Gravity and space curvature confusion

[ax53]

Hello there. I'm new to the forums obviously. And I'm also quite new to physics. I've read many existing answers about how this works but I can't really understand how it would logically work out.

From what I've understood. Gravity is not a force. Objects move in a straight line unaltered by other forces and space is curved around the gravity source which leads to the change in trajectory of light and objects. If I've understood this correctly, it doesn't make one bit of sense in my head.

Here is an image I put together to explain my confusion.

http://img407.imageshack.us/img407/4609/gravity.png

All this tells me is that the object is bigger than what it appears to be in the graph.

Also: Since objects move in a straight line. Shouldn't light have the exact same trajectory alteration around a gravity source as an object?

Thanks in advance!

Edit: Hmm, this should probably be under General Relativity.

 

[Drakkith]

The grid is just static lines that don't represent anything physical, they just show the amount of curvature of space. Imagine rolling a marble on the purple line on a trampoline towards a bowling ball. It would not act like the green line, as that would require to move AWAY from the center instead of staying on it's geodesic. http://en.wikipedia.org/wiki/Geodesic

 

[IsometricPion]

As Drakkith pointed out, the green line is not a geodesic. More to the point, the distorted grid you drew depicts curved space, while the two colored lines are trajectories through space over a certain amount of time. It turns out that the main source of deviation of the curvature of the trajectories is the curvature of time. In particular, if one assumes the coordinates do not have any intrinsic velocity with respect to the mass and that the follow geodesics (i.e., that they are straight lines in a curved spacetime) one finds that coordinates "fall" towards the object as time increases. The fact that the path of the light is a geodesic requires that it always make the same angle in spacetime with the coordinates, since the coordinates follow a curved path in time, light follows a curved path in spacetime. To get the points on the grid to always stay at the same distance from the object one would have to add in a position dependent acceleration to the equations that describe the coordinates. This position dependent acceleration is what causes the trajectory of the light beam to appear curved.

In summary, the image is misleading in two ways: 1, it is a projection of a 3D geometry in which the light beam is not actually in line with the grid line at the given initial instant, 2, the grid lines would have to be accelerated to produce the depicted projection.

 

[A.T.]

Imagine rolling a marble on the purple line on a trampoline towards a bowling ball. It would not act like the green line, as that would require to move AWAY from the center instead of staying on it's geodesic. http://en.wikipedia.org/wiki/Geodesic

What does does the path of a rolling marble has to do with a geodesic? If there was a hill (instead of the bowling ball dent) in the middle, would the marble be deflected towards or away from it? What about a geodesic?

 

[A.T.]

Here is an image I put together to explain my confusion.

As IsometricPion has noted, the key is the time dimension, not just the space dimensions you show. Here some links that might help to clear the confusion:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf

 

[ax53]

Thank you all for your help.

So an object can remain stationary in space and still approach the gravity source by moving forward in time. I've got a grasp of the concept but this type of graph still doesn't make sense to me.

http://img706.imageshack.us/img706/6175/spacetime.png
(this one was made in paint rather than photoshop as you probably see :p)

Anyways, consider that the object which is moving forward in time, is stationary in space by a gravity source. It moves forward in time but it will according to this graph never fall down to the gravity source. Am I looking at this graph the wrong way?

Edit:

I think I get it now :D The curvature of the surface of the graph makes the line move downwards and it makes the object fall over time without "moving".

 

[Drakkith]

What does does the path of a rolling marble has to do with a geodesic? If there was a hill (instead of the bowling ball dent) in the middle, would the marble be deflected towards or away from it? What about a geodesic?

You're missing the key point. The indentation in the trampline represents curvature of spacetime, not an actual hill. A marble rolling across an indentation in a trampoline caused by a bowling ball would have to roll uphill and away in order to travel the green line. Obviously this does not happen. It rolls inward towards the bowling ball because that direction is the way gravity is pulling it. Only once the marble is traveling in the right direction with enough speed will it roll out of the indentation. The whole thing is just a visualization to assist in understanding spacetime curvature.

Thank you all for your help.

So an object can remain stationary in space and still approach the gravity source by moving forward in time. I've got a grasp of the concept but this type of graph still doesn't make sense to me.

For an object to remain stationary in space it would have to apply a force to keep it away from the source of gravity.

 

[IsometricPion]

Anyways, consider that the object which is moving forward in time, is stationary in space by a gravity source. It moves forward in time but it will according to this graph never fall down to the gravity source. Am I looking at this graph the wrong way?

The lines of constant position are not geodesics. That is, they are not straight lines. If you want to know what the path of an initially stationary object (not being accelerated in any way) looks like use the interactive applet A.T. posted (the last link in post #5) and set the initial speed to zero. You will notice that unless the initial position is zero the path produced does not remain parallel to the lines of constant position.

It may help to think about a simpler object like a spherical surface (initially without any coordinates to confuse us). It is clear that if one begins walking in any particular direction one will return to the same point after going around the sphere exactly once, i.e. after walking a distance 2πR where R is the radius of curvature of the surface (in this case it is also the radius of the sphere). Now, think about a globe with lines of latitude and longitude, even though one might think that both sets of lines are straight, only one set (the lines of longitude) has the same properties as the straight line we just constructed above. The situation is similar for the coordinates in A.T.'s second link (and your most recent drawing), only one set of lines in the picture are geodesics (the lines of constant time). The other set of lines are constructed so that they will always make the same angle with the lines which are geodesics (i.e., the lines of constant position are parallel to one another and perpendicular to the lines of constant time, but are not straight lines which is possible because the surface is not flat (so Euclid's axioms (the foundation of high school geometry) are not satisfied and thus not all of his conclusions hold)).

 

[A.T.]

Thank you all for your help.

So an object can remain stationary in space and still approach the gravity source by moving forward in time. I've got a grasp of the concept but this type of graph still doesn't make sense to me.

http://img706.imageshack.us/img706/6175/spacetime.png
(this one was made in paint rather than photoshop as you probably see :p)

Anyways, consider that the object which is moving forward in time, is stationary in space by a gravity source. It moves forward in time but it will according to this graph never fall down to the gravity source

It will fall down, because moving straight ahead on the curved surface (geodesic path) will not make it stay at constant space coordinate. Here is one model to make this more intuitive (your initial situation being at rest in space, corresponds to the top af the arc where a thrown up object turns around, being also at rest in space) :

http://www.relativitet.se/spacetime1.html

Another one is sticking adhesive tape to the curved surface, without tearing or folding its edges.

 

[A.T.]

You're missing the key point. The indentation in the trampline represents curvature of spacetime,

Actually it represents only curvature of space which produces minor effects but cannot explain actual gravity that we know (mass attraction).

It rolls inward towards the bowling ball because that direction is the way gravity is pulling it.

So you explain gravity with gravity.

The whole thing is just a visualization to assist in understanding spacetime curvature.

It is a completely flawed, circular analogy which has nothing to do with th actual model, because it misses the key aspects: time dimension & geodesic paths.

 

[Drakkith]

Actually it represents only curvature of space which produces minor effects but cannot explain actual gravity that we know (mass attraction).

I was under the impression that it could.

So you explain gravity with gravity.

Only to explain why the marble wouldn't roll away from the bowling ball.

It is a completely flawed, circular analogy which has nothing to do with th actual model, because it misses the key aspects: time dimension & geodesic paths.

Believe what you want.