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As I follow up, I thought I'd mentioned that energy conservation in gravitational theories beyond Newton are a bit touchy. Here's an explanation from the physicist Sean Carrol: http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/
In everyday life, the deviations from Newton's gravitational theory are small, and even smaller are the deviations from static GR solutions. But I thought it would be an interesting follow up anyway, to clarify if one was curious how energy was conserved in red shift due to expansion of the universe, or when considering "dark energy" regarding accelerating universal expansion, etc.
Another way to state it which may be easier to visualize: if space-time is changing, there is no good way to define how much energy is contained in a volume in space. Here's some discussion on that by John Baez:
For this reason, it is even difficult to just define mass contained in a spatial region in GR,
Food for thought.
- Kevin M (age 30)
Urbana, IL, USA
Kevin- I marked your entry as stand-alone. since it's not really a follow-up to the previous thread. On starting to read it, I thought that I'd have something to add (the link to Baez), but it turns out you got that too.
(published on 02/18/2011)
Follow-up on this answer.