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Faster than light wormhole travel depicted in science fiction and in popular science articles seems to assume that rather than being flat (with dimples centered around large masses), spacetime is fairly lumpy in order to facilitate wormhole shortcuts.

Is there a plausible reason why spacetime would be conveniently "folded back on itself" as illustrated below?

enter image description here

RobertF
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  • Based on observational evidence there isn't. – CuriousOne Jan 26 '16 at 17:30
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    I am not proficient with wormholes enough to answer this, so I'd just like to state that this whole "rubber sheet" analogy is really inaccurate beyond a certain point. In standard GR and most extended gravity theories, we never deal with any "ambient" space, in which spacetime might be embedded in. The braneworld scenarios might be an exception from that. To the best of my knowledge, wormhole metrics arise even outside braneworld scenarios. – Bence Racskó Jan 26 '16 at 18:55

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There is nothing in physics that describes the sort of folding shown in your picture. I'm afraid it is an invention of the Science-Fiction community.

The best tool we currently have for describing spacetime is general relativity, but GR does not and cannot tell us anything about the global topological properties of spacetime. The sort of wormhole you show is described by the Morris-Thorne metric. Leaving aside the inconvenient detail that the Morris-Thorne wormhole requires exotic matter, which (probably) doesn't exist, all GR tells us is that the wormhole links two flat regions of spacetime. So it looks like:

Morris-Thorne wormhole

where $A$ and $B$ are two regions of flat spacetime. However the two regions $A$ and $B$ would (in this 2D representation) remain as two flat parallel sheets everywhere with no other joins between them. In effect they would be two different universes joined by the wormhole not different regions of our universe.

There are some other related questions that you might be interested in reading:

Community
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John Rennie
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  • So the whole premise of the wormhole subway network in Carl Sagan's novel Contact seems even more far fetched now. – RobertF Jan 28 '16 at 14:16
  • @RobertF: I'm afraid so, though as a life long SF fan it hasn't spoiled my enjoyment of stories using wormholes :-) – John Rennie Jan 28 '16 at 17:18