“Wormholes are hypothetical entities that show up in theoretical analyses of Einstein's theory of gravity (general relativity). Nobody has yet seen a wormhole, nor are we certain that they exist, but they seem to show up so easily when we do calculations that many physicists suspect that they might actually be out there in the real universe.”
Source : Scientific American (quote from Professor Matt Visser, School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, NZ)
The name 'Wormhole' was first suggested in a 1957 paper from American theoretical physicists John Archibald Wheeler and Charles Misner.
Since then, many cosmologists have provided theoretical (i.e. mathematical) workings which show that they could exist - not only 'connecting' parts of the universe billions of lightyears distant (as well as billions of years apart in time) but also providing 'shortcuts' to other 'universes'.
At present there is no proof that such structures actually do exist.
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