A 4,000-mph magnetically levitated train could allow you to have lunch in Manhattan and still get to London in time for the theater, despite the 5-hour time difference. It’s not impossible: Norway has studied neutrally buoyant tunnels (concluding that they’re feasible, though expensive), and Shanghai is running maglev trains to its airport. But supersonic speeds require another critical step: eliminating the air—and therefore air friction—from the train’s path. A vacuum would also save the tunnel from the destructive effects of a sonic boom, which, unchecked, could potentially rip the tunnel apart.
One proposed route for the transatlantic maglev train passes through northeastern Canada before barreling toward the British Isles and continental Europe, briefly kissing terra firma on Greenland and Iceland. Because aboveground sections would be cheaper to build than their underwater counterparts, such a route would be more economical than a direct shot through the Atlantic
To prevent drift from currents or storms, neutrally buoyant tunnel sections will be anchored 30 to 40 feet into the seafloor. Sections of the tunnel could be manufactured in drydock, then hauled to the site.
source : http://www.popsci.com/gear-gadgets/gallery/2004-11/trans-atlantic-maglev