How does curved space create gravity?

[paulicator]

We've all seen the "ball on a rubber sheet" analogy, showing how warped space near a planet can cause a light beam to alter its path. We are told that the light is actually following the shortest path in curved space.

When it comes to a *stationary* object near a planet, however, I have a harder time making sense of things.

If I assume a person (for example) is statically floating near a massive planet, *why* does curvature of space cause the person to experience a gravitational force?

 

[Al68]

We've all seen the "ball on a rubber sheet" analogy, showing how warped space near a planet can cause a light beam to alter its path. We are told that the light is actually following the shortest path in curved space.

When it comes to a *stationary* object near a planet, however, I have a harder time making sense of things.

If I assume a person (for example) is statically floating near a massive planet, *why* does curvature of space cause the person to experience a gravitational force?

You can't "statically float" near a massive planet. If no force is applied to you, you will be in freefall and not feel a force, but you will not remain "stationary" with the planet. If a force is applied to you to keep you "stationary" with the planet, you will of course feel that force.

 

[Fredrik]

*why* does curvature of space cause the person to experience a gravitational force?

The only thing that could possibly give you some sort of answer to that is a new theory of gravity that has an even better agreement with experiments than GR, and also describes things in different terms. There is no such theory today, and even if there was, it would give you a new question to ask.

 

[jtbell]

It's curvature of spacetime, not curvature of space. That makes a big difference!

To make an analogy, consider two airplanes flying north, starting from nearby points along the Earth's equator. Each plane continues to fly straight north by its own reckoning, along its own meridian of longitude. As they proceed further north, the meridians converge towards the North Pole, so the planes approach each other even though they started out flying in parallel straight lines.

Of course, in the example above, the airplanes have to move in order to make this work. But now suppose the two dimensions on the sphere are not both spatial dimensions, but instead the "north-south" direction represents time and the "east-west" direction represents a one-dimensional space, that is, the two planes both move back or forth along the same line. As time passes, the planes automatically proceed "northward" in time, and the spatial "east-west" distance steadily decreases.

 

[DaveC426913]

Of course, in the example above, the airplanes have to move in order to make this work. But now suppose the two dimensions on the sphere are not both spatial dimensions, but instead the "north-south" direction represents time and the "east-west" direction represents a one-dimensional space, that is, the two planes both move back or forth along the same line. As time passes, the planes automatically proceed "northward" in time, and the spatial "east-west" distance steadily decreases.

And note that there is no force required to bring the two planes together.

 

[A.T.]

If I assume a person (for example) is statically floating near a massive planet, *why* does curvature of space cause the person to experience a gravitational force?

As jtbell said: Curvature of space alone doesn't cause this, therefore the rubber-sheet analogy is not good explanation of gravity. Curvature of space-time causes the person to start moving in space towards the planet.

Here a strongly simplified explanation of curvature space vs. curvature of space-time effects:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[adnanrana]

I think by taking Einstein's view violation of geodesi creates the gravity and curved space time

 

[NathanJF]

I think I found a pretty good description here http://www.allsubjects.org/viewtopic.php?f=14&t=4&sid=5c02ae9e2b2a7d9cff07cb87c89a0263"