Curvature of the universe?

Question

I can't understand how an observer in either a spherical, hyperbolic or flat universe will be able to tell the difference between the three. Surely if he was to measure the angles in a triangle in all three cases, the light would bend in accordance to the curvature of the universe and show that in each case, the angles in a triangle = 180.

I can understand how this works from an outside perspective of the universe, but not how insiders like this would be able to tell the difference

help!?

Answer 1

yeah.......





actually I think thats the reason WHY we can't tell what shape it is.


the shape of the universe is STILL unanswered


correct a triangle cut out of a sphere actually appears to have angles that are 90 degrees each. = 270 degrees but this is called spherical geometry and doesn't apply to flat objects.

an example
http://www.nbmg.unr.edu/staff/house/images/earthcore.jpg

so triangles even change drastically and can "break" the "rules" according to the shape they lay on.

Answer 2

>Surely if he was to measure the angles in a triangle in all three cases, the light would bend in accordance to the curvature of the universe and show that in each case, the angles in a triangle = 180.

No, if he was to measure the angles in a triangle in the open or closed cases, the light would bend in accordance to the curvature of the universe and show that in each case, the angles in a triangle != 180. That's pretty much what curvature means.

An ant on the surface of the Earth can confirm that the Earth is round by drawing a big triangle on the Earth's surface and showing that the angles do not sum to 180. For instance, starting at the north pole, drawing south to the equator, then following the equator 90 degrees in longitude westbound, and then drawing north again to the north pole draws a triangle with three right angles in it. Similar feats are performed on any curved manifold. There is nothing magical about 180 degrees, except that is what you happen to get when the curvature is zero.

Answer 3

You are wrong about the angles in a triangle being 180. This is only true in a flat space. In a sphere I believe the angles are bigger and for a hyperbolic the angles are smaller than 180. The issue is scale. on a small scale, such as the perspect that we have, everything is flat. We don't preceive even the curvature of the Earth never mind the curvature of spacetime. Only when the scale becomes increasingly large do we preceive the curvature. Imagine driving around the block and flying a plane over half the Earth but in both cases drawing a triangle. They are going to be differet.