What Causes Earth's Motion in General Relativity?

[ShayanJ]

As I understood,GR says that mass and energy change the form of space-time and when other masses move near that place,they have to follow the new form of space-time.that's what we call gravity.But there is a point here I don't understand.
Imagine our solar system.sun bends space-time and Earth has to follow the new form of space-time.so its uniform motion is seen as a circular one.But what makes the Earth to move in the first place?because we have neglected to accept gravity as a foce in GR.
thanks

 

[Polyrhythmic]

Do you want to know why planets moved before they were caught in an orbit? Why was gravity neglected as a force?

 

[ShayanJ]

Let me clarify my question more:
We say gravity is not a force and explain it like:when a mass like Earth moves,follows the form of space-time which is curved in presence of another mass,so we see its motion like e.g. a circle but in fact its linear and uniform.
At Newtonian gravity,gravity itself was the cause of the start of motion and also its form but GR says gravity is just the thing which tells masses how to move.The motion should be started by other means.I want to know that 'other means'.

 

[A.T.]

.But what makes the Earth to move in the first place?

In GR everything advances trough space-time by default. Objects at rest in space, advance trough along the time dimension only. Free falling objects advance on geodesic paths trough space time.

See this link:
http://www.relativitet.se/spacetime1.html

 

[ShayanJ]

this does not answer my question.because we can say someone starts the motion for the apple and the apple just moves in space-time and follows its form.
imagine a nebula(the kind that stars are born in it).At first there is some gas.it starts to rotate because of gravity and the star is formed.But gravity ,as explained in GR,can't start motion,it just can lead it.

 

[ShayanJ]

At last I understand the answer.So I explain it for others.
look at the attached picture.the black line is parallel with the red time axis.its the space-time path of an object which is at rest in the frame of someone inside the gravitational field.if you take the blue axis as the main ones(look at the object from outside of the gravitational field)you see an accelerated motion path.
In fact in the gravitational field,the object moves only in time but outside of it,the space-time path contributes to motion in both time and space.

 

[A.T.]

But gravity ,as explained in GR,can't start motion,it just can lead it.

Here you are confusing "motion in space" and "advance in space-time". The advance in space-time, that is affected by space-time geometry is not "started" by anything. It is simply postulated for all existing objects by the model.

Check the first picture here:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
It shows how the geometry of space-time causes movement in space, of an object that was initially at rest in space (advancing only along the time dimension).

 

[ShayanJ]

I want you to check my last post and say whether its right or not.
If its right,it makes a prediction I that I want to ask about now.
Its like this:Just look at everything around you.they are rotating with the Earth's surface but because they are at rest with respect to you,you call them stationary.that's because you and the staff around you are at rest with respect to the Earth's gravitational field.But for someone outside it,according to my last post,a motion should be observed and that motion is the rotation of the earth.
I just want to ask are my last two posts correct?

 

[A.T.]

Just look at everything around you.they are rotating with the Earth's surface but because they are at rest with respect to you,you call them stationary.that's because you and the staff around you are at rest with respect to the Earth's gravitational field.But for someone outside it,according to my last post,a motion should be observed and that motion is the rotation of the earth.
I just want to ask are my last two posts correct?

I don't quite understand what you mean, but you seem to be on the wrong track with the rotation of the Earth. It is not relevant. The surface of a non-rotating planet is still considered accelerated in GR. Only free fallers are inertial.

Here is an interactive diagram of a free fall through a non-rotating planet:
http://www.adamtoons.de/physics/gravitation.swf
Note that when you set "intial speed" to zero, the object still starts moving trough space, just by advancing straight ahead in space time.