As it stands, all FTL requires handwavium of one kind or another. Einstein-Rosen bridges require negative energy density, as do warp drives -- the two plausible methods of FTL currently theorized. This is magic, though to a lesser degree than the One Ring or, dare I say, a Portkey.
In essence, we're quibbling over word choice here. Perhaps you'd prefer 'handwavium' to 'magic', though one is really a subset of the other -- magic with marginal justification and some quick talk around the sticky points.
the problem with FTL is that it is in itself a rather murky territory. It deals with a higher degree of physics that we know jack s*** about. We do have some theories thrown around that don't have any real proof behind them except that it "appears" to work. Appears is the key word.
While some of the most basic laws of the universe are very likely to be correctly interpreted by us, the higher up the food chain you go and the more you throw in newer theories, the less solid they are.
FTL is improbable. And AT THE MOMENT it appears it might break something (frankly, I think the whole casuality argument sucks. It just makes so very little sense to me). But FTL is the smallest of all plausabiltiy evils you can come up with in Sci-Fi.
I don't understand what you say breaks logic on a fundamental level, and whatever point you tried to make by introducing 'conservation of energy' and 'action and reaction' is lost on me.
I can give you a lot of examples. Like introducing technology that does X and not taking into account that if it does that, it should also be doing Y and that would change Z. And you leave Z the same.
Another good example would be that shapechanger for ST: DS9.
Changing it's mass and volume like that would require amounts of energy equal to a atomic bomb. Not to mention that when they shapechange, even scanners can't tell them apart from the real thing. They are in essence physicly a perfect copy - which is beyond any logic, since then they wouldn't be able to change back.
check this:
http://www.projectrho.com/rocket/rocket3al.htmlLook under UNINTENDED CONSEQUENCES