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So I've somehow built my wormhole. I've stuffed the thing with negative energy so it's stable and traversable. I've got one end in orbit around Earth and the other in orbit around Mars.

My question is how long does it take to travel from one end of the wormhole to the other? The two ends are constantly changing position relative to each other in real space as the Earth and Mars move around the Sun but is the length of the wormhole changing too?

If I moved the Mars end of the wormhole to a distant star system, would the transit time through the wormhole be instantaneous or would it take longer than when it was in orbit around Mars? If so how long?

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  • $\begingroup$ I want a square backyard of $100m^2$. What dimensions should I get the land? The equation gives two solutions, either $10m$ by $10m$ or $-10m$ by $-10m$. Land is expensive, so I want to explore the negative solution. All I need is to get a piece of land with negative dimensions. Say, I've managed as much and am enjoying my new $100m^2$ yard. My question is, have I taken away any land from the neighborhood or have I actually given as much back to the community as I gotten for myself ($+10-10=0$ on each dimension)? And would it take longer for me to get home if I build this yard across the town? $\endgroup$ – safesphere Aug 8 '18 at 23:16
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    $\begingroup$ The point of my analogy above is that mathematical equations that describe the physical reality typically have some redundancy, meaning that they describe real solutions, but also often some unreal solutions, as if describing something that doesn't actually exist. Not all solutions of the gravitational field equations must exist or even make sense, especially those requiring negative energy. Just a comment, I will leave the actual answer to the experts. $\endgroup$ – safesphere Aug 8 '18 at 23:27
  • $\begingroup$ See the answers & comments in the related question: physics.stackexchange.com/q/19754 $\endgroup$ – D. Halsey Aug 9 '18 at 0:06
  • $\begingroup$ Doesn't the answer here depend on which wormhole metric is used? I think different wormholes have different throat lengths, varying from zero to a large distance. $\endgroup$ – Anders Sandberg Aug 9 '18 at 7:14
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The separation between the two mouthes of the wormhole on the "outside" is technically independant from the separation of the throat. There may be some subtleties involves (it's hard to really discuss exact realistic solutions), but a simple example is to consider the thin-shell wormhole in Minkowski space. In there, the throat distance is always zero, and the distance between the two wormholes is arbitrary, as well as the matter distribution being completely independant from the distance.

In the case where the distance is large enough, I don't think it should have much influence at all even in a more realistic case, as the space around the two mouthes will be roughly Minkowski and as such the local matter distribution will not depend (much) on the distance between them. Slight caveat if the wormhole is near time machine formation (ie, the time shift between the two mouthes is almost equal to the distance between them), in which case quantum effects will probably have some influence on the whole affair.

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