In Star Trek, a transporter takes a person apart atom by atom and then reassembles them somewhere else. It's been postulated that the transporter effectively kills the person and creates a duplicate. According to canon, this is not what happens (the inventor of the transporter dismissed the idea in an episode of Enterprise) but suppose this is exactly how it works.
Would you use it? Would you use a machine that kills you, then duplicates you with such accuracy that the new you doesn't realize that the original was killed, if it makes your ("your?") life incredibly convenient?
I am well aware ST canon says they don't work this way. I'm asking IF the transporters worked by the kill-and-copy method, would you use them?
This presupposes continuity of consciousness. Just because we are experiencing a moment of consciousness, complete with memories of past events, does not necessarily mean that consciousness has continuity.
Further, the TNG technical manual does state that the person’s atoms and data are simultaneously transferred via a confinement beam. So the reassembled “you” is made from the same matter as the disassembled “you” (duplicate Rikers notwithstanding).
But of course I think we all agree that consciousness is not tied to the specific atoms that make up a person — perhaps a physicalist would say it’s tied to the quantum and electrical states of those atoms, but then in that case, what percentage of your brains’ atoms could I replace with quantum identicals before your conscious experience is altered?
The simplest, and I suspect therefore correct, answer to these questions is that there is no continuity in consciousness, and a transporter duplicate of you has as much continuity with you as you a Planck time ago.