Basic questions about General Relativity

[calvinjhfeng]

I know little to nothing about G.R. but it is interesting to look up knowledge,especially physics, so please correct me if I am wrong..
It is easy to picture how one giant mass distorts spacetime on 2D scale, but what if there is multiple bodies of masses present and would this turn into a complete mess?

Also GR proposes that gravity is no longer a force, rather it is merely a distortion of space time. It is easy to see that any thing in motion will circulate around a massive body because of the curved geodesic path, but what about something that is at rest? Gravity still has to accelerate it, so according to Einstein, how does curved space manage to do that?

When does general relativity come in handy? The field equations are a set of ten nonlinear diff.equations, that is a huge pain in the *** to solve without computers. Einstein didNT have computers, so what was his original intention of coming up with GR*.? I heard it was something about Mercury's orbit.

Thanks

 

[Vorde]

what if there is multiple bodies of masses present and would this turn into a complete mess

It does, this is why you practically never find exact solutions in general relativity.

but what about something that is at rest? Gravity still has to accelerate it, so according to Einstein, how does curved space manage to do that

Because it's still moving through time.

When does general relativity come in handy? The field equations are a set of ten nonlinear diff.equations, that is a huge pain in the *** to solve without computers. Einstein didNT have computers, so what was his original intention of coming up with GR*.? I heard it was something about Mercury's orbit.

The anomaly in Mercury's orbit was one of the signs that a new theory of gravity was needed, but that wasn't the motivator. GR was Einstein's (incredibly successful) attempt to extend his Special Relativity to accelerated reference frames. The discovery that this was equivalent to extending SR to include gravity was a huge discovery, and it's now called the equivalence principle.

 

[arindamsinha]

In my readings of Einstein's papers and books, I remember coming across something like the below (though I can't remember the reference now):

'The geometry of space used in GR does not mean that space (empty vacuum) has properties and attributes of its own. Rather it is a convenient and simple mathematical representation of the interaction of matter and gravity in the Universe.'

These are not the exact words, I am just trying to put down the sentiment I recollect understanding.

There could just as easily be theories of gravitation where gravity is a real force, and provide the same conclusions, mathematically or otherwise, as GR. Einstein considered the GR framework to be the simplest such framework as a theory of gravitation.

 

[tom.stoer]

There is a mathematical framework of Weitzenboeck geometry with vanishing curvature but non-vanishing torsion which is strictly equivalent to general relativity which formulated in terms of Riemannian geometry with non-vanishing curvature but vanishing torsion.

Have a look at Teleparallelism

In these teleparallelism theories gravity acts somehow as a force.

 

[Naty1]

It is easy to see that any thing in motion will circulate around a massive body because of the curved geodesic path, but what about something that is at rest? Gravity still has to accelerate it, so according to Einstein, how does curved space manage to do that?

I like the answer provided, already:

Because it's still moving through time.

Although not precisely correct, you can also say in a general way space is practically flat so most curvature is actually that of time! We don't generally see much curvature of space in our universe, except maybe near black hole singularities. [The actual curvature or flatness of space (as opposed to spacetime) is a coordinate dependent idea...dependent on the observer.]

but I am guessing your 'easy to see' perspective in one case and not the other is because you have perhaps not carefully thought about the two cases...how are they different?

Classically, F = ma or F = GmM/r² does not rely on motion [speed] and 'at rest' should be carefully thought through. Think of a ball rolling down a hill as form of 'curvature'...except for friction, it's acceleration from rest is the same as from velocity v. Another good way to think about this was posted in these forums: Any situation where you ask about a rapidly moving massive body's gravitational effect and a 'stationary' observer can be transformed to an equivalent question about the interaction between a rapidly moving observer and a 'stationary' massive body. So all observations relating to a rapidly moving massive body can be answered as if the body is stationary.

Note: Relativity ideas take some thought and getting used to...some different ways of thinking from our everyday observations. The math tells us things we cannot directly see.