What causes the apparent falling of objects in general relativity?

[daniel_i_l]

Everything that I've read about GR says that gravity is caused because mass wants to "slide" down the warping of ST like a marble falling to the center of a warped trampoline. But the marble falls because of gravity! We are trying to find out what gravity is! Some articles explain that moving masses (and light) always follow the shortest path and that makes them look as if they are falling. But if you drop a ball, then it was never moving (through space) in the first place! So why should it all of a sudden start moveing through the curves of ST? I've been wondering about this for a long time, could someone please help?

 

[Jimmy Snyder]

But if you drop a ball, then it was never moving (through space) in the first place! So why should it all of a sudden start moveing through the curves of ST?

No object is stationary in spacetime. An object which is stationary in the 3 spatial dimensions is still moving in the 4th temporal dimension. It travels at the unimaginative speed of 1 second per second. The geodesics are not spatial geodesics, but rather 4 dimensional ones.

 

[daniel_i_l]

Thanks, but why should geodesics in time have effect on motion through space?

 

[Jimmy Snyder]

Thanks, but why should geodesics in time have effect on motion through space?

They are not geodesics in 1-dimensional time and they are not geodesics in 3-dimensional space. They are geodesics in 4-dimensional spacetime.

Remember that time by itself and space by itself only have meaning in a particular coordinate system. Without a coordinate system, you only have spacetime. By imposing a coordinate system, you can speak of a three dimensional spatial trajectory for the object. In other words, for each moment in time, there is a spatial position for the object given by the spatial coordinates of the point on the geodesic corresponding to that time. This spatial trajectory will not be a geodesic in any sense, and will not even be meaningful in any other coordinate system.

Another thing to remember is that spacetime is not Euclidean. The geodesics are not paths of least Euclidean distance, but rather paths of least interval separation. The difference between these two is in the line elements. For Euclidean space plus time (as far as I know, no one has found a use for this distance) it would be:

$$ds^2 = dt^2 + dx^2 + dy^2 + dz^2$$

but for Minkowski spacetime it is:

$$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$

That minus sign has profound influence. Spacetime in the presence of gravity is not Minkowski, but for the weak fields found in the solar system, the minus sign on the t term dominates offsetting effects. In the general case, the line elements are more complicated and thus even further away from being Euclidean.

 

[DaveC426913]

...mass wants to "slide" down the warping of ST like a marble falling to the center of a warped trampoline...

Don't take the analogy too literally. It is not gravity that is pulling the marble "down" the warp.

"...But the marble falls because of gravity! We are trying to find out what gravity is!..."

1] Saying that "the marble falls because of gravity" does not explain how gravity acts upon the marble.


Sorry, I'm stuck there. I can't build up a more elucidating picture...

 

[derz]

Thanks, but why should geodesics in time have effect on motion through space?

jimmysnyder already explained it, but I always seem to get people to understand curved spacetime better with this simple semantic presentation:

Imagine that you take a ball at your hand and throw it at an angle of 45°. What happens if spacetime is Euclidic (ie. non curved)? The ball moves away from you at a constant speed along a straight line.

What happens if spacetime is curved? The ball will still move along a straight line, but in a curved spacetime. For you, the ball seems to move along a curved path in Euclidic 3D space because of gravity, but actually it moves along the straightest path in a curved 4D space. Big difference in way of thinking.

Same thing if you just drop the ball from your hand. If spacetime would be Euclidic, the ball would just float in the position where you laid your hand off it. But because spacetime is curved, the ball seems to be pulled towards Earth by gravity.

Sorry if my english is poor, I am not a native speaker

Hope you understand my point tho

 

[Caesar_Rahil]

No.
I have not undertood it.

 

[eon_rider]

Imagine that you take a ball at your hand and throw it at an angle of 45°. What happens if spacetime is Euclidic (ie. non curved)? The ball moves away from you at a constant speed along a straight line.

What happens if spacetime is curved? The ball will still move along a straight line, but in a curved spacetime. For you, the ball seems to move along a curved path in Euclidic 3D space because of gravity, but actually it moves along the straightest path in a curved 4D space. Big difference in way of thinking.

That's a good example.

I'm not sure if this one works but I'll throw it out there. Imagine you're in a plane traveling across the planet. From the plane's point of view you seem to be traveling in a straight line. Straight ahead.

But you are actually curving around the planet and traveling in a circle. You can't tell but you're traveling straight through a curvature.

best

Eon.

 

[pervect]

What you need is the idea that it is _space-time_ that is curved, not space. The keyword "geodesic deviation" may also help.

