One of the big problems with any teleporting method that doesn't involved destruction at source and reconstruction at site from new material, that is, the Star Trek style of conversion to energy and reassembling same energy into matter at a focal point is the same as that of "Doc" Smith's FTL drive.
Let me explain for those who aren't familiar: Smith's drive worked by creatign a field that negated inertia ( Basically, prevent the Three Newtonian Laws from applying ) to the ship under drive, making it possible for it to accelerate up to and beyond lightspeed and doing so with being affected by relativity because that only applies to normal matter. Ignoring whether the relativistic time distortion would apply or not, the fact is that science says this *would* work; A ship could not only move at or possibly above lightspeed like other real-world particels without mass and inertia, it would make completely elastic collisions- Literally stopping instantly without damage on impact with another object while under this condition
But and to the point, Smith noted one thing about this drive; A sensible point as well. If a ship went "Free" ( Cancelled it's inertia) on the surface of the Earth, flew to Mars and landed, and switched off the drive to go "inert" , it woudl *STILL* have all the velocity it had while sitting on the Earth's surface, on a planet moving at a different speed and in some ways direction relative to Earth. This would be dangerous to catastrophic depending on the differences in relative velocities, so ships would never do this, usually going "inert" and matching velocities before landing.
So, how does this apply to Star Trek style transporters? Well, imagine a starship is orbitign a planet at the same height as the ISS does Earth. If a person is beamed down to the surface, the atoms in their body on board the ship are moving at a rate of 7.66 Kilomteres a second ( Or as a better illustration, in the time it takes to play The Proclaimers "Five Hundred Miles ( I'nm Gonns Be )" the ISS has moved almost precisely 1000 miles ). When the transporter moves them to the surface, what happens to that velocity? Energy, in this case kinetic energy, cannot be created or destroyed, so is it drained by the "beaming" in some way, perhaps as thermal energy? Because if it isn't, then the trasported person is going to suddenly be moving at the speed of a rifle bullet or better instantly. Even using such a transmitting of matter from point to point on a planet would have a similar problem – The rotation of a globe leads to differing speeds at different parts of the surface, so the velocity problem is lesser, but similar.
