21st
The scientists at CERN have been able to trap and test antimatter for the first time in history. So a Spaceship with a warp drive could actually be built in the (somewhat) near future.
Add that to the list of Star Trek sciences that have come true.
“The energy per unit mass (9×1016 J/kg) is about 10 orders of magnitude greater than chemical energy, about 4 orders of magnitude greater than nuclear energy that can be liberated today using nuclear fission, and about 2 orders of magnitude greater than the best possible from fusion.
The reaction of 1 kilogram of antimatter with 1 kilogram of matter would produce 180 petajoules of energy or the rough equivalent of 43 megatons of TNT. For comparison, Tsar Bomba, the largest nuclear weapon ever detonated, reacted an estimated yield of 50 megatons, which required the use of hundreds of kilograms of fissile material.”