Cosmological redshift: Where does the energy go?

[ellipsis]

A few small questions:

Observationally, why do we conclude that the metric of space is increasing, rather than that light increases in wavelength as it travels cosmological distances? Or are these two conclusions isomorphic?

Since wavelength is negatively correlated with energy, where does the energy go, when its wavelength increases?

EDIT: Don't tell me... the energy isn't being converted to space, is it? What would that even mean?

 

[PeterDonis]

Or are these two conclusions isomorphic?

Yes.

Since wavelength is negatively correlated with energy, where does the energy go, when its wavelength decreases?

Nowhere. Global energy conservation does not hold in a non-stationary spacetime. Locally, "energy" is frame-dependent anyway; the conserved quantity is 4-momentum, or more generally the stress-energy tensor. But that's only local, and the cosmological redshift is a global phenomenon.

See this article by Sean Carroll for more discussion of this point:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

(Note that, towards the end, Carroll does consider an alternate way of interpreting what is going on: that the energy lost by the photons as the universe expands goes into spacetime, or "gravitational energy". But, as he notes, that interpretation raises as many questions as it answers. I agree with him that it is better just to say straight out that global energy conservation doesn't hold in GR in a non-stationary spacetime.)

the energy isn't being converted to space, is it?

No. As you surmise, that is meaningless.

 

[Chronos]

There is no point in talking about conservation of energy in GR when the concept is not even well defined. Like asking if a blue flower smells better than a Bluetooth.