That depends on what “you” are. If you are just your brain or nervous system, as in the specific atoms and such that make up that brain, then sure, obviously those atoms can’t be in two places at once, so you are wherever they are. On the other hand, if you are the structure of those atoms and particles, the way they are arranged, the patterns of movement they form as they go about their work, the information they contain by all this; then it stands to reason that a sufficiently perfect copy is the same as you, because if whatever makes you “you” is part that structure, whatever makes it “your” consciousness instead of someone else’s, and the copy has exactly the same structure, then the copy must also contain whatever that part is that makes it “you” and not someone else, and therefore has to be you as well.

This isn’t a settled question, so one sort of has to decide what answer one thinks is more likely, I personally think the second.

Consider a hypothetical for a moment. Suppose there are two people, I’ll call them Bob and Bill for the purposes of distinguishing them. Suppose they get captured by some sort of mad scientist, who runs an experiment on them both. They wipe the brains of both people in such a way as to not completely kill them, but such as to remove every trace of their memories, personality, etc, essentially rendering them braindead, but without the physical damage that usually entails. Then, they painstakingly re-create those same neural pathways, same memories, personality, etc, but they recreate Bob’s persona in what is originally Bill’s body, and likewise, recreate Bill’s memory and personality in Bob’s. Which of these two people is now Bob (or if one thinks neither really are and that Bob is just dead, who at least has the better claim)? The one that has the physical brain, nervous system etc of the original Bob, but remembers and thinks exactly like Bill? Or the one that acts like Bob, and remembers being Bob, and probably thinks he is Bob and would insist on his being such, but does not have the same material in his brain as the original? If one of Bob’s friends raids the lab trying to rescue him, which should he take back home?

The activity of something is essentially information (consider how computer programs are ultimately just the activity of the components of a computer). If I copy information from one substrate to another, and do so with no changes, I don’t have any new information. Applying that back to brains, assuming that consciousness really is only brain activity (which seems highly likely, but since we don’t really understand the nature of consciousness, isn’t completely proven), then I’d disagree with the new brain= new activity step

then we get to really specifically define individual, perspective, and perception (can you perceive while unconscious? I guess?), all sorts of fun knots to tie oneself into. I always thought the difference in sense vs. perception was the thinking about it, but if it’s processed at all by the “unconscious” I guess it’s still perception? I mean, I’m gettting twisted up thinking if my individual consciousness has a perspective from which it perceives the world