Jan 13th 2018, 03:36 PM
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Join Date: Apr 2008 Location: On the dance floor, baby!
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I don't recall if I have responded to your other threads. Sorry. But I'm afraid I don't have time right now to go through your other posts (for now) but you have made a bit of a mistake here, not so much in the Math but in your understanding of what GR does in terms of how certain properties are conserved. Your comments on conservation of gravity are mirrored by the similar problem of conservation of matter and the conservation of energy. Neither energy nor momentum is conserved (even in SR.) However in SR the energy-momentum 4-vector is conserved. $\displaystyle p_{\alpha} p^{\alpha} = m^2$ ) In the same way we have that the "force" of gravity is not conserved either, but the energy-momentum tensor is conserved. It is in this sense that gravity is a conservative force.
We can also talk about it in reference to the metric and the gravitational potential. The gravitational potential and the metric components are intimately related. If gravity was not a conservative force then the "metric" derived as it normally written would not satisfy the conditions that a metric tensor must have.
-Dan
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Last edited by topsquark; Jan 13th 2018 at 05:29 PM.
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