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A wormhole is not just a thing from a science fiction novel. There is sound theory for them based in physics. Although there is no visual evidence of a wormhole, it is defined basically as a short cut through space and time. A wormhole conceptually has to fold the two dimensional concept of space and time to create a three dimensional situation. The wormhole then becomes the bridge from one dimension to the other. A wormhole is theorized to be made up of three parts: two mouths and a throat. Again, I want to point out that there has never been a wormhole observed or created.A wormhole is a valid solution to some problems in Einsteins theory of general relativity; however, the case for a wormhole relies on the existence of exotic matter which, in itself, is a conceptual aspect or particle physics. Basically, you need to have matter that breaks a couple of established laws of behavior for particles and can not have known baryonic particles in it. Lots of stuff has to happen that no one has ever observed before you can have a wormhole. That leaves the problem of having a stable wormhole. Based on the information given above, any wormhole created would be immediately collapsed by any changes in space or particles in or around it. So, in order to have a wormhole you must have exotic matter(matter with a negative mass), but if you do not have that, and none is known, you must have a perfect vacuum where there is no matter and no energy. That area would have to be able to exist despite the constant attack of matter and energy from without. Even in space there is constant zero point energy that would cause the immediate collapse of any wormhole that happened to form.
I mentioned that there are theories that maintain the conceptual possibility of a wormhole. They are called Schwarzschild wormholes or Einstein-Rosen bridges. These are bridges created in theory when applied to vacuum equations in Einstein’s field equations. They are essentially a bridge between white holes and black holes. They have been shown, with physics, to be unstable and collapse immediately. Then along came Kip Thorne who proposed that a wormhole could be kept open with matter that has a negative mass and energy(exotic matter). The exotic matter was the factor needed to make it possible to travel through a wormhole. I think I have heard this concept explained in an episode of Stargate SG-1. Boy, that Samantha Carter character explained a lot of cool stuff on that show.
So, why care about a wormhole? Just like in science fiction, science fact is looking for a quick way to travel from one point in space to another as quickly as possible. Another proposed application would be to create an engine that constantly creates its own wormhole for space travel. Both are awesome possibilities, but, on a practical note, completely out of our scientific realm at this time. Someday, hopefully!
Here is a good article about a wormhole and here is a link with several conceptual diagrams of a wormhole. On Universe Today we have a great article about the chance that the LHC could create a wormhole and another about whether or not a wormhole could create its own magnetic field. Astronomy Cast offers a good episode about using a wormhole to power a spacecraft.
Sources:
Wikipedia
How Stuff Works

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