It has been argued that if you duplicate a person the duplicate will not be the
What makes you the same person over time may not be that there is some essence that you have at each time, but rather that your different 'slices' are related to each other in the right way. Think of climbing rope. Modern synthetic ropes do have a single filament running their entire length, but the old-fashioned ropes are made of of many relatively short fibers woven together. So there is no fiber that runs the entire length, but still different 'slices' of the rope are all part of the same rope, because of the way they are connected to each other. Admittedly, just what 'related to each other in the right way' comes to in the case of people is a more difficult question. If you want to pursue the topic of personal identity, a good place to start is John Perry's A Dialogue on Personal Identity and Immortality.