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Nov 14, 2018 at 21:41 comment added Andrew Steane "The apple would be weightless far from any masses where spacetime was flat." I guess this needs some qualification in view of the constantly accelerating frame in flat spacetime: apples have weight in such a frame.
Nov 14, 2018 at 15:08 vote accept R. Romero
Nov 14, 2018 at 15:08 comment added R. Romero I think that answers my question! $A^\alpha$ is 0 traveling along a geodesic. So the proper acceleration is 0. So that's the since in which it's not accelerating when its moving. It experiences a proper acceleration when it is held up by the tree, but isn't moving, at least not relative to the branch. Further, this analysis can take place with a minimum of external reference. I didn't know how to ask the question, but I think this is exactly what i was looking for. Thanks!
Nov 14, 2018 at 12:17 history edited John Rennie CC BY-SA 4.0
Tweak
Nov 14, 2018 at 12:12 history answered John Rennie CC BY-SA 4.0