Try for instance

https://www.physicsforums.com/showpost.php?p=592202&postcount=10

it's short, I'll quote it

Hmmm! Thanks to everybody's patience. Now it is more clear.

I guess the kind of drawings that show a weighty ball deforming a plane, elastic surface down, are terribly misleading in the end. They send the mental image that it is SPACE that curves. Perhaps a more accurate (though simple) example is to imagine two objects on the Earth's equator, and forced to move steadily North (latitude representing time). In this example, space is only 1-dimensional (longitude), and while nobody is pushing the objects IN SPACE (along longitude), they do join at the north pole.

you can also look at

https://www.physicsforums.com/showpost.php?p=607454&postcount=12

https://www.physicsforums.com/showpost.php?p=574193&postcount=5

and their attached threads for some of my previous responses to this frequently asked question.

 

[pmb_phy]

Everything that I've read about GR says that gravity is caused because mass wants to "slide" down the warping of ST like a marble falling to the center of a warped trampoline.

Then you're not reading the right books. The most obvious book for you to read right now is Relativity; The Special and the General Theory, Albert Einstein. If you read this book then you'll know the basic ideas behind general relativity and you won't get lost/distracted with the "warped trampoline" buisness. Most people love to focus of curved spacetime when they speak of GR. I suppose its because the notion of a curved spacetime is an exotic idea. But Einstein was not the one who started this exclusive focusing on curved spacetime when speaking of GR (that was due to others, such as Max Von Laue).

But the marble falls because of gravity! We are trying to find out what gravity is! Some articles explain that moving masses (and light) always follow the shortest path and that makes them look as if they are falling.

If a marble is moving soley under the influence of gravity then it is following a geodesic in spacetime. This means that it is following the straightest possible path in spacetime (even if the spacetime is curved). It does not mean that if follows the straightest possible path in space nor does it follow the shortest geodesic in spacetime.

If a body is moving under the influence of gravity then this does not mean that the spacetime is curved as you may have otherwise concluded. Reading Einstein's book on this subject will clarify these notions for you and get you to understand what it was that Einstein said regarding GR. You can then choose to go read what others said about it. Then you can see how they are not identically the same.

Pete

 

[pervect]

While daniel may have minor bragging rights if he reads Einstein's book on general relativity, he may have better luck with popularizations like "General relativity from A to B" or other semi-popular works, depending on his background.

There's a good list of semi-popular relativity books at

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html#semipopular

 

[pmb_phy]

While daniel may have minor bragging rights if he reads Einstein's book on general relativity, he may have better luck with popularizations like "General relativity from A to B" or other semi-popular works, depending on his background.

I don't understand what you're trying to say here pervect? Please clrify - Are you saying that its better to read only material such as whart you're referring to? If so then the poster already indicated that this was what he was doing.

There is more to posting in physics regarding "Bragging rights". We post to understand sometimes, such as this. I'd love to read that book someday myself.

Pete

 

[pervect]

I don't understand what you're trying to say here pervect? Please clrify - Are you saying that its better to read only material such as whart you're referring to? If so then the poster already indicated that this was what he was doing.
There is more to posting in physics regarding "Bragging rights". We post to understand sometimes, such as this. I'd love to read that book someday myself.
Pete

I'm trying to fit the best book recommendation to a person who's background I don't know much about. Judging from the quesitons being asked, though, I get the impression that a popular treatment is being sought rather than a detailed mathematical exposition - that's my best guess, anyway.

The sci.physics "relativity booklist" link I mentioned has a list of many book recommendations about special and general relativity, with a little bit of discussion as to what "level" the various books are at. It even includes Einstien's book, IIRC.

Einstein's book is obviously of great historical interest. That does not necessarily make it the simplest, clearest, easiest introduction to the topic available nowadays, however.

 

[daniel_i_l]

Thanks everyone!
I have a similar question but I didn't want to open a new thread:
The ball "falls" to the Earth because it is really following the shortest path through ST. This shortest path that makes the ball move to the Earth through space is caused by curves in ST by the massive Earth (the Earth forms the warps in ST).
But doesn't the Earth also move through ST at almost the same speed as the ball? Wouldn't that mean that the curves themselves are changing all the time? - Even before the ball starts to move? If the time difference matters then I'll ask about two balls of equal mass that are attracting each other.
For example, in the longitude metaphor, the two ball would be attracted through space and touch at the northpole because as the move "upwards" through time, the space between them gets smaller. But since the warps themselves also change through time then shouldn't the balls always stay at the equator? Thanks!