A question about wormholes and their typical representation

[Breo]

Why the wormholes are typically represented as follows:

instead:

Is the same? in that case why there are two type of draws?

Another question, why the wormhole has length? or at least that seems in the draws and in the movies like interstellar or contact.

 

[phinds]

It is to emphasize the aspect of these theoretical beasts of being able to "short-cut" spacetime. The first pic shows that and the second not only does not, it in fact makes it look as though the wormhole path is LONGER than a traditional path between the same two points.

 

[A.T.]

Is the same?

Topologically, yes.

http://en.wikipedia.org/wiki/Topology
"a topologist cannot distinguish a coffee mug from a doughnut"

 

[jerromyjon]

The best logical "visualization" I have ever heard is taking a piece of paper, and mark 2 dots on it... the paper flat on the table represents flat spacetime and 2 distinct points with a distance between points in 3D space at 1 time. Now fold it in half so the 2 dots touch is a wormhole (laymen's terms infinite distance tends to 1) or curl it in a tube as a physicist might to align 2 inertial reference frames of space in a singularity in spacetime. It doesn't matter philosophically if you think space doesn't exist between the points or energy doesn't "exist" on the trip through space, as long as you realize the twisty rollercoaster ride through a tube from A to B is not predicted, hinted or in any way I know of supported by science.