Posted: Mar 02, 2011 3:40 pm
Xaihe wrote:I know what you're trying to explain, but I don't think you understand my point exactly. What I'm questioning is whether there is an assumption here and whether that assumption is valid.
First, my own assumption is that mass curves spacetime and that this accounts for gravity and time dilation. Then, the assumption necessary for the picture you laid out is that spacetime at a particular point can be curved in multiple (possibly opposing) directions at once. And this opposite curvature would then account for the apparent decreased acceleration and increased time dilation. I'm just having some trouble wrapping my head around this idea (which is no argument).
If my interpretation is wrong, please let me know where (and if you would, why).

I don't know how to answer your question, but just to clarify what seems to be a misconception: time dilation is a result of Special Relativity, which has nothing to do with gravity. And curvature is a result of General Relativity, which has everything to do with gravity.

Now, it's true that a difference in gravitational potential will affect clocks -- for instance, this is taken into account for GPS operation, but this gravitational correction is not referred to as time dilation.

Neeedless to say, time dilation and gravitational correction are calculated using entirely different equations.

Time dilation: dτ ≈ dt ( 1 + v2/2c2)
Gravitational correction: dτ ≈ dt( 1 + GM/Rc2)

Hope this helps