But rethinking the transporter so it almost sounds quasi-possible, we're left with maybe a device that generates a stable wormhole with a finite range and apparently only the ability to be focused in the location and not the actual time part of spacetime. The warp drive itself does something similar by creating a stable wormhole around the ship during FTL flight, though its called the warp bubble, and it CAN sometimes be used to alter spacetime in more than the spatial directions.
Anyway it would explain why the transporters sends you forward and back with your clothes and items and not butt naked.
"Beam me down to Alpha Centauri A.. also remove 50% of my cellulite. I'm feeling lucky"