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1) Why are we talking about space curvature as if we know what space is?

Every question about gravity seems to evoke an answer involving "space curvature" which seems like an undefined placeholder concept no different than 'ether'.

2) Can we define what "space" is and how its elements (and which of its elements) curve before we use it to build other definitions?

3) Are we truly confident that gravity propagates at the speed of light?

4) and is that truly the limit of gravity itself or is it the limit of the methods of its observation (themselves involving light and devices based on electromagnetism)?

5) Or is it the introduction of the undefined concept of a precurved "space time" our indirect acknowledgement of instantaneous propagation?

The use of math can be a conceptual trap since the practice tends to provide accurate extensions cantilevering from original presumptions. Much like with Zeno's paradox, math does not negate the presumption, but merely confirms Achelies' distance to be asymptotic to a limit (the limit artificially set by our original presumption).

6) How confident are we really today that the speed of gravity is a done deal?

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    $\begingroup$ You ask too many rhetorical questions in one question. And I cant help it, but to me this "question" looks rather like a nonconstructive rant against SR and GR for example. $\endgroup$ – Dilaton Oct 6 '12 at 17:48
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    $\begingroup$ You might want to read up on the precession of Mercury's perihelion, the measurement of gravitational red-shift, observations of gravitational lensing and frame dragging. Posts that lead off with some versions of "I don't [know about|believe in] <some theory with lots of experimental evidence>" often encounter many downvotes. That seems to have been the case here. $\endgroup$ – dmckee --- ex-moderator kitten Oct 6 '12 at 21:38
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    $\begingroup$ There are too many questions here--edit it into one or two main questions, and I may reopen it. You may want to read the faq first... $\endgroup$ – Manishearth Dec 22 '12 at 21:01
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What separates physics theories from mathematical theories is that physics theories are developed in order to explain data and in order to predict phenomena that would validate those theories.

No physics theory can be considered proven in the way of QED of mathematical proofs. Theories are validated and are accepted to hold until they hit a disagreement with experimental data. Then they are falsified and overtaken by newer theories.

The trust in the curvature of space that general relativity formulates comes from the validations of the theory by the data. Up to this point no experimental data has disagreed with GR.

The velocity of light as a limit coming from special relativity is also an experimentally validated fact up to the present . Gravitational waves have not been yet experimentally observed so as to have their velocity measured. Nevertheless, as theories are being built up to include all observations at the moment it seems that the velocity of light will be the velocity by which gravitational waves will be moving.If experimental evidence proves the opposite then new approaches to gravitational theory will have to be attempted. At the moment the system is working slowly towards a theory of everything based on string theory.

In physics nothing is a done deal with theory until a lot of experimental validation occurs.

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  • $\begingroup$ This doesn't answer the question of why we are talking about this when we have no idea what space is!!! $\endgroup$ – StackOverflowOfficial Apr 27 '18 at 3:19
  • $\begingroup$ @Goldname we have an idea: we have a mathematical model, i.e. general relativity, it fits all data up to now and predicts future measurements, as with the GPS astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html . that is why we accept that it describes space with a curvature, and space does not follow a galilean one. $\endgroup$ – anna v Apr 27 '18 at 3:39
  • $\begingroup$ yes but how can you define space when its existence is a trivial solution to a proof on page 32 of my university physics textbook $\endgroup$ – StackOverflowOfficial Apr 27 '18 at 3:44
  • $\begingroup$ @Goldname as I do not have your text book I do not know what you are talking about. (x,y,z,t) have to be taken as axioms for any mathematical model, that they exist. their functional behavior is to be constrained by the model so as to conform with data, and be predictive. $\endgroup$ – anna v Apr 27 '18 at 3:55

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