The inverse of spacetime curvature?

[LilPhysics]

Let's say you can bend a paper...how about bending it upward. a slope
I'm saying as we saw spactime in 3d...we all know how it looks..the lines are attracted toward Earth but why doesn't it deflects them and maybe negative mass is linked with it.
In other words, someone under the trampoline pushing you up instead of you bending the trampoline.Instead curving...it deflects
Maybe black holes deflects light throught spacetime and hence the problem is what occupies the void of 4D if deflected

 

[Dale]

Let's say you can bend a paper

That type of bending is called extrinsic curvature. General relativity deals only with intrinsic curvature. If you draw a triangle on a piece of paper then the angles sum to 180 deg regardless of how you fold it.

 

[A.T.]

...someone under the trampoline pushing you up instead of you bending the trampoline...

Someone living within the 2D trampoline sheet wouldn't notice any difference between these two symmetrical cases, because the sheet's intrinsic geometry (distances within the sheet) would be the same. That is what matters in this analogy, not how the curved 2D surface is oriented within the 3D embedding space.

See also:
http://demoweb.physics.ucla.edu/content/10-curved-spacetime

 

[LilPhysics]

Then what if spacetime deal with extrinsic... Anyone watched the 3D visualized Spacetime curve of earth. You kr what it looked like but what happens when it deflects that's what I'm saying. You might want to google 3d spacetime...what if spacetime is extrinsic also , there must be a link for it with negative mass, -ve mass's inertia is different and so can the curvature be different

 

[LilPhysics]

here

 

[stevendaryl]

Let's say you can bend a paper...how about bending it upward. a slope
I'm saying as we saw spactime in 3d...we all know how it looks..the lines are attracted toward Earth but why doesn't it deflects them and maybe negative mass is linked with it.
In other words, someone under the trampoline pushing you up instead of you bending the trampoline.Instead curving...it deflects
Maybe black holes deflects light throught spacetime and hence the problem is what occupies the void of 4D if deflected

As John Baez describes here: https://arxiv.org/pdf/gr-qc/0103044.pdf, the content of Einstein's theory of gravity can be understood in terms of what happens to a ball of dust, initially spherical and initially at rest in some locally inertial reference frame. If you release this ball in a gravitational field, its shape will be warped; it will become stretched in some directions and compressed in other directions. If the ball is in outer space, and is not passing through any matter (or energy), the volume will remain unchanged. It doesn't matter that there might be a gravitational source outside the ball; if the ball passes near the Earth, its shape will change but its volume will not. But if there is a source of gravity inside the ball, then the volume will contract. The fact that there is no negative mass means that if the ball is in freefall (no forces acting on it other than gravity), its volume can only contract or remain the same through interaction with gravity, it can never expand.

 

[jbriggs444]

Then what if spacetime deal with extrinsic...

We would have no way to notice any difference.

 

[A.T.]

here

https://www.physicsforums.com/threads/space-cannot-be-curved.922309/page-4#post-5832954

 

[Dale]

Then what if spacetime deal with extrinsic

As @jbriggs444 mentioned, if spacetime is extrinsically curved in some higher dimensional embedding space then we would never know. All that we can detect is the intrinsic curvature, there is no way, even in theory, to measure the extrinsic curvature.

Edit: just noticed this

there must be a link for it with negative mass, -ve mass's inertia is different and so can the curvature be different

No need to bring in extrinsic curvature here. Positive mass leads to positive intrinsic curvature (triangle has >180 deg). Negative mass leads to negative intrinsic curvature (triangle has <180 deg). Or at least it does if it exists, which is doubtful.

 

[Sorcerer]

Regarding the trampoline example, being pushed up or pushed down, am i to understand that since a simple change of coordinates can make the two situations identical (i.e., reverse the positive direction on your axes and suddenly “up” becomes “down”), then there isn’t any “curved spacetime,” that is, no tidal forces that are present in one situation but not the other?

 

[jbriggs444]

Regarding the trampoline example, being pushed up or pushed down, am i to understand that since a simple change of coordinates can make the two situations identical (i.e., reverse the positive direction on your axes and suddenly “up” becomes “down”), then there isn’t any “curved spacetime,” that is, no tidal forces that are present in one situation but not the other?

Yes. It is an obvious isometry. However, that is not to say that there is no curvature. It is to say that the intrinsic curvature is identical in the two cases.

 

[A.T.]

Regarding the trampoline example, being pushed up or pushed down, am i to understand that since a simple change of coordinates can make the two situations identical (i.e., reverse the positive direction on your axes and suddenly “up” becomes “down”), then there isn’t any “curved spacetime,”

The trampoline has intrinsic curvature, but it represents space, not spacetime.

 

[LilPhysics]

Thanks guys a lot, btw I'm just a student about to sit for A level exams and it's my first year plus physics is DOPE