Of course they're possible! In 1593, a royal guard FROM the Philippines found himself in Mexico, which was several weeks travel time away. No one believed he was instantly transported FROM the Philippines, so to prove his claim, he stated that the governor of the Philippines had been murdered the previous night. More than a month later, people who traveled FROM the Philippines to Mexico by ship verified his claim.
Today, there are people who claim to have been transported through space or through time by an unseen force. Many of these people SHOW signs of exposure to radiation.