In the simpliest form, a wormhole is a theorized tunnel connecting two points in space. It is also known as the Einstein-Rosen bridge or Einstein-Podolsky-Rosen bridge after the people who theorized about the concept. The most well kown of these three people is Albert Einstein, the German born American scientist. The other two are Nathan Rosen and Boris Podolsky. All three published a paper called `Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?`. If you have watched anyone of these programmes, you would have come across a wormhole in some form of other (Farscape, Star Trek, Andromeda (Known as a slipstream), Stargate).
Take a piece of paper, make a hole near the top and a hole near the bottom. The shortest between those two points is a line ? Wrong, fold the paper over and line up the two holes. Imagine a tunnel between the two holes, that would be the wormhole.
They came about because of Einsteins` Theory of gravity, aka General Relativity. They`ve not been spotted or created but the maths proves they exist so spotting or creating one is the next step. In 1919 Arthur Eddington, proved that mass warps space which is a major feature for wormholes. He did this by travelling to the West African Island of Principe for the solar eclipse. He proved that the Sun bent light from the stars as it passed in front of them. Einstein said that to create a wormhole, we would need the power of an exploding star. The only available star is our Sun which is probably not a good idea to do.
If you are familiar with wormholes in Farscape and Deep Space Nine then you are familiar with Lorentzian Wormholes. These wormholes use a lot of negative mass to support them and not fall apart. Visser describes Negative Mass as "where the energy of the universe is less than that of ordinary universe". How I understand it ( according to Miami ), if you pushed something with normal mass, it moves away but negative mass, the object would come to you. If the two equalise, then the wormhole will fall. If you are in the wormhole as you travel through, there is the strong possibility you would become trapped inside. All the wormholes that you see on television are Lorentzian wormholes. As they are the ones that people can traverse through, they have therefore caught more people`s imagination.
A Schwarzschild wormhole can be thought of a one-way wormhole, you go through, you don`t come back. They are believed to be found in the centres of White and black holes. They are extremely unstable and would collapse immediately after creation. They exist because of Eisteins equations.
These wormholes are more of interest to particle physicists. They seem according to my research, something that isn`t for people to be travelling through.
Inter wormholes connect a location from one point in our universe to another point in our universe as we see in Deep Space Nine et el. Intra wormholes are those made famous by the Sliders television series where they step through the wormhole and arrive at exactly the same spot in a mirror/parallel universe.
In the Voyager episode `Eye of the Needle`, the crew find a wormhole that could send them back home so soon after beginning their voyage. What they later realise is the entrance is forty years in the past. The whole time travelling question has yet to be answered but when it is, then the question of whether time-travelling wormholes can exist theorectically be answered if not discovered.