Teletransportation, Fission, and Identity Puzzles

Derek Parfit's teletransporter thought experiment, presented in Reasons and Persons (1984), imagines a machine that scans a traveler's body on Earth in complete physical detail, destroys the original in the process, and transmits the information at the speed of light to Mars, where a second machine assembles an exact physical duplicate out of new matter, complete with all the traveler's memories, personality, and intentions apparently intact. Parfit asks whether the person who steps out on Mars is really you, having survived an unusual but ultimately benign form of travel, or whether you have died on Earth and been replaced by a mere replica who merely believes, falsely, that they are you.