The year is 2055, and some eccentric billionaire of the future has invented a technology called the teletransporter. If you enter the teletransporter, it will scan your entire bodily composition. It will map every neuron in your brain, every synapse, every atom in your body from the top of your head to the bottom of your feet. And then it will atomise you.
It will send these atoms at the speed of light across to Mars, where another teletransporter will reconstruct you perfectly, atom by atom, the way you were.
And so, Derek Parfit asks in this thought experiment, "Is the person on Mars the same person that left Earth? Or have you actually killed the Earthling and reconstructed a Martian replica?"
The thought experiment is confused even more if we suppose that we could create thousands of replicas of you on Mars without even destroying the Earthling version. There would be thousands of people walking around with your body and your brain, and (we suppose) your memories and your personality.
And so, the question that Parfit leaves us with is, "What makes you you?" Because while we all change over the course of a lifetime, this change is not drastic in the way that the atomisation of the teletransporter really is.
So, would you enter the teletransporter, or are you worried that it would be a quick death and somebody else would walk out on Mars?