The wormhole is a favorite tool of science fiction
authors though very few have actually taken the task of tackling their use beyond simply saying "I open a wormhole and go through to a point way
far away" (a la Star Trek
Before going too far into the uses of a wormhole, it is necessary to sit down and look at what one is.
A wormhole is a geometry of four-dimensional spacetime ... in which two regions of the universe are connected by a short narrow throat. A classical large scale wormhole is a solution of the Einstein's field equations, which governs the curvature of spacetime.
There (may) exist two types of wormholes - the "classic" Schwarzschild wormhole (also known as Einstein-Rosen bridge) that are two connected black holes (or one black hole with two throats in either diffrent parts of the universe or two diffrent universes). The Schwarzschild wormhole uses the negative square root as the solution for the geometry of space giving a wormhole where two places connect (potentially different universes) at the event horizon. The other solution aside from a black hole for the Schwarzschild geometry is the impossible white hole. With this it is seen to be a double ended black hole where you could see light falling into the other black hole the other place/universe once you were inside the event horizon too - not that would do you much good.
It is theorized that at the Planck level (really really small - see Planck length) there exist a multitude of wormholes constantly forming and dissolving so fast that light cannot pass through before the wormhole
closes. The challenge here is to isolate one (very difficult) and then hold it open large enough to send something through it.
Holding it open is likely more close to being solved than isolation of one. To do this, one needs a source of "negative pressure" to keep the wormhole from collapsing. The tension in the matter that would provide this pressure turns out to be greater than the energy density of matter. The only type of matter that provides this is exotic matter - it has a negative energy density relative to light traveling through it. This type of matter is thought to exist and glimpses of its nature can be seen in the Casimir effect.
Ok, let's assume we've got a wormhole (or rather, a pair of mouths connected by a throat) that is big enough to be interesting (and safe) to more than physicists. What can you do with it? The most obvious thing is to send stuff through it and have it instantly pop out the other side. In one mouth and out the other. Makes things like the refrigerated storage in a soda machine pointless - you instead connect it up to a warehouse and never have to worry about running out. Taking a trip to is easy as walking
down a hall.
Well, thats neat but when you start thinking of the other possibilities its rather boring. Let's take one mouth and send it on a trip at a relativistic speed. "Why?" you ask? Ahh - this is where it gets interesting. So, we sent one wormhole out and back. While doing this, it aged less than its companion mouth. Now you've got a time machine. If the loop trip (in space) aged it a day more than its companion then if you look through the younger mouth you will see tomorrow. Take care and realize that you can't go backwards in time to before the mouth was created (no, you couldn't use a time machine to visit the 13th century because the mouth wasn't created them). However, you can go back and forth between the opening of the mouth and the closing of the mouth to your heart's content.
In exploring this time machine some the grandfather paradox crops up. Assume for the sake of argument that the throat of a time separated wormhole existed enabling you to go back in time. As many physicist-philosophers understand it, free will is limited - the past and the future are already set forth in stone. It is simply as impossible to change the past (or future!) as it is to walk through a solid object. You cannot kill your grandfather or alter the past. Period.
It is in the realm of hard science fiction that wormholes have been most explored. This is most often used as a time travel device, though rather to receive information about the future than to change the past (though it is realized that this is all fixed anyways). From Robert L. Forward with Timemaster as the the most real and believable (and in interesting scene done three times over with the main character meeting himself from different points in the future) to Stephen Baxter with his more speculative The Light of Other Days along with Arthur C. Clarke (though it isn't as accurate on the time travel aspect - what would happen if you could hold a wormhole open long enough to see another place in history?) and again with Stephen Baxter with Timelike Infinity and Ring (part of the Xeelee series) where Humanity is dragging wormholes on a loop trip of thousands or millions years to get to the end of time.
Realize, that much of this is up for debate (and often is in the rooms of astrophysics grad students). Some claim that it is impossible to stabilize the black hole and the impracticality of threading the throat of a wormhole with exotic matter to force the throat out of the event horizon of the singularity that forms the wormhole.
(not found or used, but reccomended:
M. S. Morris & K. S. Thorne (1988), ``Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity'', American Journal of Physics, 56, 395-412)