context: After claiming he is an extraterrestrial from the planet 'K-PAX', 1,000 light years away in the Lyra constellation, prot (uncapitalized and pronounced with a long O) is committed to the Psychiatric Institute of Manhattan. There, psychiatrist Dr. Mark Powell attempts to cure him of his apparent delusions. However, prot is unwavering in his ability to provide cogent answers to questions about himself, K-PAX, and its civilizations. Dr. Powell introduces him to a group of astrophysicists, to whom prot displays a level of knowledge that puzzles them.
  prot also exhibits total control over the other patients at the Institute, each of whom believes unquestioningly that he is indeed from K-PAX. prot, who claims to have journeyed to Earth by means of "light-travel", explains that he can take one person with him when he returns. Thereafter, most of the patients at the Institute ask to be taken by prot on his journey back home.
  Upon learning that many of his patients expect to leave Earth on July 27, Dr. Powell confronts prot, who explains that it is a predetermined date. However, Powell believes this to be a significant date in prot's life, a day on which he suffered a severe psychological trauma. Powell decides to subject prot to regression hypnosis, which works well. Using information gained from these sessions, Powell figures out that prot may simply be an alter ego of Robert Porter, a man from New Mexico whose life had been devastated by the murder of his wife and child in 1996.
  On July 27 as the hospital staff watch, the camera in Porter/prot's room cuts to static at the precise time prot said he would leave Earth. Powell finds Porter lying on the floor in his room, catatonic, prot having apparently left Porter's body for the light travel back to K-PAX. The other patients do not recognize Robert as he is being wheeled out of the room. In addition, one of them is missing: Bess, a woman who had remained mute since her home was destroyed in a fire and who had been among the patients that asked to go to K-PAX with prot. She is never found. Powell continues to take care of the catatonic Porter and tells him about how the patients he helped have gone on to live normal lives again, but Robert does not respond. Powell is left with no absolute answer as to whether prot was in fact an alien entity or just a coping mechanism of the traumatized Porter, but seems far from convinced that prot/Porter's behavior was a delusion.
  The final scene's voiceover is prot explaining to Powell that the people of K-PAX have discovered that our universe will repeat its events again and again, so the mistakes we make will be repeated forever, and prot encourages Powell to make this time count as it is the only chance we have. With this in mind, Powell reconciles with his estranged son.
question: How had Prot travelled to Earth?
answer: light-travel