Posted: Mar 02, 2011 4:04 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).

It's a bit difficult to pick the bones out of this, but I'll try. The best analogy I can come up with is to think of a gravity well as being somewhat like a tornado, but one that lies in all directions. The classical image of the gravity well is this:

Which is not very accurate, not least because the bottom of the well would be centred on the centre of mass of the planet. If you think of that same gravity well existing in every direction, you begin to see a picture that looks a bit more like this:

Although even this isn't very accurate, not least because it's almost impossible to represent this phenomenon in a two-dimensional image, due to the inherent limitations in such a representation.

Now, if you take the image of the gravity well as a tornado, you can think of the centre of that gravity well that exists in all spacetime dimensions as being somewhat like the eye of the tornado, where everything is calm. Indeed, even given a one-dimensional well, it would still be relatively calm, because there's no further to fall when you're at the bottom of the well, but the curvature of spacetime still exists there, and it is maximal for the appropriate mass. Thus, time dilation is still in effect, because the warping of spacetime is still in effect, and it can indeed be curved in lots of different directions at once, because it's curved in all directions.