This is an embedding diagram — the standard way relativists visualise curved space. Two flat sheets, each representing an ordinary, asymptotically flat region of space, are punctured and joined by a curved tube: the wormhole's throat. Anything that slides down one funnel, through the throat, and up the other side has crossed between the two sheets without travelling the (potentially enormous) distance that separates them in ordinary space.
b₀ in the Morris–Thorne wormhole metric.A traversable wormhole like this one requires "exotic matter" with negative energy density to hold the throat open — nothing in this diagram violates general relativity, but no confirmed source of the exotic matter needed to build one has ever been observed.
An interactive embedding diagram of a traversable wormhole: two flat sheets of space, each standing in for a distant region, joined by a curved throat. A glowing probe crosses the shortcut while the numbers compare the throat's proper length to the distance separating the two mouths in ordinary space.
Embedding diagrams let relativists visualise curved spacetime by bending a flat surface through an extra dimension. The throat radius and flare steepness reshape the curvature exactly as the parameters of the Morris–Thorne wormhole metric would.
Adjust the throat radius and flare to reshape the wormhole, set how far apart the mouths sit in normal space, then send a probe through and watch the shortcut factor update live.
Kip Thorne and Michael Morris first worked out the physics of a traversable wormhole in 1988 — at the request of Carl Sagan, who needed a scientifically defensible shortcut for his novel Contact.