I've written a previous article explaining how teleportation and/or mind uploading will actually be "the real you". But I realized it was hard to read, so I'm going for a simpler, condensed explanation in this article (with pictures).
The essence of this "proof" is a very simple proof by induction common to mathematics.
Imagine there are two brains, A and B. Brain A is your original brain. Brain B is a perfectly physically identical copy of your brain that was created/materialized in a new location.
- Swapping a 1-atom chunk from each brain, won't result in your consciousness "jumping over" from brain A to brain B.
- If swapping an X-atom chunk from each brain won't result in your consciousness "jumping over" and changing locations, then neither would swapping an X+1 atom chunk. For example, if in one case the swapped chunks were 1 trillion atoms big, and you hypothesize there is no "jumping over" in this case, it would be irrational to claim that there would have been a jumping over if the chunks had been just 1 atom bigger.
- #1 establishes the base case, and #2 establishes the proof-by-induction ladder all the way to swapping the whole brain. Therefore, swapping your whole brain must be the same as not swapping anything at all.
- You are your physical brain: False. You are the information which is produced by the physical brain. Your consciousness is the information itself, not whatever substrate the information happens to be running on.
- There is a continuous self, aka "I think therefore I was": False. There's only "I think therefore I am". You can consider your present self to be a new consciousness that beliefs they're the old one from yesterday. There's no physical evidence for an extra thread of continuity to your past self any more than what your brain's memories are telling you to believe.