of energy in GR, focusing on global problems of definition (and why conservation shouldn't be expected, in general in GR due to Noether's theorems). However, it also does explain, correctly, that cosmological redshift is no more a loss of energy than Doppler, and it can be modeled as a concatenation of small Doppler shifts.

https://people.smp.uq.edu.au/TamaraDavis/papers/SciAm_Energy.pdf

 

[Vanadium 50]

that cosmological redshift is no more a loss of energy than Doppler, and it can be modeled as a concatenation of small Doppler shifts.

This is true.

The thing I don't like about it is that if I throw a baseball a cosmological distance, over time it gets closer and closer to a co-moving frame. Where did it;s energy go? The Doppler explanation only works for light.

The hand-wavy explanation that I don't very much like is that in a non-comoving frame, a body feels a gravitational force from the rest of the universe pulling it into a co-moving frame. I do not like this, because it's the overall curvature that does this, not just what is generated by matter (dust if you like).

Maybe it's OK as a plausibility argument.

 

[pervect]

I still like the old sci.physics.faq, though the short and accurate answer there may not be seen as helpful. Also, I find that most PF readers don't appear to pay much attention to it, for whatever reason.

"Is energy Conserved In General Relativity", https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

In special cases, yes. In general, it depends on what you mean by "energy", and what you mean by "conserved".'

They go on to explain more. In particular there is a form of local energy conservation that is built into the very fabric of GR (I'm not sure if the FAQ mentions that this local conservation law is built into the theory), but that particular form of energy conservation does not lead to a global conservation law - it can also be thought of as energy conservation in an infinitesimal volume rather than in a finite volume.

 

[PAllen]

This is true.

The thing I don't like about it is that if I throw a baseball a cosmological distance, over time it gets closer and closer to a co-moving frame. Where did it;s energy go? The Doppler explanation only works for light.

Actually, Davis addresses exactly this point in her article:

"In the case of matter, the paradox is explained by
the fact that we are measuring velocity in differ-
ent frames of reference — that is, relative to the re-
ceding galaxies."

She also gives a quantum explanation, treating the matter ad de Broglie waves, for which Doppler shift applied to them exactly predicts the change in measured KE by successive comoving observers.

The hand-wavy explanation that I don't very much like is that in a non-comoving frame, a body feels a gravitational force from the rest of the universe pulling it into a co-moving frame. I do not like this, because it's the overall curvature that does this, not just what is generated by matter (dust if you like).

Maybe it's OK as a plausibility argument.

I think both if Davis arguments are better than this.

 

[Ibix]

The thing I don't like about it is that if I throw a baseball a cosmological distance, over time it gets closer and closer to a co-moving frame. Where did it;s energy go?

I think the Milne universe provides a helpful insight here. A baseball thrown by a Milne observer passes each subsequent Milne observer with lower and lower energy. From the global Minkowski perspective it's obvious what happened - the energy basically got dropped between the observers' local Minkowski frames.

I think that works (in the presence of some handwaving) in a general FLRW universe, too, doesn't it? If you and I are close enough that I can use my local inertial frame, I see you as having a small velocity. So my 100mph fastball reaches you slower than that (that's my story ) but the energy didn't really go anywhere.