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Conservation of momentum, I know, so I'll make this as brief as possible.
The mass of a nucleus is less than that of its constituent parts. Imagine that it were feasible to fission and recombine an atomic nucleus repeatedly, while at the same time oscillating it back and forth in a given direction.
energy would be pumped in and out, the mass would fluctuate. The individual nucleons would be moved in a given direction, translating the ship a given distance. It'd then be stopped, and the combined nucleus would be moved in the opposite direction translating the ship a smaller distance than before. Repeat, net movement of the ship.
That part seems to follow newton's third law, but obviously looking at the whole system, it doesn't.
I do not have a degree in physics. So I kindly request that someone explains to me why it won't work, instead of just telling me it won't.
||Intriguing - after all, f=m.a
And, as we all know, e=m.c²
So, in unifying these two equations, we should be able to describe e(nergy) in terms of mass and acceleration - and in doing so, power yourself along quite merrily.
||This is where it falls down - in order to gather your energy, you need to capture it as it is released from your oscillating nuclear reaction - however, since the reaction is going to zoom particles out in all directions, you have to choose between capturing all of them (resulting in zero acceleration since you can't capture only those particles that fly off in the direction opposite to the one you want to travel in) or letting some go, and in doing so, losing some of that energy you'd need in order to continue the oscillation.
||Imagine you build a petrol driven version - if you capture all of the enregy created in combustion, say, in a closed cylinder - you should conceivably (if we ignore the details for a moment) be able to recombine the constituent gasses etc back into unburned fuel, ignite and start again - however, because it's all in a sealed tube, your engine isn't going to go anywhere, because all the energy generated is utilised in keeping the engine running for the next cycle.
||What you may be missing is that photons also have momentum, even though they don't have mass.