NEW: U.S. Coast Guard crews searching for a medical plane that vanished on its way to Boston have found a debris field off Nantucket confirmed to be connected to the missing aircraft. The Gulfstream G100 was carrying six people, including four crew members and two passengers traveling from Bermuda to Boston for medical care, when air traffic controllers lost contact early Saturday. The discovery shifts the massive search as crews continue looking for the six people who were aboard. The flight's final communications reveal a troubling exchange with air traffic control before contact was lost. Read what happened before the plane disappeared: