Main Question or Discussion Point
If wormholes connect two areas in spacetime, wouldn't that require 5 dimensions? (an extra dimension past 4d spacetime.)
This bears repeating. Although human minds may require an extra dimension to visualize what's going on here (To use the lower dimensional analogy, if you imagine a wormhole connecting two points on a piece of paper, we extend the "throat" of the hole into the 3rd dimension. You're assuming something similar for 4d spacetime with wormholes), the mathematics do not require a higher dimension! It's not even a question of whether or not we can in principle detect other dimensions -- this is a separate question entirely. The fact is that within the realm of differential geometry (upon which GR is built), you do not need extra dimensions to curve spacetime.It may look like extra dimensions are needed to embed that world in some higher dimensional Euclidean space. But since we are confined to our four dimensions, there is no way to detect anything outside that, and it's perfectly consistent to do physics without assuming that anything else exists.
Ok well, I find that to be crazy.you do not need extra dimensions to curve spacetime.
The world is 3D last time I checked. The third dimension is there, even if you're not immediately using it (well, actually you are using it because you can't have only 2D in reality).But your example is connecting two points in 2d spacetime isn't it, there is not 3rd dimension supposedly, yet you used it to connect the two points.
your analogy doesn't have the same dimensions as reality, if it did why would u call it an analogy?The world is 3D last time I checked. The third dimension is there, even if you're not immediately using it (well, actually you are using it because you can't have only 2D in reality).
dude, 2d spacetime connecting 2 points through 3rd dimension.Of course it does. To be an analogy it has to be similar, that's all.
It's not hard to understand! He's using a 3d piece of paper and folding it to put two distant coordinates next to each other, no extra dimension theredude, 2d spacetime connecting 2 points through 3rd dimension.
There isn't a 3rd dimension in 2d spacetime...
Are you saying there is 5th dimension in our 4d spacetime?
I'm asking if that's the case.
The paper is supposed to be 2d, that is the point. The real fact that it is 3d, (has thickness) is irrelevant. Then your saying our spacetime has thickness in some 5 dimensions??It's not hard to understand! He's using a 3d piece of paper and folding it to put two distant coordinates next to each other, no extra dimension there
[Note: The piece of paper in what follows is to be thought of a two-dimensional surface, i.e. no thickness]I thought wormholes folded space to connect two points.
A simply analogy, if I draw to points on a piece of paper and then fold it in half so they touch, have I used an extra dimension? Of course not.
Jared Nathan James = my whole name.EDIT: He=Jaredandjames
My point with the 3 dimensions is that we must have them, there is no real object that only exists with 2 dimensions. So we're folding with the three and not needing to invoke another, as per your explanation, if you only use the two to explain you don't need to invoke a third.[Note: The piece of paper in what follows is to be thought of a two-dimensional surface, i.e. no thickness]
This is irrelevant, jared. If you want to make your analogy correct, you need to think of it differently. The curvature induced on the piece of paper is a property of the piece of paper and the piece of paper alone. It can be described completely adequately by referring only two two-dimensional coordinates labeled on the paper.
Specifically, you do NOT need a 3rd coordinate to describe the curvature. So while it is true that in every day life to impose this curvature we bend the paper through the third dimension, one does not need to extend this to the universe (as OP would like). That is, the curvature of our universe can be described by referring only to our four dimensions, without any need for invoking a fifth.
The act of "visualizing" a surface necessarily involves an extra dimension. But that means absolutely nothing about the existence of such extra dimensions, only that if we wanted to visualize them, we would need them.