A wormhole is a shortcut through space; like tunnels through a mountain. They named these theoretical tunnels "wormholes", because there are like the tunnels a worm leaves when it goes through an apple. Some people think that black holes are connected by wormholes through space.
It turns out that because of the way space bends, wormholes may not be stable. They may only exist for extremely short times, like millionths of a second or even less; too short for even light to pass through. If a way could be found to hold a wormhole open, it would by ok to travel through. One might wonder what would happen if it snapped shut while you were inside, trapping you in an eternity of...who knows!
The solution to this problem, although difficult, is not impossible. Another disturbance or "perturbation" would be needed to exactly oppose the one created by the spaceship, canceling it out. This would require a gravitational wave receiver/transmitter placed in the throat of a wormhole to record the disturbances and send out waves to cancel them before they can destroy the tunnel. That would be a cool job to sit in the wormhole and cancel gravitational waves. If the transmitter malfunctioned, though.......
Carl Sagan first desired to establish a physical basis for wormholes to use in a science fiction novel, "Contact", which in 1998 became a movie. Not being an expert in theoretical physics, he turned to two graduate students (Morris and Yurtsever) in the lab of Professor Kip Thorn at CalTech. Einstein had realized in the 1930's that black holes could theoretically be hyperspace links between two regions of space, but it was also believed that it would not be physically possible for human life.
The two graduate students found that nothing in the laws of physics prevents travel through wormholes, including the passage of human bodies. Of course, a lot of technology would be needed to get to and pass through a wormhole safely, but in the future it may be possible. With this info, Sagan wrote his novel "Contact" and published it in 1986.
Another problem is that wormholes can be hyperspace links to other universes, not just within our own. Also, a human would have to crash right into the point of singularity (extremely dense mass at the center that actually creates the wormhole) to pass through. This might be resolved by "charging" the wormhole with electricity and/or slowing it's normally rapid rotation somehow, altering the conditions at the point of singularity.
All of these obstacles aside, an advanced civilization could put together the technology to maintain and operate a wormhole. What a monopoly they would have on space-time!
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