Why do you think that it isn't you? I think that it is you, just in a different spot at the same time, like a mirror image but this one reacts independently from you.
Think about it in the 3 different scenarios:
1) The original body is destroyed and 'you' are transported.
2) The original body grows old and dies, then 'you' are transported.
3) The transport happens, but without the destruction of the original body.
With (1), it's pretty easy to picture. I can picture myself stepping into the transporter, thinking about wanting ice cream. I appear on Mars still thinking I want ice cream, and go on about my day. No problem, right?
With (2), the same things seems to be happening. My body is destroyed (it dies) and yet it doesn't seem like my consciousness would somehow be transferred into this new body. So why would it with (1)? There's some doubt.
With (3), my body and consciousness stay right where they are. It seems ridiculous to say that my consciousness has been transferred.
The conclusion of this, at least for me, is that there is something non-physical going on. Now, it could be an artifact of a physical construct (like the brain) but I'm having a hard time pinning down exactly what is going on here.
But more to the point. Say, in (3) you look at that other 'you' but clearly that isn't you! You're you! That's just an exact replica of you. Sure, the experiences of each will differ once the copy is made. But the problem is explaining why we might think that consciousness would transfer in (1) but not in (3). The conclusion to draw is that we're mistaken - our consciousness would not transfer in (1). But now we get into 'spooky' stuff.
Please dont turn this into another religious thread.
I would hope you would know better than to think I would try to do that. On the other hand, if the only reasonable explanation for the inconsistency between (1), (2), and (3) is something non-physical, then we shouldn't close our minds to that.
your thinking "im still right where I was" and he's thinking "now i'm over here but the original self is over there"
Let's change (3) a little, because I like were you're going. Let's say that you enter a chamber, are a bit disoriented, come out, and there's another you. You're thinking to yourself "Oh, cool. It's my clone." But then your clone says "Oh look, it worked. There's my clone."
Because you both had identical mental states, you would both think you're the original. And you know that your clone was created intact with all your memories up to and including the cloning process. How can you be sure you're actually the real you and haven't just popped into existence? There's no experiential difference!
*Note: I keep using the word 'clone' here, which is misleading. I should say twin or something like that. A clone is genetically identical. But this process produces something that is physically identical at even the molecular level. Hopefully this won't get too confusing.