suddenly having two would violate the conservation of matter
Ah, is time travel possible? That's a totally different argument, which I did not address, accepting it as a given in the story. As shown on screen, the episode does not invoke any paradoxes, but I addressed paradoxes because of the original post.
So I figure that when the Enterprise goes back in time, the first-time-around ship must vanish from that location ... skipping over part of the timeline and getting instantly to where the ship now appears.
And that would
be a paradox because then the "inexperienced" Enterprise
would not be there to undergo the events that led to the engine implosion and time displacement.
Just for the record, some sci-fi authors try to slide around causality by invoking quantum mechanics (e.g. Orson Scott Card's PASTWATCH). And QM is a form of magic accepted by most contemporary physicists. Working from the assumption that time is broken down into quanta like the frames of a film, a paradox can happen from the point of time displacement forward—basically, an effect pops out of nowhere with no cause, as the paradox erases its cause. But by this "logic," causality ceases to have any meaning, and so the paradox becomes a paradox. (Again, magic. It happened that way just because the author wanted it to happen that way, and audiences accept it because it is "scientific.")
Look up Klein bottle—that is the shape of time (or at least some topologists use it as a bong). That is what the mythical "outside observer" would see, like a projectionist with a reel of film. The reel contains all events from start to finish; the events do not "happen" to the outside observer. That history simply "is."
And conservation laws are a philosophical construct. As with many other notions in science, they cannot be proven
, but we accept them until such time as they might be falsified.