This may come as a big surprise to some folks, but it is acknowledged that energy is not necessarily conserved in large-scale GR. I once thought of a paradox about that: Have either an infinite or closed hyperspherical, now-expanding universe. Let's say it is filled with a bunch of devices (acting like "galaxies" in cosmology) in a closed Cartesian array (i.e
. like integers in x, y, x.) Have them connected together (as "given") with elastic bands. Since the elastic forces on each object cancel out, the spatial standards of the universe and these objects can retreat from each other without being "held back." It's as if no bands, just gravity, right? But as this universe expands for awhile, the bands can accumulate whatever amount of elastic energy they can hold from W = (1/2)ks^2 (for some duration.) Note that if we want to avoid complications from elastic stress terms, we can imagine connecting cords used to turn generator rotors around as the cords unwind, etc.
(Similar recently posted in comments at "Gravity is Entropy is Gravity is..."
Sorry to Bee, I should have linked to here instead of spilling it there.)
This makes a problem of sorts about energy conservation. It may already be accepted that such things are possible, given the acknowledged issues with CoE in GR, but wouldn't you be surprised if this could work? It seems so much like that crank stuff that just is supposed to be possible.
Labels: general relativity, paradoxes