The short answer is that we can’t, and that’s why we’re not doing it.
Wormholes are an interesting thing; like black holes, for many years they were considered to be possible, in principle, but it was unclear whether the actually existed in the universe. Black holes have since moved from the realm of “I guess they’re possible” to “there’s a massive one in the center of every galaxy”, but wormholes have remained only a theoretical possibility.
General relativity gives us a set of rules for how the fabric of space time can behave, and there’s nothing in there that explicitly forbids wormholes from existing. You can even make a geometrically correct wormhole with a sheet of paper, if we assume space and time is a 2 dimensional sheet.
(If you want to do this, get a sheet of paper, and cut two identically sized complete circles out of opposite sides of the paper. Fold the paper over, and tape the inside edges of the circles together. Presto: you’ve created a wormhole in your paper space-time.)
The problem is, we have no idea how to get this to happen with 3 dimensional space-time. Not only do you have to distort space-time immensely to create a divot deep enough to punch through to some other part of space, you have to bend the other part that you want to reach to meet it. Otherwise, you just have a really big black hole. We’re pretty sure space is intrinsically flat (like your sheet of paper), and trying to bend space that much is effectively impossible. Since we have no idea how nature could go about creating one (there is no mechanism known to physics right now that could make one) it’s pretty hard to go about replicating that process to build our own.
However, if we had any idea how to go about making wormholes, I am 100% sure we would be all over that. Any way to cheat the huge expanses of space is good for exploration!
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