This question seems to be a close parallel of this one, but it's about a different design by a different author.
I read a news article about a "helical engine" design by NASA engineer David Burns. The design allegedly exploits relativistic effects to seemingly violate conservation of momentum (as in the earlier question). It involves an oscillating mass which travels faster in one direction than the other, thus having higher relativistic mass on one side and imparting unbalanced momentum to its container.
But, Burns asks, what if the ring’s mass is much greater when it slides in one direction than the other? Then it would give the box a greater kick at one end than the other. Action would exceed reaction and the box would accelerate forwards (see video below).
Now, I'm not a physicist, but I'm just smart enough to have gotten the sense that this is almost certainly nonsense. As soon as I read "may violate the laws of physics" in the headline, in fact. Is it nonsense, and if so, what is unaccounted for in this model that would balance the momentum transfer at each side of each oscillation? How does the math play out?