What happens to the energy lost by photons in gravity?

[PeterDonis]

The Lagrangian observer sees the photon maintain the same wavelength when it is reflected between two mirrors as the mirrors drop down toward a source of gravity. This is because the Lagrangian observer tracks the photon along the length of its path.

I'm not sure what you mean by "tracks the photon". The key thing is that the Lagrangian observer is falling with the mirrors.

the immobilized Eulerian observer measures just a short segment of the photon's path on one level and again at a lower level

This is because the Eulerian observer is not falling with the mirrors.

Without the GR conservation of energy requirement included, the photon has gained energy according to QM.

The "GR conservation of energy requirement" is included. The photon has gained kinetic energy according to the Eulerian observer, but it has also lost height and therefore has lost potential energy. The two cancel out; total energy is conserved.

In the expansion of the cosmos, the loss of energy during the photon's red-shift is transferred to mass

No, it isn't. I have no idea where you are getting this from.

Conservation laws use higher order derivatives than Noether's first order derivatives in her Lagrangian equations.

I have no idea where you are getting this from either.

GR is incomplete with respect to the full explanation of energy conservation laws

What do you mean by this?

 

[Hugh de Launay]

This post is a series of responses to Peter Donis's observations in post #36.

I became aware of my misstatement of "tracks the photon" last night and planed to edit a correction into post #35 (which has been accomplished). Peter Donis caught the error also.

Yes, the Eulerian observer does not travel alongside the two mirrors.

I agree that the kinetic energy and the potential energy combined assure the validity of the law of conservation of energy. I excluded this law to emphasize the gain in energy by the photon between the mirrors. This was a restatement in my own words of what I read in post #7.

The red-shift loss of energy must have gone into the energy that expands the cosmos. I must have misstated what I read in post #7.

With respect to the higher order derivatives comments, I was trying to restate in my own words what was stated in post #7. I may not have been successful in doing this.

Again, I was trying to restate in my own words what was stated in post #7.

Thanks for your input Peter Donis.

 

[PeterDonis]

The red-shift loss of energy must have gone into the energy that expands the cosmos.

This is not correct. There is no "energy that expands the cosmos" (apart from dark energy, but the density of dark energy is constant so it doesn't exchange with anything else and can be left out of consideration here). Total energy is not conserved in an expanding universe. You need to go back and read the Sean Carroll article I linked to in post #12.

I must have misstated what I read in post #7.

You did. Post #7 is not saying that what you said is true. It is saying that what you said "sounds rational" but can't be true because such a model doesn't explain what we actually observe.

With respect to the higher order derivatives comments, I was trying to restate in my own words what was stated in post #7. I may not have been successful in doing this.

You're right, you were unsuccessful. I would ignore that part of post #7; it's talking about speculative hypotheses, not about our best current mainstream models.

 

[Hugh de Launay]

read the Sean Carroll article I linked to in post #12.

Thanks for your input. I will read that article.