Teletransportation

Suppose we discover how to make a teletransporter that works like the one on Star Trek. It decomposes your body and your brain and records all the information about them. It then radios a signal to Mars, where another machine uses raw materials on Mars to create a person who perfectly duplicates you. This person walks and talks just like you. It thinks it's you. It seems to remember your life. Would this person be you? Would you survive going through this teletransporter? Or would this person on Mars merely be a copy of you? Would you use such a teletransporter?

Suppose that I kill you, painlessly and without warning, but I introduce a perfect duplicate of you into your life. So no one knows you're gone, because they all falsely believe that the duplicate is you. Even the duplicate thinks he is you, because we gave him a bunch of false memories of your childhood.

Some philosophers think that's exactly what it would be like, if you went through a teletransporter. On their view, teletransportation isn't a way to TRAVEL. It's a way to get yourself killed, and to have a perfect duplicate of you made at the other end. It might not make much of a difference to your family and friends, whether they're dealing with the original or the duplicate. But since you're not the duplicate, you're you, and you'd like to still be around next week, it will make a big difference to you.

Suppose you step into the teletransporter, and it records all the information about your body without destroying you. Then as before, it creates a perfect duplicate of you on Mars. You can hang around and talk to the duplicate on the phone or via webcam. Then after an hour or so, we'll kill the person left on Earth. (Since it would be inconvenient to have two versions of you running around.)

In this case, when there's a delay between the time when the machine records the information about you and the time when your body on Earth is destroyed, it does seem that the person who comes out of the teletransporter on Mars is only a copy of you. So why should things be any different if your body is destroyed immediately after the teletransporter records the information about you? Or if it's destroyed simultaneously? Why should those matters of timing make a difference to whether the person who steps out of the teletransporter on Mars is really you or just a copy of you?

So now we have two different views of how teletransporters work. Which is correct?