- #36

PeterDonis

Mentor

- 46,731

- 23,257

The motivation was simple: once you have the idea of spacetime, it is obvious that the spacetime of Special Relativity is flat. That means that two objects that are always in free fall, if they are at rest relative to each other at any given instant, will remain at rest relative to each other forever.Shirish said:I'm trying to understand the motivation of modeling gravitation using spacetime curvature.

But in the presence of gravity--"real" gravity, produced by a real object like a planet or star, not the "fake" gravity produced by being at rest in an accelerating rocket--the above is no longer the case. Objects that are always in free fall, and are at rest relative to each other at some instant, in general will not

*stay*at rest relative to each other. In Newtonian terms, this is called

*tidal*gravity. And in GR terms, it is called spacetime curvature, because geometrically, freely falling objects move on geodesics, and if they are at rest relative to each other at some instant but don't stay at rest relative to each other, that is geodesic deviation, which is already known to be equivalent to curvature of the manifold.

Notice, btw, that in the above I didn't mention any of your 6 points at all. IMO all of the things you are looking at in those 6 points are distractions. You can't really understand this issue by looking at coordinates. You have to understand the

*physical*and

*geometric*reasons why GR models tidal gravity as spacetime curvature.