It is the year 2112. Telepods have been in use for a decade to instantly transport matter from one part of the universe to another. You are waiting in line with your family at a telepod station to go to Tau Ceti. In front of you in the queue you meet the inventor of the telepods. He tells you that the telepods only appear to move matter, what they actualy do is create an exact duplicate at the destination and destroy the original in the process.Do you get in the telepod?
You don't need a telepod for this. The structure of our bodies is continually being replaced - we are in fact being destroyed and renewed constantly. The telepod is merely an extreme version of what life does to us anyway.
See also http://en.wikipedia.org/wiki/Ship_of_Theseus