His design only accelerates the circular motion of the particles, so he assumes their speed forward and backward along the axis of the rocket should remain constant. But in relativity, as the mass of the particles increase, their speed along the axis would slow down. This is due to the relativistic effects of time dilation and length contraction. As a result, the particles give the rocket an equal push at both ends. Einstein’s theories don’t let you get around Newton.
In fairness, Burns knew his idea was a long shot, which is why he put it out there for others to review. That’s what science is all about. That’s also why it’s worth getting just a little excited when ideas like this are put forward. Most of them will fail, but someday one just might work. We could get to the stars after all, but only if we’re willing to keep testing new ideas.