Spacetime sometimes resembles a sheet of paper in which you can punch a hole and connect the edges with a short tube: you get a wormhole. In the simplest mathematical models of such wormholes, massless scalar fields appear — something like an invisible fog filling everything around. This fog behaves strangely: its values become imaginary. In physics, imaginary numbers are not a fantasy but a working tool — much like an accountant uses negative amounts to track debts. Only here, imaginaryness signals that we have peered beyond the edge of the familiar description.
Usually, such fields are interpreted as coupling constants — quantities that determine the strength of interactions, like how strongly a magnet attracts a nail. If you mentally move these constants into the realm of imaginary values, the theory predicts that at some step a wormhole will emerge. The authors argue that the very possibility of such a wormhole sets a limit — the 'imaginary distance bound.' It's like a rubber band that can only be stretched to a certain length before it snaps. Here, what snaps is not the band but the very ability to describe the world with simple equations.
In some cases, this bound coincides with already known theoretical constraints. For example, with the weak gravity condition — the idea that gravity is always weaker than other forces, like the quietest whisper in a noisy room. Or with the Kontsevich–Segal–Witten condition, which rejects unphysical complex metrics, like a filter that blocks impossible shapes of spacetime. Such a coincidence hints that the 'distance bound' might be a universal rule for any world with wormholes.
Imaginary numbers, which seem like pure abstraction, describe quite real probability waves in quantum mechanics — without them, you couldn't calculate where an electron will be in the next instant.
In Carl Sagan's novel 'Contact,' a wormhole serves as a transport tunnel to a distant star, but no one discusses what mathematical prohibitions might make such a tunnel impossible.