Point of interest:
I may have missed it in this discussion but I distinctly recall Dr. McCoy hating the transporter and objecting that it wasn't the same persn after his molecules had been scrambled and beamed through space.
Several writers have toyed with the idea of sending the pattern by some means usually faster than light and using that pattern and local stock of chemicals in a vat to produce a flawless copy of the body.
It was in a Rod Serling show once;also a book I have somewhere in which a Civil War soldier is recruited to be the stationmaster for Earth,due to his isolated homestead and no close relatives.In these stories the body of the teleportee is broken down and chemicals stored for subsequent travelers on the travelers departure.
The one that is more comfortable philosophically to me is the method in the book "Jumper";a juvenile escapism and coming of age novel. The character eventually discovers he is stepping through a "door" to whatever other place he 'ports to;he also must know the destination well enough to accurately picture it in his mind.
Now this reminds me of the string theory of instant movement in which two points distant are momentarily considered to be congruent .
I'm not certain but I think Heisenberg or Heidinger cat may have stayed with me;that cat could disappear in only 3 rooms and a closet;hours of searching would reveal no cat,and the next morning she would be sitting there wanting breakfast.
Sadly,she got out whilst I was bringing in new furniture one fall day,never seen again. :-?