its ok. Its clear quite a few folks are far from Physicists or chemists or biologists.
And actually transporters destroy matter, convert it into energy, according to E=MC2 this mass is preserved as an equal conversion. This energy is used to REFORM matter at the destination from raw energy. converting energy back into mass particles. You cannot move matter close to C through space without a warp field. You get around this by converting the mass to energy. The simplest example is antimatter annihilation. You take the complete mass of the object and convert it into its constituant parts (pure energy , no protons or neutrons or electrons just pure EM emissions). If you took hydrogen, and anti hydrogen which equals 1 proton 1 neutron 1 electron and 1 antiproton 1 neutron and 1 positron you would get 0 protons 0 electrons 0 positrons and 0 anti protons and instead get a massive amount of EM radiation. So energy IS matter, and matter IS energy...in a certain form. Startrek DID get this part right ....
Transporters are stated on many occasions to borrow from this idea , converting mass to energy, and converting energy back into mass. For this to work it would imply sensor and computer capacity and modulation from the hardware sophisticated enough to direct these converstions on a nano scale. Which is what the transporters do.
It is also clearly stated several times in canon and in the manuals replicators DO function based on transporter technology. They use raw materials, and using transporter technology reengineer it on a nano scale. "flesh from a cow" has quantifiable properties, it has atoms in certain locations. These can be duplicated if you have the scanning resolution ...and ....a transporter.
Problem with AUTHOR notes ...is that startrek retcons itself on every occasion possible. I go with the scientificly plausible and the technical manuals ..not the author notes