Properties of Mass in Curved Space-Time

[danielatha4]

From what I understand of GR, time dilates due to the gravity of massive bodies. I like to think of it as the three coordinates of space drag, or lag, through time at a slower rate resulting in distortion of space-time. Correct me if my logic is flawed.

But my question is this; why do bodies of mass fall towards areas of greater time dilation? or I guess in a 2 dimensional model of space it falls to the "lowest" point, the dip caused by the massive body? Does mass long to travel through time at slower rates?

 

[A.T.]

From what I understand of GR, time dilates due to the gravity of massive bodies. I like to think of it as the three coordinates of space drag, or lag, through time at a slower rate resulting in distortion of space-time. Correct me if my logic is flawed.

Intrinsic curvature means a distortion of distances, but you can alternatively visualize it as variable density of a medium, that slows down the advance trough it.

But my question is this; why do bodies of mass fall towards areas of greater time dilation?

Speaking in the "variable density" metaphor: For the same reason light rays bend towards the denser region in a medium. Note that the light ray represents a world line (space-time path) of an object, in this analogy.

or I guess in a 2 dimensional model of space it falls to the "lowest" point, the dip caused by the massive body? Does mass long to travel through time at slower rates?

There is no "lowest point" because there is no "down direction", but there is a point with the locally lowest potential, where the gravitational time dilation is maximal as well.

To understand why everything tends toward that point in terms of geodesics in curved space-time I recommend these links:
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

 

[Naty1]

why do bodies of mass fall towards areas of greater time dilation?

Because that's where curved spacetime moves them.

 

[danielatha4]

Because that's where curved spacetime moves them.

Why not towards areas of space that travel through time at a faster rate?

Does the Principle of Least Activity have anything to do with this?

 

[A.T.]

Why not towards areas of space that travel through time at a faster rate?

Space doesn't travel trough time. Space and time are dimensions other stuff can travel trough. This picture explains how gravitational time dilation and gravitational pull are connected:

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

Does the Principle of Least Activity have anything to do with this?

In a way, yes. Moving locally straight ahead on a distorted grid, leads you towards the area with more 'stretched' distances.

In the alternative 'variable density' analogy you are pulled towards the denser area which breaks you more. Imagine driving a car with two wheels on the road, and two on the grass.