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.
The
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.