Parfit asks us “to imagine entering a "teletransporter", a machine that puts you to sleep, records your molecular composition, breaking you down into atoms, and relaying it to Mars at the speed of light. On Mars, another machine re-creates you (from local stores of carbon, hydrogen, and so on), each atom in exactly the same relative position. Parfit poses the question of whether or not the teletransporter is a method of travel—is the person on Mars the same person as the person who entered the teletransporter on Earth? Certainly, when waking up on Mars, you would feel like being you, you would remember entering the teletransporter in order to travel to Mars, you would even feel the cut on your upper lip from shaving this morning.
Then the teleporter is upgraded. The teletransporter on Earth is modified to not destroy the person who enters it, but instead it can simply make infinite replicas, all of whom would claim to remember entering the teletransporter on Earth in the first place.
Using thought experiments such as these, Parfit argues that any criteria we attempt to use to determine sameness of person will be lacking, because there is no further fact. What matters, to Parfit, is simply "Relation R", psychological connectedness, including memory, personality, and so on.”
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