Re: OT: Gravity, Dark Energy, Universal expansion
In my first post I said, "for the universe expanding at the speed of light"... which is an assumption. The rest follows from the balloon model of an expanding universe (the diagram above). In this case, the balloon model is an expanding 4-sphere [due to symmetry the number doesn't matter... it could be any n-sphere n>3], where the balloon's outer surface is 3-space.
Yes, the size of the visible universe is different from the size of the universe, which as I said, can make the universe untraversable... that is was one of my main points.
However, for an n-dimensional balloon model of the expanding universe, it does not by any means imply a closed universe, only a finite one... it can still be open if it expands forever. In any manifold/topology, any point can still have a farthest point... like two opposite sides of the balloon... it is a matter of spatial symmetry, and has nothing to do with the openness. Every point on a circle, or sphere, or n-sphere has a farthest point.
"speed of light perpendicular to 3-space" is not nonsensical, just non-physical... imagine a balloon who's radius is expanding at the speed of light. Mathematically, that perpendicular-ness allows speed and distance to be defined for more dimensions using the same symmetry that allows time being the 4th dimension (ie time= distance/c).
r^2 = x^2+y^2+z^2 where r=c*t (t being the age of the universe)
as t increases, any two "fixed" points (x1, y1, z1) and (x2, y2, z2) will be moving away from one another.
(Personally, I would like to draw the light cones for that diagram, but the curves are pretty hard to photoshop.)
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