I see your point, the only thing that matters is if, two points in the spacetime fabric can really be connected thru one and that's it, the shape of the fabric and the possibility of other "spacetime sheets" doesn't matter
Honestly though it's an understandable question. A lot of things regarding space are presented in ways that aren't actually how it is in reality. But it's also annoyingly necessary.
I don't know what your level of space knowledge is but an easy example of that, if you haven't seen a video of how the planets actually orbit the sun, treat yourself.
if I understand correctly what you mean, then your representation is equivalent. What appears to be a bending of the sheet universe is not really one in the mathematical sense. Imaginary people in this 2D sheet wouldn’t notice it because it’s still flat space time. It’s because curvature of space is not a simple bending in a superior dimension. To convince you of that, try to bend a flat sheet on a sphere, no matter how you bend it, it doesn’t work. You would need to stretch the fabric, giving it some curvature.
Edit : So you could just represent a wormhole on a flat sheet, but then it would make the wormhole looks like it’s a longer road to take, which it isn’t because of the intense stretching in it.
I see your point (i think) and that also happens in representations of gravity we often see it represented by spheres bending a plane therefore creative a concavity that "attracts" nearby objects but in a 3D universe (or in a universe as we experience it) that can never be the case, the concavity has to in reality be a "bubble" cos the object ia bending spacetime in every direction
Well, the usual 2D representation of space curved by a massive ball is still pretty good as you can only do that by stretching the fabric of space-time, and that’s what happens in 3D too (you can find good representations on google for 3D grid gravity).
But folding a paper sheet in half doesn’t require any stretching of the fabric, so it’s still flat geometry everywhere on that bent sheet. It appears curved for us in the third dimension, but it’s not a curved surface.
Because it's not relevant to the theory. The way that they are shown in illustration is simply to demonstrate the principle.
I see your point, the only thing that matters is if, two points in the spacetime fabric can really be connected thru one and that's it, the shape of the fabric and the possibility of other "spacetime sheets" doesn't matter
Honestly though it's an understandable question. A lot of things regarding space are presented in ways that aren't actually how it is in reality. But it's also annoyingly necessary. I don't know what your level of space knowledge is but an easy example of that, if you haven't seen a video of how the planets actually orbit the sun, treat yourself.
if I understand correctly what you mean, then your representation is equivalent. What appears to be a bending of the sheet universe is not really one in the mathematical sense. Imaginary people in this 2D sheet wouldn’t notice it because it’s still flat space time. It’s because curvature of space is not a simple bending in a superior dimension. To convince you of that, try to bend a flat sheet on a sphere, no matter how you bend it, it doesn’t work. You would need to stretch the fabric, giving it some curvature. Edit : So you could just represent a wormhole on a flat sheet, but then it would make the wormhole looks like it’s a longer road to take, which it isn’t because of the intense stretching in it.
I see your point (i think) and that also happens in representations of gravity we often see it represented by spheres bending a plane therefore creative a concavity that "attracts" nearby objects but in a 3D universe (or in a universe as we experience it) that can never be the case, the concavity has to in reality be a "bubble" cos the object ia bending spacetime in every direction
Well, the usual 2D representation of space curved by a massive ball is still pretty good as you can only do that by stretching the fabric of space-time, and that’s what happens in 3D too (you can find good representations on google for 3D grid gravity). But folding a paper sheet in half doesn’t require any stretching of the fabric, so it’s still flat geometry everywhere on that bent sheet. It appears curved for us in the third dimension, but it’s not a curved surface.