PointLess
Paranormal Novice
The laws of physics might not be able to be violated, but as you said we do not have a complete understanding of them.
My own thinking about propulsion systems is not as mathematically based...I'm more of a conceptual thinker. What if one was able to "turn off" gravity? What if one was able to "multiply" gravity, or just tap into it's source? Since humans don't even know what gravity really is, we don't know how it works. All we really know about gravity is that it exerts acceleration upon an object. I suspect that once we discover the mechanism of gravity, we will be able to advance our propulsion systems accordingly.
Anti-Gravity does not exisit. There are two reasons for this, a technical and an 'obvious one':
a) the technical reason is that physical forces are transmitted via particles called bosons. These bosons are always their own anti-particles (the photon (electromagnetic force) is its anti-photon, the w-boson consist of 3 members (w+, w-, z0) and so there is always its anti-particle within (weak force) and for one gluon there is alway an anti-gluon (strong forces); for gravity its the same although the graviton is still not discovered but it is coincidentally its own anti-graviton; this mean there is no reason to think of an isolated particle called anti-graviton. And I dont know any theory which allows this particle as a separated particle.
b) the 'obvious reason' is: think of a society capable of producing anti-gravity which annihilates gravity so that any machine is able to hover; What do you think would happen if thousand (or millions) of these machines would run on that planet? Of course these machines would alter the orbit of their earth arouond their sun (because of the missing gravity they annihilated)...and this is not funny, I think

I think to make these mile-long-things fly they are somehow able to alter the other part of Newton equation (roughly: weight = inertia). They are able to turn off and turn on the inertia and that would explain why they are able to fly instantly from zero to I-dont-know-velocity (besides 90 angle degress and so on)...