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Things I know already

1) Rubber sheet analogy of GR is yet another misleading piece of info
2) differential geometry makes sense
3) equivalence principle makes sense
4) special relativity makes sense

I am trying to develop a better understanding of curvature in space-time.

Current Dilema

Trying to refine understanding of the effect of curved space-time on a stationary object. We all know that stationary objects do fall. Curvature, I reasoned, can surely only be experienced, (and therefore only cause an effect, such as an apparent acceleration), if an object has a trajectory; if it is moving relative to the curve. Massive stationary objects have a trajectory only in time, so the answer must be that curvature of time alone can be responsible for the effects we call gravity.

Question I Think I Need to Ask

This is a theoretical scenario. A point mass is;
a) stationary in
b) a spatially flat volume, which
c) is curved in time in a simple way
(a geometry that is purely theoretical, but allows the question to focus on the effects of time)
d) by what mechanism does this mass experience a change in velocity?

I know I haven't used many mainstream GR terms, but I hope the question makes sense.

Other Aspects

Curved space is not a massive conceptual challenge, but curvature in space-time is more difficult. There seem to be less familiar concepts to relate distortions of the temporal dimension to.

The answer I am not looking for is that GR can only be "understood" by directly using the maths. In this case I would initially think that would really just mean you don't know (It's not like the philosophy struggle people go through with, for example, the meaning of wave-functions). However, I'd be happy to be pointed to a mathematical treatment of this kind of scenario that I can scrutinise; (that will be easier for me if lower level constructs are used).

Thanks in advance for your help.

JMLCarter
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  • If I throw a stone at you, you will probably agree that massive objects have trajectories which are not 'only in time'. –  Mar 10 '17 at 17:44
  • Surely irrelevant as the question is about stationary objects. How did you read the question so quickly? – JMLCarter Mar 10 '17 at 17:47
  • If I put a rock on your head you will probably agree that massive stationary objects experience gravity? – JMLCarter Mar 10 '17 at 17:59
  • Throwing mud, fair enough, but exchanging rocks...........OK, somewhere I am missing your point, my apologies but practically speaking, how can you have a spatially stationary object? –  Mar 10 '17 at 18:06
  • It's a theory question/thought experiment, neglecting various practical aspects for simplicity. A theoretical point mass, stationary in a gravitational field. Do you mean to suggest it wouldn't experience effects of gravity? – JMLCarter Mar 10 '17 at 18:12
  • So that tells me that a temporal-only four vector "velocity " is indeed translated by space-time curvature to a radial-only acceleration. I can see I had a mental block considering space curvature and time curvature as, "non-interacting" for some reason. You have given me more to think about now - thanks. – JMLCarter Mar 10 '17 at 18:59
  • Can be marked as duplicate. I didn't find it on search, but I did do one. – JMLCarter Mar 10 '17 at 22:31
  • Can I just link this one in as well, I think it could be relevant. http://physics.stackexchange.com/questions/106447/can-we-think-of-gravity-as-space-itself-moving

    The idea that gravity can make space move was an option I'm still thinking about to facilitate understanding that elapsed time can equate to a distance. (might be trivial) This would be way more intuitive than trying to understand what it means to curve time in space-time.

     – JMLCarter Mar 10 '17 at 23:43
  • @JMLCarter So now: define ’stationary' and you're done (hint: you can't, and that was my point). –  Mar 11 '17 at 01:33
  • I've been saying stationary object, but it is a theoretical question; the results of which hold whether there is some additional movement or not. It's pretty obvious that when I release an object in nearby space, for the purposes of this discussion on the effects of gravity, it is initially stationary with respect to the gravitational mass of the earth; In fact when I release an apple near the surface of the earth I could consider it was stationary in the rotating frame of reference. Not a problem because the dominant effect is gravity from the nearby body. – JMLCarter Mar 11 '17 at 01:49
  • in fact your comment is the same as RaSullivan's answer below. – JMLCarter Mar 11 '17 at 01:50

1 Answers1

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If you could find a stationary object you would have found the center of everything. There are no stationary objects, so basic premise fails.

RaSullivan
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  • It only needs to be stationary relative to the gravitational field, and the mass causing it. A valid initial condition. I'll edit that in.
    • – JMLCarter Mar 10 '17 at 18:15
  • You are suggesting that microscopic perturbations in a nearly stationary object are responsible by sme mechanism for the effects of gravity on it
    • – JMLCarter Mar 10 '17 at 18:17
  • This is a useful comment but it is not an answer – John Rennie Mar 10 '17 at 18:25
  • Actually can I just keep the question theoretical. I'm think trying to bring in real gravity rather than a temporal curvature complicates it unnecessarily. – JMLCarter Mar 10 '17 at 18:27