Wouldn’t the whole copy thing only apply if teleportation was achieved through entanglement? If I remember correctly, Star Trek’s transporter converted matter to energy and vice-versa, so really you’re just changing the form of your body to energy and back to matter. Not creating a copy.
No, nothing like that happens in Way Station.
As for teleportation demonstrating the existence of a soul; to semi-steal an idea from Spider Robinson (he used it in regard to cryogenics), if you teleport Bob Harrison of Colorado and end up with someone in his body who has the personality and memory of John Anderson of Idaho who died twelve years ago that would be good enough for a soul hypothesis to be taken seriously.
So I think you’ve established that the transported “you” is a different person, regardless of when the original is destroyed. The key is that the new you won’t remember having been killed, but the old you will have joined the choir invisible.
No; “when” matters because it requires change and therefore time for the two instantiations of the person to diverge.
What is a perfect copy of you? Is it you or isn’t it you? The answer has to be the same regardless of when the original is terminated.
No, because the copy and original will both immediately start changing once the copying process is complete; unless both are frozen solid the “perfect copy” state can only last for a moment. People aren’t static.
That only addresses the question of how long a perfect copy remains perfect. It doesn’t go to the question of whether it’s actually you.
See, I would consider a perfect copy of me to be me as well. Just that there are two where once there was one.
And we would watch Pierce Brosnan movies together, and braid each other’s hair, and paint each other’s toenails, and talk about boys . . . Oh, and there could be a pillow fight! 
Would having sex with your duplicate be homosexual or just advanced masturbation?
Just ignoring the joke for a moment –
So identical twins are a single person?
Would you have one consciousness that recorded all the sensory experiences of both bodies? Would the two bodies have just one set of thoughts?
Here’s the nub of the problem – the person entering the teleporter would experience a shutting off of consciousness. How could you possibly recreate that conscious entity? It wouldn’t be like going under general anaesthesia and then waking up. What appeared at the other end would be akin to a copy with a new consciousness.
And furthermore–what if it is? What if, every time you go under anesthesia, you die? If every time you sleep, you die?
Do you? If so, then we have a problem, don’t we? Wouldn’t we want to avoid general anaesthesia?
We don’t have evidence that sleep results in death, do we? We actually have monitored people sleeping. Have we found that they die?
What evidence regarding sleep indicates that it’s akin to disintegrating the body entirely?
The copy thinks he’s me too- he only knew he was a copy because he noticed that he’d moved and that the original was standing where he’d been standing a moment before. If you want to up the fun by confusing the issue you make two identical rooms with a glass wall between them, such that each room looks the same from the other. Then you put the victim in one room, and then make the copy spontaneously appear in the same place in the other room. Assuming there are no tells like a puff of smoke, both the original and the copy will see the same thing (a copy of them appearing in the other room), and neither will be able to tell they’re the copy.
You can be nearly certain that both will assume that they’re the original - or if they don’t, then both will assume they’re the copy. Assuming you made the rooms good enough duplicates of the other, anyway. You could then kill the copy and the survivor would think he was the copy.
Does it? I’d think it depends on how you define ‘you’.
I can talk to people, I have a recognizable personality, I can solve intellectual problems, and so on. I walk into a room, and while I’m in that room, something happens that causes me to not have a recognizable personality, to be inable to solve intellectual problems, and incapable of talking. Then, a while later, a person walks out of the room again, who seems to have my personality and problem-solving skills and so on.
Did I die and come back to life? Did I die and some new person replaced me? Did I just sleep and wake up? Does it matter?
The term ‘dying’ has meaning. Assuming you’re talking about that thing you do on a nearly-daily basis, you didn’t die, unless you’re lekatt.
Whether you’re a new person - how would you tell? Well, if you left behind another person in ther room who was wearing the clothes you went in with, you might have reason to be concerned. But otherwise we humans tend to use occam’s razor with regard to the changeling hypothesis.
Maybe it doesn’t matter if you’re just an observer of the guy walking into the room, but if you’re the guy who’s about to step into a teleporter, it does matter.
another way to look at it - if you throw a (multi-universe) time machine into the mix, are your alter egos you? does the existence of a time machine itself means everyone is immortal? perhaps by the time we attain godhood by creating life and mastering time, we’ll understand what 42 means and the concept of self wouldn’t matter much anymore.
It’s only a problem for the copy if you see the original and have your illusion of continuity of self shattered.
It only matters to the original if it hurts or is scary. (Seeing your copy appear and seeing the dude pointing the blitzer at you would certainly qualify.)
Though it will matter to both/either of them if they think about it too much - but then, you could say the same about riding in an airplane. Do you have any idea how high you’ll be, shooting along how fast in an aluminum can with jet engines strapped to it???!?!!?
The higher the likelihood of my being disintegrated while riding an airplane, the higher the likelihood that I would think twice about doing it. If there’s a 100 percent likelihood of it, I’ll forego it.
What if there’s a 100% likelihood that you’ll step out at your destination unharmed with no memory of any disintegration?