> They do though. Particles have a unique path through time and space that cannot be replicated.
That path is not encoded in the particle state. If you brought me two samples of isotopically pure carbon, one sourced from the earth, presumably there since the planet formed and another bunch synthesized in a fusion reactor and I put them into a black box that shakes, whirrs, spits out two equally sized boxes of carbon and then destroys itself you will not be able to tell whether it mixed them or passed through the original samples.
This kind of information can only be inferred from ensembles of particles and even then only under some assumptions about the underlying processes.
We only recognize fossils by radio-dating, the rock layers they're in, their mineralogy and so on. Never by things encoded in individual particles. So if you can assemble things atom by atom then with enough effort you could make a perfect forgery. And assembling things atom by atom, well, that's what this supposed teletransportation "paradox" is about.
> Hypothetically, if a gunman has you, and a clone of you in a room and is going to kill one of you, are you saying you have no preference which dies?
Assuming the copy was made moments ago and I am 100% confident that this is indeed a perfect copy (and that kind of confidence is rather hard to come by) and the outcome is that exactly one of me will die is entirely inevitable then it does not really matter which one it is. Intuition does not work in these cases because such scenarios do not occur all that often in real life. Alter the situation slightly and my preferences would start to shift.
> If these things are the same, how is it he could kill the clone in a different room and you wouldn't know?
You seem to be ignoring the point of copies diverging over time (I explicitly mentioned that in my previous post). If I were copied and then immediately thrown into a cell and then one of the copies get killed I would not be able to tell which one was the original and which one the copy. Thus the distinction is irrelevant at that moment. I would be more concerned with my redundancy getting reduced further, hitting zero means irrecoverable loss.
> Similarly, I still arrive if ships identical to the original state sank while I am en route.
Let's assume you're actually traveling inside a hotel container on a container ship. Assuming some gentle crane action while you had the container doors closed you wouldn't be sure whether they just moved around your container within the same ship or moved you onto another ship that looks identical.