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On teleportation: A thought experiment

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I would be glad to know your Lordship's opinion whether when my brain has lost its original structure, and when some hundred years after the same materials are fabricated so curiously as to become an intelligent being, whether, I say that being will be me; or, if, two or three such beings should be formed out of my brain; whether they will all be me, and consequently one and the same intelligent being. —  Thomas Reid letter to Lord Kames , 1775 If only nature could provide some way to distinguish between identical and the same  then one could answer Thomas Reid's question.  If a reconstructed Thomas Reid were the same being then that being would be him; if it were an identical being then it would merely be a person with the same memories, but without any continuity of experience linking it to the original Thomas Reid.  Incredibly, it turns out that nature does provide a way! A well known feature of modern physics is that if you perform the same experiment t