Well, let's start with the basics. To implode is to burst inward, as opposed to an explosion, a bursting outward. An implosion happens when the pressure outside a vessel or container becomes sufficiently greater than the internal pressure that it causes a sudden catastrophic inward rupture or collapse. The original use of the word was to describe the effect of high pressure in the ocean depths on, presumably, a diver or submersible.
So the simplest, least technobabbly answer to what could cause a starship to implode is that it ended up in an extremely high-pressure environment, for instance, deep in a Jovian atmosphere. The alleged negligence could have been a failure to shore up the structural integrity fields sufficiently for the maneuver.
Alternatively, if a ship flew into a particularly dense clump of nebular matter (and all Trek nebulae are extraordinarily dense compared to the real thing) at high sublight velocity, and without a sufficiently effective navigational deflector, then that might exert a considerable pressure on the front of the ship and cause a hull implosion -- maybe.
I'm not sure quite how to make sense of the "controlled implosion" in "The Naked Time," but it was presented as something that would
prevent the ship's destruction rather than causing it.
SCOTT: Captain, you can't mix matter and antimatter cold. We'd go up in the biggest explosion since --
KIRK: We can balance our engines into a controlled implosion.
SCOTT: That's only a theory. It's never been done.
... If you wanted to chance odds of ten thousand to one, maybe, assuming we had a row of computers working weeks on the right formula.
And later:
SPOCK: Obviously, we were successful. The engines imploded.
http://www.chakoteya.net/StarTrek/7.htm
It sounds like they're saying that "cold" matter and antimatter would react catastrophically in an explosion, but the theory is that the forces could be redirected in such a way that they'd be focused inward, containing and presumably amplifying the reaction. Not sure that makes sense, but I suppose it could be likened to the idea of a shaped explosion, something that directs the force in a desired and useful direction rather than destructively outward in all directions. But it's something that only happens if the calculations are exactly right, otherwise you get an
explosion.
Whatever the case, though, if implosion happens successfully, then the ship survives (although it might experience the odd time warp here and there). So if the conspirators were claiming that an implosion destroyed the
Horatio, this wouldn't have been what they were talking about.
Hard to say what a "subspace implosion" could be. How do you define pressures in subspace? Perhaps something similar to a warp bubble, something creating a spacetime metric that causes a region of subspace to collapse in on itself like a black hole.
Brilliant!
