Doesn't it Galileo's transporter you?
...takes the you matter and dissolves it into a stream of particles which are reassembled in a different location, so when transport is 50% done, you're in two places at once (whilst the "plan" for you is in the pattern buffer, don't know where the matter is exactly)... i mean, it forms you into a beam of molecules right? Beams you up.
At one point there's a Barkley episode and he seems conscious for most of the process, just in a kind of super position.
After the half way point, there's more "you" in the destination than in the original location...so who are you? Where are you?
Then again, we know that accidents and reflections can be produced... So maybe I'm wrong and new matter/particles are being introduced otherwise how would Tom Riker exist...
...I mean, after all, Tuvix wasn't twice as dense as your average crew member.
Anyways, Dr. Polaski supposedly has McCoy's attitude towards transporters. However I think even she gave in here and there, as did McCoy.