In mathematics, a subspace is a subset A of a topological space X with the inherited topology: the open set in A consists of the intersections of the open sets of X with A.
In the Star Trek universe, a domain outside of the normal spacetime continuum through which communication signals and data streams are able to travel faster than the speed of light (see FTL travel). In ST jargon, a subspace fracture is a rupture or tear in the subspace continuum that allows subspace to enter normal space.
Something akin to subspace or faster-than-light communication might be possible if a theory reported by Fabrice Petit of the Belgian Ceramic Research Centre and Michael Sarrazin of the Facultés Universitaires Notre-Dame de la Paix, in Belgium, in September 2007 in the journal Physical Review D, proves to be true. These researchers describe what amount to shortcuts through extra dimensions.
Petit and Sarrazin, inspired by string theory, describe a situation in which the universe we know is actually just one sheet or brane in a higher dimensional spacetime. In this model of reality, our universe includes a second sheet that we're not normally aware of because we're confined to our own sheet. Petit and Sarrazin describe a specific "braneworld" scenario in which there are just these two branes. In this case, although particles can't exist between branes, they can travel back and forth between the sheets by way of quantum mechanical tunneling, which allows passage across barriers that classical physics considers insurmountable. Under the right circumstances, a powerful magnetic field can cause a particle to oscillate between the two branes. If the other brane is warped in a certain way, distances there may be shorter than in our own brane. This means if a fast-moving particle were made to travel in the other brane for a while before returning to ours, it could actually get to a distant part of our universe much faster than a light signal confined to our brane.
Petit and Sarrazin point out that their theory only works for fermions – particles that include protons and neutrons, but not all types of atoms. Since our bodies contain a lot of atoms that are not fermions, humans could never take such shortcuts. But by making electrons or other fermionic particles take shortcuts through the other brane, it might be possible to communicate faster than light speed, just like in Star Trek. Breaking the light speed barrier is normally thought to be impossible because it allows particles to time travel, leading to problems with causality – paradoxes that spring up when effects can happen before their causes. The Petit-Sarrazin scenario needn't violate causality because the shortcutting particles get to their destination faster than light only when confined to our brane. When their path through the extra dimension is taken into account, they actually obey an overall speed limit, allowing causality to be preserved.