Is the trampoline analogy an accurate representation of space-time curvature?

[pivoxa15]

Textbooks usually illustrate space and our solar system with the planets lying on a sheet where the heaviest object at the centre is the sun. Other planets surround it in orbits. The attraction towards the sun is due to the dent created by the sun. This is a result of GR. If this theory is correct than when we observe the solar system, it should look something like in the diagram provided where the ring of planets is above the sun. Is this what happens? Could someone give a link of an actual aerial view of all the planets and the sun?

 

[russ_watters]

The curvature is not in the 3 spatial dimensions, so we just see the solar system as a plane.

 

[pivoxa15]

Why do they illustarte it as if it is in 3 spatial dimensions? Is the dimension of time missing? Is the diagram a way of illustrating how forces and centripetal acceleartion are communicated and manifested?

 

[yenchin]

The illustration is an "embedding diagram", look for more info on this. : )

 

[MadScientist 1000]

4d on paper would be really hard to illustrate in a 3d world.

You have to remember that we consider time the 4th dimension graphed.

 

[Phobos]

As noted above, the diagram/model you are talking about is a helpful way to visualize what is going on in 4-D spacetime. Now you just need to visualize the curvature in all directions rather than just 'down'. :)

The 'curvature' is analogous to the sun creating a dent in the flat plane, but that's not what we actually see in 3D space...the sun and planets are essentially in the same plane.

Perhaps rather than getting stuck on the word 'curvature' we could consider the 'behavior' of spacetime instead (an attractive force between masses rather than a physical slope shown in the drawing).

 

[neutrino]

The bowling-ball analogy strikes again. ;)

 

[neutrino]

Could someone give a link of an actual aerial view of all the planets and the sun?

I'm afriad that no man-made craft has gone that far, at an angle to the plane of the solar system, to get such a photo. I don't think it'll look any different than the usual diagrams.

 

[pivoxa15]

As noted above, the diagram/model you are talking about is a helpful way to visualize what is going on in 4-D spacetime. Now you just need to visualize the curvature in all directions rather than just 'down'. :)

The 'curvature' is analogous to the sun creating a dent in the flat plane, but that's not what we actually see in 3D space...the sun and planets are essentially in the same plane.

Perhaps rather than getting stuck on the word 'curvature' we could consider the 'behavior' of spacetime instead (an attractive force between masses rather than a physical slope shown in the drawing).

Interesting.

The bowling-ball analogy strikes again. ;)

What do you mean?

 

[neutrino]

What do you mean?

To explain space-time curvature in non-technical terms, most physicists describe how a heavy bowling ball placed on a trampoline creates a dent, in which smaller marbles take different trajectories. I believe it was Einstein who came up with this in the first place(I could be wrong, though). Although it gives a vague idea, it's very misleading, because people start associating a 'down' direction in space, and stuff like that.