Definition
A wormhole is a hypothetical tunnel-like connection between two regions of spacetime — possibly two distant locations in a single universe, possibly two separate universes — whose throat is shorter than the external distance between its mouths.
The simplest example, the Einstein-Rosen bridge of 1935, arises naturally in the maximally extended Schwarzschild geometry but is non-traversable: it pinches off too quickly for anything, even light, to cross.
Why it matters
How it works
Karl Schwarzschild's 1916 solution for a non-rotating black hole, when extended to its full maximal form, contains two asymptotically flat regions connected by a thin tunnel — the Einstein-Rosen bridge. The bridge exists in the maximally extended geometry but evolves rapidly: it forms, opens briefly, and pinches off, all before any timelike or lightlike signal can pass from one side to the other. As a transportation device it is hopeless.
Kip Thorne and his students, prompted by Carl Sagan's novel Contact, asked the inverse engineering question in 1988: what stress-energy tensor would make a wormhole traversable? Their answer: a static throat that observers can fly through requires matter with negative energy density and negative radial pressure — what is now called "exotic matter." Such matter exists in quantum field theory (the Casimir effect, squeezed vacuum) but only in tiny amounts and for short times, constrained by quantum inequalities. Building a stable, human-scale wormhole would require an implausibly large coherent source.
Even granting one, wormholes raise causality concerns. If one mouth is taken on a relativistic round trip and brought back, time dilation makes the two mouths disagree about "now" — and a signal sent through can return to its sender's past. The wormhole has become a time machine, and a closed timelike curve threads its interior. Hawking's chronology protection conjecture, based on diverging vacuum fluctuations along the would-be loop, predicts that quantum effects pre-emptively destroy any such configuration.