So does teleportation work by having a cloud of invisible-to-everyone nanobots disassemble you in one place and reassemble you in another, or by opening up an Einstein-Rosen bridge through advanced gravity manipulation?

Take a look at Karl Schroeder’s Ventus for inspiration for this, and then read his Lady of Mazes because it’s just plain fun (as well as a prequel to Ventus). Also Elizabeth Bear’s Dust.