Why does an object fall from rest in a gravitational field?

[tickle_monste]

From what this layman can comprehend of Einstein's relativity is that mass causes a curvature of space-time. This space-time is a 4-dimensional geometrical construct. An object moving through a gravitational field would deviate from its straight space-like path in order to achieve the closest thing to a straight path in a curved space, which would be the equivalent of a straight line through space-time. Another way to think of it would be that if the object were to follow a straight space-like path, this would result in the object moving to a position further from the center of gravitation. This would require work being done on the object, so the law of conservation of energy would forbid this path, and the path of the object would become curved in order for it to not violate the conservation of energy.

I understand that this would apply to an object MOVING through a gravitational field, but I see no reason why this would cause an object initially "at rest" in the gravitational field (such as a cup sitting on a table) to begin falling, unless there were some sort of pressure of space pushing the object down.

 

[feynmann]

From what this layman can comprehend of Einstein's relativity is that mass causes a curvature of space-time. This space-time is a 4-dimensional geometrical construct. An object moving through a gravitational field would deviate from its straight space-like path in order to achieve the closest thing to a straight path in a curved space, which would be the equivalent of a straight line through space-time. Another way to think of it would be that if the object were to follow a straight space-like path, this would result in the object moving to a position further from the center of gravitation. This would require work being done on the object, so the law of conservation of energy would forbid this path, and the path of the object would become curved in order for it to not violate the conservation of energy.

I understand that this would apply to an object MOVING through a gravitational field, but I see no reason why this would cause an object initially "at rest" in the gravitational field (such as a cup sitting on a table) to begin falling, unless there were some sort of pressure of space pushing the object down.

No, there is no pressure of space pushing the object down. What happen is the cup want to move but is blocked by the table and the table bend a little bit. Now the question is why the cup want to move in the first place? Well, the cup sitting on a table does not move in space, but it still travel in time, and nothing can stop it from traveling in time, that's why...

 

[tickle_monste]

Could you possibly elaborate on what you mean by "You can't stop an object from moving through time?" If you mean it in the sense that the object will never "stay in the past" or "speed off into the future" then I understand.

It seems though that you imply that the object would have some sort of "inertia through time" rather than through space, like an object with velocity. If this is what you mean, then I need some elaboration because that is a foreign idea to me. The object at rest, in my mind, would have no inertia, and it's position changes simply because position moves. The velocity of a gravitated object increases like x^2, and I see this as having two equal components. The position of the object changes location due to natural time evolution to a location closer to the center of the Earth, like x. As the position of the object changes, the object would generate an inertia equal to x, resulting in a cumulative velocity that increases like x^2.

Is this the right way to think about it? I'm just trying to make some sense out of the matter. All the resources I can find on gravitation and relativity make too much use of math that is currently beyond my scope for me to get any sort of grasp on it.

 

[A.T.]

Could you possibly elaborate on what you mean by "You can't stop an object from moving through time?" If you mean it in the sense that the object will never "stay in the past" or "speed off into the future" then I understand.

You can see it like this: Everything is advancing trough space-time with the same constant speed. The speed trough space is just a projection of that space-time-advance on the spatial dimensions. And the speed trough time (tick rate of the object's clock) is just a projection of that space-time-advance on the time dimension:
http://www.adamtoons.de/physics/relativity.swf
The only way to stop the advance in time is to move at light speed trough space.

Objects at rest in space are not affected by space curvature, as you correctly stated. But they move along the time dimension (their clock is ticking), and the curvature of space-time changes the direction of their space-time-advance, so they start moving along the spatial dimensions:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

Here is more visualization:
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf

 

[tickle_monste]

Huh. Thank you guys, I think I actually get it now.