The teletransporter
Derek Parfit · Reasons and Persons · 1984
You step into a teletransporter. The machine records the exact state of each of your cells, destroys your body, then transmits the information to Mars, where an identical body is rebuilt from fresh matter. The person who walks out has all your memories, your character, and the feeling of having just stepped into the booth. Convinced she is you, she takes up your life where you left it. Usually the trip goes without a hitch; but today, a question holds you back on the threshold.
Is the person who wakes on Mars you, or did you die in the booth, replaced by a copy who believes she is you?