# Curvature in space time ? Gravity

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## Main Question or Discussion Point

Can someone explain how a curvature in space-time,can cause motion?
(Without telling the pillow example)
Thanks

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bcrowell
Staff Emeritus
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Nothing causes motion. This is true even in Newtonian mechanics. Aristotle thought that a force was necessary in order to cause motion, but he was wrong.

If you want to learn about relativity, a good book is Relativity Simply Explained, by Gardner.

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What you mean nothing causes motion?Please explain clearly
thanks

Dale
Mentor
This is Newton's first law, an object in motion remains in inertial motion unless acted on by an external force.

DaveC426913
Gold Member
Nothing causes motion.
If you place a ball, motionless, 100 miles above the surface of the Earth, it will most assuredly begin moving in a decidely downward direction.

The OP is interested in what it is about spacetime being curved that would instigate this movement.

Anything that is not experiencing a force travels 4-dimensionally on a geodesic. When the ball is being held it is not on a geodesic path. When it is released, and no longer feels the restraining force, it immediately begins geodesic motion.

pervect
Staff Emeritus
Anything that is not experiencing a force travels 4-dimensionally on a geodesic. When the ball is being held it is not on a geodesic path. When it is released, and no longer feels the restraining force, it immediately begins geodesic motion.
Exactly.

Gold Member
Ok.Based on equivalence principle,I put a*t instead of v in lorentz transformations to have them for gravitational fields.then I drew space-time diagram below.For the mass to be at rest relative to S' it should be in several places at the same time relative to S(as you can see)which is obviously incorrect.What's wrong with my reasoning?

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pervect
Staff Emeritus
I'm not quite sure what you're trying to do. I can say that you can't in general draw a space-time diagram when there is gravity on a flat sheet of paper, because space-time is curved. If you replace the sheet of paper with the curved surface shown in figure 7 of

http://arxiv.org/abs/gr-qc/9806123

then you can draw a space-time diagram on said surface, which represent the r-t plane of a massive body or of a black hole. To do so, you have to replace straight lines (on the paper) by geodesics (on the curved surface of figure 7).

You'll also note that Lorentz transforms, unmodified, only work in a limiting sense. If you take a small enough piece of the curved surface in figure 7. small enough that it's nearly flat, you'll find that the Lorentz transforms work properly on that small piece - and that geodesics look just like straight lines on that small piece. But the Loretnz transforms will only work on an area small enough where the curvature doesn't matter.

bcrowell
Staff Emeritus
Gold Member
If you place a ball, motionless, 100 miles above the surface of the Earth, it will most assuredly begin moving in a decidely downward direction.

The OP is interested in what it is about spacetime being curved that would instigate this movement.
It was already moving, because the earth was spinning and orbiting the sun. What happened was a change in its motion.

DaveC426913
Gold Member
It was already moving, because the earth was spinning and orbiting the sun. What happened was a change in its motion.
It was motionless with respect to the Earth. Not sure why that didn't go without saying.

The OP simply wishes to know how the curvature of spacetime caused by the Earth's mass causes the object to begin falling toward the Earth.

The OP simply wishes to know how the curvature of spacetime caused by the Earth's mass causes the object to begin falling toward the Earth.
I would like to know the answer too, Thank you.

Mass-energy curves space-time and it's this curvature that causes gravity. When an object moves in a geodesic along a curved surface it gets "bent" with sufficient distortion one will fall inwards. If you have a flexible sheet and put a bowling ball in the center, it will curve inwards, now place a less massive object on it and set it in motion, it will orbit the center of mass of the bowling ball. Obviously it will fall in eventually but that is due to loss of energy due to friction and air resistance.

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Hey kevin I said don't talk about the pillow example because it gives us nothing.
I think I understood it.So I explain it for others to understand.
If you draw a cartesian coordinate system in a gravitational field,the axes are bent.in order for a mass to be at rest relative to such a coordinate system(according to the first newton's law)it should have a world line prependicular to the X axes and parallel to T axes.But both of them are bent.So if you place such a world line in a coordinate system out of a gravitational field(which has straight axes)you see an accelerating motion.This is Gravity.
But another question arises.We say that a free falling object is at rest relative to the bent coordinate system.But whose coordinate system is that?I mean is such a coordinate system connected to earth?or sun?or what?Better to say relative to which object,a free falling mass is at rest?