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)

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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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General Relativity treats space as its own thing rather than just the arena where things happen. It can expand, compress or be deformed in many other ways depending on what is currently in said space. We see the stretching as the expanding of distant space and compression near massive objects(this is why light bends around stars and black holes). We could also in theory deform space in such a way that we link 2 otherwise very distant areas through a much smaller distance known as a worm hole.

Worm holes work in the math but are most likely not a real thing. They require negative energy which isn’t something we think can actually exist.

Wormholes are purely speculative. There is nothing that says that should exist and no evidence that they exist, so how they would theoretically work is meaningless. Regardless, you’re fundamentally misunderstanding how space works. A wormhole would, speculatively, link 2 distant regions in spacetime. That has nothing to do with space being a vacuum. Spacetime is not a literal fabric but it’s a thing that exists. Changing spacetime itself has no bearing on whether or not there is stuff in space.

It’s a hole in the space itself, not in something *in* space. The very “go into that direction” gets warped. If you select a set of coordinate axes and then go one mile forward, one mile left, one mile back and one mile right in normal “flat” space, you will arrive at your starting point. In warped space your coordinates are screwed and you will end up somewhere else. A hole in space is just a special case of warp.

Wormholes aren’t actual holes, if you consider holes as “absence of matter”.

Wormholes are holes in space-time, and for our perception, an end of a wormhole would be similar to a black hole.

Its really hard if not impossible to grasp for us 3 dimensional beings with minds built to think in 3 spatial dimensions. That’s where the pen and paper analogy tries to compress it down to 2 dimensions, so that we, in that example higher dimensional beings, can see the third direction that allows the 2 dimensional space of the paper to fold and join two points.

To truly and intuitively understand how a wormhole would connect two places in our 3 dimensional space we’d first need to understand how a 4th dimension fits into our 3.

Well, space isn’t a fully vacuum.

But you need to forget that space is only 3 dimensions. Only then it makes sense.

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.