(adsbygoogle = window.adsbygoogle || []).push({}); "non-stationary" means in an expanding universe ? PeterDonis said: ↑For purposes of the remark you quoted, there are two: stationary (gravitational potential energy is well-defined) and non-stationary (it isn't well-defined).

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

I didn't get this part. For the system in my example of two massive particles, can we not say that the density of gravitational energy decreases as the particles move away from each other ? maybe I didn't get what "density" of gravitational energy means. First, unlike with ordinary matter fields, there is no such thing as thedensityof gravitational energy. The thing you would like to define as the energy associated with the curvature of spacetime is not uniquely defined at every point in space. Sothe best you can rigorously do is define the energy of the whole universe all at once, rather than talking about the energy of each separate piece.(You can sometimes talk approximately about the energy of different pieces, by imagining that they are isolated from the rest of the universe.) Even if you can define such a quantity, it’s much less useful than the notion of energy we have for matter fields.

I didn't get what "matter field" actually means, is it like saying (with respect to my example) kinetic energy is positive and gravitational potential energy is negative so they cancel each other out and so energy is conserved ? The second reason is that the entire point of this exercise is to explain what’s going on in GR to people who aren’t familiar with the mathematical details of the theory. All of the experts agree on what’s happening; this is an issue of translation, not of physics. And in my experience, saying “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” does not actually increase anyone’s understanding — it just quiets them down. Whereas if you say “in general relativity spacetime can give energy to matter, or absorb it from matter, so that the total energy simply isn’t conserved,” they might be surprised but I think most people do actually gain some understanding thereby.

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# I On gravity and the conservation of energy

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