If space is a vacuum and not a fabric made out of a material how do wormholes work? (Please avoid the pen through paper analogy)

Question

I’m struggling to understand how someone can create a hole in space if space is already a vacuum. I mean, you can’t create a hole in emptiness. So where does that leave wormholes?

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Answer 1

Wormholes aren’t holes in the sense of having something and then drilling through it.

One way of thinking about wormholes is as having two bits of space that are connected in more than one way.

Normally if you have two points in space, and you find two paths between them, you can deform one a bit to get the other; imagine getting a bit of stretchy string and connecting the two points – you could bend or twist that string to get any other possible path between the two points.

But you can’t do that with a wormhole; there are two completely different routes between either “side” of the wormhole. One way normally through space, and the other “through” the wormhole. Although that doesn’t necessarily mean either route is the “real” route and the other isn’t – they could just similar. All it means is that the two bits of space are joined together in more than one way.

If you want an analogy, think about the inside of a doughnut shape. Pick two points and there are two distinct routes between them – depending on which way around the hole you go. But neither is the “normal” one.