Yes--conservation of mass is problematic.
Well... conservation of mass is a problem in the real world, but the transporter's specifically stated function is the conversion of mater into energy and then reconverting it back.
Like the holodeck and replicators, they create matter from energy.
I just want to say something a little off this topic but about Enemy Within. Scotty calls and says he's found a new problem with the transporter, there's a big hole blasted into the machinery. Ok. I guess Kirk and Spock didn't mention that? It was the hole from Kirk v2.0's phaser. Don't you think you should mention to your Chief Engineer that there was a big hole blasted into his equipment before he has to just stumble upon it? That always makes me wonder a bit. I know they may certainly not wanted to mention there are two captains and one of them shot it trying to kill the other one but maybe just tell him there was damage in engineering. Maybe they did tell him and that's how he found it, but it seems like he's discovering it himself the way he delivers the lines.
Like the holodeck and replicators, they create matter from energy.
Replicators just assemble objects from pre-existing material stores, like a more elaborate 3D printer. Holodecks only shape force fields and volumetric imagery into the illusion of solid matter; any actual solid object in a holodeck is replicated.
I just want to say something a little off this topic but about Enemy Within. Scotty calls and says he's found a new problem with the transporter, there's a big hole blasted into the machinery...
Yes, Kirk was losing his power of command even that early in the episode was dropping the ball on a lot of stuff. More info here:
http://www.trekbbs.com/showpost.php?p=7338859&postcount=12
I think in one of the novels (the one where the Kirk's ship almost meets Picard's ship) they explain how the transporter works to Zefram Cochrane and I sort of bought the explanation there. What was best about it was that nobody 'died' in the transport processGiven the absurd energy and data requirements in taking a person apart atom by atom compared to how often the Transporter is used under low power conditions (shuttles' emergency transporters, using a hand phaser to power one, operating them using emergency power in TWOK etc) I also strongly favour a different interpretation.
From the little evidence we have about the transportee's POV during the process (Barclay in Realm Of Fear, Kirk's ongoing conversation in TWOK), it does seem that they are awake and conscious throughout. That would strongly suggest that the subjects are somehow phased whole (perhaps into a semi-energy state) and then relocated to the target destination where upon they remerge into our familiar dimension of existence.
Timo has expounded on this theory better than I elsewhere on the BBS.
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