Understanding Gravity: The Curvature of Space-Time and Kinetic Energy

[gonzo]

I have some question that might be hard for me to phrase clearly, but I'm going to give it a try.

So, as far as I understand it, according to GR gravity is a side effect of the way mass (or mass energy, or whatever) curves space-time. So that when an object "falls" to the Earth, it isn't really being attracted to the Earth, but is just moving in a "straight line", which the Earth is also doing, and these lines (geodesics, right?) meet back up in such a way that it looks like the object is being attracted to the Earth.

Am I understanding this, more or less, so far?

It seems to me that if this understanding is correct, then it must mean that everything is moving really fast through space-time initially, right? I mean, it wouldn't matter if space was curved in such a funky way by itself, unless everything was moving with some serious speed to start with. If this is true, does this mean that everything has kinetic energy from this base movement?

A related question, is this base movement just universal expansion? Is that possible? Though if that's true, what would that mean if the universe started to slow down? And I seem to remember that gravity itself effects expansion, so that can't really be right, can it?

And a final question, if the attraction of gravity is just from bending of space time and geodesic movement, why does it cause acceleration? Or is that not something can be "visualized" in a meaningful way and just comes out of the math?

Thanks for any and all help.

 

[Chronos]

GR plays off the Einstein equations. The solutions are mathematically sound. You can't talk about speed without relating it to some other object. The mathematically valid solution without any matter in the universe is called Minkowski space. The solution that includes matter is called the FRW model. Space-time curvature is not a 'side effect', it is the geometry of a background independent universe constrained by a finite speed of light.

 

[Garth]

I have some question that might be hard for me to phrase clearly, but I'm going to give it a try.

So, as far as I understand it, according to GR gravity is a side effect of the way mass (or mass energy, or whatever) curves space-time. So that when an object "falls" to the Earth, it isn't really being attracted to the Earth, but is just moving in a "straight line", which the Earth is also doing, and these lines (geodesics, right?) meet back up in such a way that it looks like the object is being attracted to the Earth.

Am I understanding this, more or less, so far?

Yes!

It seems to me that if this understanding is correct, then it must mean that everything is moving really fast through space-time initially, right? I mean, it wouldn't matter if space was curved in such a funky way by itself, unless everything was moving with some serious speed to start with. If this is true, does this mean that everything has kinetic energy from this base movement?

Yes right again - When we use four dimensions and define four-velocity through space-time by U^a = dx^a/dtau then all objects have a total four-velocity equal to c. In our own frame of reference we are stationary wrt movement through space but we are all moving through time at one second per second! As across space-time a second in time is equivalent to 186,000 miles in space, we are all moving through space-time at 186,000 miles/sec the speed of light! If stationary in space this movement is entirely in the direction of the time axis, and so your "kinetic energy from this base movement" actually can be considered our 'rest' mass, the total energy we have when 'moving' through time alone.

A related question, is this base movement just universal expansion? Is that possible? Though if that's true, what would that mean if the universe started to slow down? And I seem to remember that gravity itself effects expansion, so that can't really be right, can it?

No and a qualified yes! This movement for any observer in their own frame of reference is just the passing of their time. However, if you interested in Self Creation Cosmology, (page 27) I am tempted to add that in the Einstein frame of that theory the cosmological model is that of a space-like hyper-sphere with time as its radial coordinate. In this model the passing of time and the expansion of the universe are two separate ways of experiencing the same phenomenon, and your answer would be correct, except that as it is a strictly linearly expanding, or freely coasting model, the expansion does not slow down.

And a final question, if the attraction of gravity is just from bending of space-time and geodesic movement, why does it cause acceleration? Or is that not something can be "visualized" in a meaningful way and just comes out of the math?

As Chronos has said the solution of the GR equations of motion results in Newtonian (almost) acceleration.

I hope this has helped.

Garth

 

[gonzo]

Thanks Garth, that was tremendously helpful and clear. I think I have a much better grasp on what was confusing me now. Thanks.