Identity and Change in Conscious Beings
The problem of personal identity relates to change as applied to people. The molecules that make up each individual change almost completely over a period of years. Usually, there is no trouble in saying that a little girl in 1920, for example, is the same as an old woman in 1998, even though they share a relatively small number of molecules in common. The same person is just described in two different ways, first as a little girl, and second, as an old woman. In fact, we are confident enough of our ability to reidentify people over time that we are given names that are supposed to last us from when we get them until we die many years later. The question is exactly why we call the old woman in 1998 the same person as that little girl in 1920.
However, according to quantum physics, individual molecules (and atoms, electrons, protons etc.) have no identity. For example, every electron is the same and in quantum mechanics, one can not keep track of an individual electron precisely. Therefore any electron can interchange with another one with no observable physical change of the system at all. Thus, any real object cannot remain the same, also because of movement of its physical parts (even much bigger than molecules). Similarly to Leibniz solution, in a real life, we can say the person (or any macroscopic object) is the same, because all signs refer to the person (or object) in the past, which evolved in time.
Read more about this topic: Identity And Change
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