Ah, this is a classic thought experiment! And it has an easy solution. The solution is to get rid of a silly assumption, namely that
that doesn't make sense, does it? I can only be *one*
Let's say you get a copy made at time X. The copies will immediately begin to diverge, as you suggest. Both of them, however, will be 'you', complete with your unshaken conviction that you are you
and that the other one is just a copy. So, while you can be only *one*, there are now *two* of you, and both of them are the 'real' you.
This is because the process that made the copy is no different from what happens to you every day of your life: different material cycles through your body, but the overall pattern of information remains the same.
Here's a thought experiment that helps illustrate that: you have created a copy which is linked to you by a neural bridge. This bridge keeps the copy in perfect sync with your thoughts. It will only begin to diverge when the link is broken.
You are hit by a car and you die. What do you experience?
Well, one minute you're walking along. Suddenly, WHAM. You wake up in a lab in your replacement body. "Holy ****," you say. "I'm glad I had that copy."
Meanwhile, EMTs resuscitate Old You. What does Old You experience? Well, from Backup's POV, Old You walks in and looks you over and says 'wow, that's a good copy.' You think that it's going to be really awkward explaining this to your wife.
From Old You's POV, you walk in to a room, find your copy, and say 'Wow, good copy.' You think to yourself that it's going to be really awkward explaining this to your wife.
You've forked. But both of the forks are the real you. They will now develop into different people - just as you are different from the person you were five years ago.