There's a theoretical way to stabilize it: put 'exotic matter' in the middle. Unlike all other matter, exotic matter has a negative energy density. This is the same sort of matter that would be needed to create an Alcubierre warp drive.
Unfortunately, we don't have any idea how to go about creating exotic matter. The closest we've come is the Casimir effect, when a region between two very close conductive plates will in some ways act as if there were negative energy.
[1] http://www.bibliotecapleyades.net/ciencia/negativeenergy/neg...
A priori, I don't see any reason to believe that creating it should be possible. It's never been observed, and I'm assuming there aren't any models which predict any methods by which it might come into existence. That's as good as saying it's made up to me.
Imagine a billiard table with a wormhole, which curves and goes three seconds backwards in time. It's set up so you can roll a ball into the wormhole, and it will emerge three seconds earlier and knock itself off the path, so it doesn't enter the wormhole. Paradox!
Except actually it emerges with a slightly altered path, and strikes itself only a glancing blow.
And why did it emerge with an altered path? Because it was struck a glancing blow.
https://en.wikipedia.org/wiki/Novikov_self-consistency_princ...
To get to the entrance, you must leave the Earth (with the entrance) at time X. After you've left, you can enter the wormhole and emerge from the Earth side at time X+e.
You leave Earth in 2020. You leave one end of the wormhole here, and take the other with you on a near-light-speed journey 40 light years away. One year goes by for you due to relativity, you pick up a burger from alien McDonald's, then step into your wormhole- which exits in 2021, not 2040.
Edit: no wait, I can't be understanding this right. You could just journey back home with your wormhole and give it to someone else.
This is where the “exotic matter’s” negative energy comes in.
This is the mechanism Stephen Baxter used in his Xeelee sequence novels.
What ever mechanism that prevents the paradoxical violations also makes this not very exciting (as far as time travel goes): you have to spend the "40 years" between you visiting one end of the wormhole and you entering the other at near-luminal velocity (hence you would only perceive it as 1 anyway). It's not so much "time travel" as an instant return ticket (where only your personal real time is spent, assuming your ship is exactly as fast as the one that carried the wormhole).
Which does actually have an interesting effect if you make them in pairs. It makes books like The Commonwealth Saga technically almost viable (e.g. where they build networks of portals and then just run trains through them non-stop to travel between worlds). Except that instead of using portals to explore new worlds, they would have to send a probe to those planets with a wormhole on board, at near the speed of light. And trips might cost you a bit of relative time to make a trip and return (e.g. the difference between the speed of light and the speed the probe delivered the wormhole from both portals added together would be how far in the relative future a trip would send you).
This all of course requires exotic matter which probably doesn't exist; which is why this whole thing probably doesn't work in the first place (e.g. why stable wormholes probably don't exist). Still might make it's own excellent sci-fi book if someone ran with the constrains of this, and it would technically be harder sci-fi than most.
universe@backhole-42> configure
universe@backhole-42> set stable MAX_VALUE
universe@backhole-42> commit
..changes successfully committed to blackhole-42
universe@backhole-42> exit
universe>
My understanding (which is very small) is that the multiverse theory takes care of not violating this law, since it’s not an isolated system.