The Teleporter Problem

Consider a teleporter that scans every atom in your body, transmits the information, and reconstructs you perfectly at the destination while destroying the original. Is the person who arrives you?

If identity is an information pattern, then yes — the reconstruction is you. If identity is physical continuity, then the teleporter kills you and builds a copy who merely thinks it is you. You would never know the difference, which makes the problem even more disturbing.