The problem is that this idea relies on a fundamental misunderstanding of Special Relativity.
Newton's second law of $F = ma$ doesn't work, exactly, in Special Relativity.
But if you instead write down Newton's second law as $F = dp/dt$, where $p$ is momentum, this does work exactly (and equally for all observers), even in Special Relativity.
The source cited in the question is Helical Engine, (the PDF of the slides) written by David Burns, Manager, Science and Technology, Office Marshall Space Flight Center.
I am still looking for the quote, but I believe I recently read that Burns readily admits that the treatment seems to violate conservation of energy and is therefore suspect. By presenting the idea as slides, in a meeting of scientists and engineers, the goal is to allow the treatment to be vetted by others since Burns has not been able to yet identify a possible flaw.
This is absolutely fine! This is how science works. The problem lies in the clickbaiting internet articles in the popular media.
Note the last section on the final Conclusions slide:
- Basic concept is unproven
- Has not been reviewed by subject matter experts
- Math errors may exist!
Then have a look at the recent article published in Forbes. Here is a short section of the extensive article For The Last Time, No, A NASA Engineer Has Not Broken Physics With An Impossible Engine
The article is thorough and in-depth and is worth reading in its entirety to get a better idea how conservation of energy, special relativity and electromagnetic theory need to be taken together. The article laments recklessly (my word) published clickbait articles that have been put in the popular press about it as well.
The specifics of Burns' idea are fundamentally flawed in a way that's very common among non-physicists. (Burns has a Ph.D. in electrical engineering.)
The problem is that this idea relies on a fundamental misunderstanding of Special Relativity. It's true that when you accelerate an object close to the speed of light, the same acceleration (or thrust) will increase your speed by much smaller amounts the faster you're moving; Newton's second law of $F = ma$ doesn't work, exactly, in Special Relativity. No object can ever move at the speed of light, and so as you continue to apply a force to a relativistic object, it's like you're increasing its mass, not just its speed. Different observers will disagree on the mass and speed of the object.
But if you instead write down Newton's second law as $F = dp/dt$, where $p$ is momentum, this does work exactly (and equally for all observers), even in Special Relativity. If Burns had properly accounted for the total momentum of the box+ring system, which must include the energy/momentum of the applied fields and forces required to accelerate the individual components (like the ring) inside the box, he would have noted that the total momentum never changes, even under relativistic transformations and perfectly elastic ring/box collisions.
Instead, he examined the ring alone, and that's led to his math errors and his untenable conclusion. In fact, pre-existing fixed-target experiments at particle colliders have already demonstrated a conservation of momentum that serves as a counterexample to Burns' expectations. His idea is already dead-on-arrival.
Source (click for full size)
Perpetual motion has long been a holy grail of tinkerers and inventors, but it violates the laws of physics, including Newton's 3rd law and the laws of thermodynamics. Burns' new 'helical engine' is just the latest example of a self-deception making its way into mainstream science discussions. NORMAN ROCKWELL / POPULAR SCIENCE
See also this Reddit page (found here) in which this post includes:
The "paper" is on the NASA technical reports server because its author is the director of Science and Technology office at NASA Marshall space center. He is a CEO-level manager.
The mistake in the paper is in the undergraduate-level physics.
But lots of even good students make silly mistakes -- it is super common. Fortunately their mistakes do not get sensationalized like this one has become. It's a huge face-palm.
in it's extensive criticism of the overpopularization of the talk.