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This is actually a long standing controversy in the philosophical world. The question, while likely to predate him, really became interesting when Des Cartes came out with his whole 'Cogito ergo sum' theory. In the Cartesian frame of reference, its easy to prove that you exist and are you so long as you keep thinking. However, if you stop thinking, even for a second, there is no guarantee that the person who starts thinking again is the person who was thinking before. So, physically, unless you plan on stepping intact through a wormhole as your teleportation, you are going to have a finite amount of transit time in your discombulated form. So, if you want to define thought as being a purely physical process, you have a bit of a problem, because your neurons are most assuredly not able to transmit their electrochemical impulses when separated.
The real problem is not the definition of thought but the definition of identity. This is what I mean: logically speaking, you can't ask what if questions about identity. In the world of logic, we can create an infinite number of possible combinations of the state of the universe (as a logical space not a physical space). So it is natural to ask, is there a link between yourself in this universe and all the other possible universes. In other words, if you were of the opposite gender would you still be you, or if you had a different color of hair would you still be you, or if you were taller or had a different favorite color, and on and on. There are two problems of note here. One, in logic, x=x is a tautology, meaning it is always true, but the question we are asking is what if x!=x, which makes no sense because it can't happen. On a more tangible level, the problem is that for any difference that you may have with bizarro you will express itself physically sooner or later, and after that point you and bizarro you will be accruing different memories, which is what most people associate with their identity. So, basically, if you want to talk about YOU in a non-physical way you have to pretty much admit that you can't really define what makes you you.
Peace be with you
G
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