Exotic Matter is matter or equivalently, energy with negative mass hypothesized to exist as a result of solutions to Einstein's equations for General Relativity. Evidence for its existence is seen in the Casimir Effect. It would allow for traversable Worm Holes, Warp Drive, Time Travel etc. Not the same as Anti Matter although perhaps there is a way to transmute from one to the other (neo-alchemy?). For more details see
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It is not equivalent to energy with negative mass, nor is it correct to refer to energy with mass of any sort in the first place. It is not even particularly related to the Casimir Effect (which in itself has only small, not large, experimental support), let alone does the latter provide evidence for Exotic Matter. It is not even a little bit related to Anti Matter, and it is about as meaningful to speculate about transmuting water to exotic matter: i.e. complete nonsense. Anti Matter may sound futuristic and cool and exotic, but all evidence is that it utterly normal in all regards except for its definition of inverted charge. There's no relationship to Exotic Matter.
If Exotic Matter turns out to exist, it might (not "would") allow for cool science-fictional uses of one sort or another, but then again, it might not. Most physicists would say probably not, even if it exists.
See original on c2.com