Wormholes
Wormholes have always captured the imagination in science fiction, to be able to move from one place to another, where that place could be a great distance away, almost instantly is amazing. Famous science fiction with wormholes include Stargate, Star Trek, Dr Who and if you go back quite a few years "The Time Tunnel".
Scientific theory states that there could be millions of wormholes being created and destroyed at a quantum level all the time. The great challenge is to: (1) create one at a quantum scale which goes where you want it to go and (2) grow it big enough so that you can safely travel through it without being ripped to bits. Both of these tasks are currently impossible with current technology, although if we could make a quantum scale wormhole we do know how to make it get bigger, just simply use anti-gravity. Unfortunately science has never seen anti-gravity although it has not disproved it either. To create anti-gravity you would need negative energy and current technology hasn't developed negative energy!
The bottom line is that it's not absolutely impossible in theory, but our current knowledge of science isn't anywhere near sufficient and will not be for a very long time. The exciting aspect is that it could be possible!
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