The shape of the earth

[haydxn]

Hello there,

 

I was thinking yesterday about earth, space, and general relativity. A particular idea popped into my head, but I could find no existing literature about it; whilst that probably indicates how stupid it is, it's also a little frustrating to not have a go-to debunking (as is usually the case for such flights of fancy!). I figured I would post it here for those cleverer than I to say "well, I think you should stop thinking that right now".

 

The presence of matter results in gravity via the warping of spacetime. As such, orbiting bodies, travelling in a straight line through curved space, are taken in a path around their 'host' - a path which our geometry can sensibly describe as being circular/elliptical.

 

So far you're hopefully still with me. Nothing strange there.

 

Now, bear with me...

 

If this curvature applies all the way around the earth, then what if the earth is actually 'flat'? That is not to suggest that it is not spherical; in our geometry, it clearly is. However, perhaps this sphericity only arises from the fact that space is curved all the way around it; we are right to perceive it as spherical, given the geometry we apply to it, and the manner in which observable features of the universe can be detected by ourselves and our instruments. But, if we were to consider space 'unwarped', would the geometry of the earth's surface not then be effectively two dimensional? It would be a strange kind of surface that loops back on itself in all directions (like a pacman world), and its unique area would be proportional to the size of the body... but flat nonetheless. Could it be that our restricted three-dimensional observational capabilities prevent us from conceiving of such a structure to the underlying geometry of existence?

 

So, anyway, that's what I was pondering. If anyone has ever encountered any such thoughts, postulations, discussions, debunkery etc.. I'd be happy to hear them. It's not like I'm trying to prove anything; right now it's just an annoying thought in my head - a limited head without the experience or skillset to further probe any implications or possibilities (or otherwise) of the notion.

 

Puzzled,

haydxn

Edited December 8, 2011 by haydxn

[Schrödinger's hat]

You should never stop thinking. Just don't close your mind off to the (quite likely when anyone is speculating like this) possibility you may be wrong.

 

Re. space being curved to make earth round:

This is kinda what makes the event horizon to a black hole round, but space around earth is not curved enough to do this.

 

We can detect curvature in space, even if we can't get to a higher dimension to look at it.

 

If you imagine an ant on a balloon that can't see the third dimension. Let's name him Steve.

From Steve's point of view, he's in a two dimensional space.

 

He could try and figure out how curved the balloon/space is by going around in a loop and doing something called paralell transport.

This is a bit hard to explain without a bunch of maths, but one way to look at it is like driving a car without turning the wheels.

If you drive a car along one of those tracks with extremely banked corners it will turn even though the wheels are straight.

First he drives forward. Then does a similar action to the right (without turning the car, or maybe has a car on a car pointing the other way, the analogy breaks down a bit :/) then backward, then left.

If he is in flat space he winds up facing the direction he started

but in curved space he'll wind up pointing in a slightly different direction.

This turning is one way of measuring curvature, and in earth's gravity it isn't nearly enough to make the surface loop right around.