Okay, here’s a question that’s puzzling me. From Brian Greene’s talk on superstring theory, a frame showing the usual means of picturing the general theory of relativity:
In the center, you’ve got the Earth warping three-dimensional space, depicted here as the two-dimensional plane in which the Moon orbits. (Actually, it’s depicted as the plane one lunar radius below the orbital plane, as the Moon appears to be rolling.) The Moon is pulled by the Earth in the same way that a marble would roll down a similar incline. Simple enough.
Here’s the question: in which direction is space warped? That is, to depict the warping of a 2-dimensional plane, you need three dimensions; we use depth here to show the inclination of the moon to head back into the Pacific basin from whence it came. Therefore, since it’s actually 3-dimensional space that’s being warped, presumably the direction of the warp must be into a fourth spatial dimension.
The obvious answer is that the direction of the warp is an artifact of the depiction: 3-dimensional space doesn’t need a direction to warp, any more than you need three dimensions to stretch out a flat sheet of pizza dough. But if that’s the case, if we’re talking about a warped three-dimensional space, don’t we need an external 3-dimensional frame of reference against which to measure the changes to our own space? And if so, is that a purely mathematical construct, or is there a physical analogue?
I have a gut feeling that this question is either blindingly brilliant or blindingly obvious. Probably the latter.
Barkeep – I’d like a shot of whatever he’s been drinking, please…
hey, just ran accross this question and i dont know if your still interested, or if u want to take an opinion from a junior in high school
you can quote me on this, but dont quote me exactly because i cant spell haha
einstein came up with his theories of general and special relitivity based on the fact that space is 3 dimensional yet flat. how is this possible?
i was drawing with a bunch of different possibilities for our space. based on your understanding of the question i assume u know what a moibus strip is. i had a picture in my mind of an number of moibus strips all next to eachother by a fraction of an angle, so many thats it just >infinate
for a clearer picture, imagine a tube thats curved perfectly around itself, like if its 6 radians long and curve it, it will be a perfect circle with no whole in the middle, not like an O
therefor it would be one flat surface and it would be a flat surface, have one side, and be 3d
This is my idea and understanding, but not my knowledge, because i understand uncertainty to the exception that proves the rule : )
-Connor Pipkin