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.

  • $\begingroup$ If I throw a stone at you, you will probably agree that massive objects have trajectories which are not 'only in time'. $\endgroup$ – tfb Mar 10 '17 at 17:44
  • $\begingroup$ Surely irrelevant as the question is about stationary objects. How did you read the question so quickly? $\endgroup$ – JMLCarter Mar 10 '17 at 17:47
  • $\begingroup$ If I put a rock on your head you will probably agree that massive stationary objects experience gravity? $\endgroup$ – JMLCarter Mar 10 '17 at 17:59
  • $\begingroup$ 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? $\endgroup$ – user146020 Mar 10 '17 at 18:06
  • $\begingroup$ 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? $\endgroup$ – JMLCarter Mar 10 '17 at 18:12

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

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  • $\begingroup$ 1) 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. $\endgroup$ – JMLCarter Mar 10 '17 at 18:15
  • $\begingroup$ 2) You are suggesting that microscopic perturbations in a nearly stationary object are responsible by sme mechanism for the effects of gravity on it $\endgroup$ – JMLCarter Mar 10 '17 at 18:17
  • $\begingroup$ This is a useful comment but it is not an answer $\endgroup$ – John Rennie Mar 10 '17 at 18:25
  • $\begingroup$ 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. $\endgroup$ – JMLCarter Mar 10 '17 at 18:27

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