I'm surprised there isn't a thread for this already, because this is interesting to say the least.
2 weeks ago this paper was published (https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20190029294.pdf) that proposes a helical particle accelerator that would use mass changes to accelerate a craft without propellant1. The engine would bounce ions back and forth, but accelerate them to relativistic speeds at one end of the device, increasing their mass and creating an inequality that results in a net movement of the entire device. This does not seem to violate conservation of energy, as it requires hundreds of megawatts of power. However, it appears that only one person has worked on this paper, and no experimental evidence exists.
1 It technically uses 1.776E-11 kg of ions per year, plus the nuclear fuel needed to power the ship.
Some basic calculations: If this ship had a mass of 2,000 tons, after 1 year it would have a velocity of 17 meters per second. So, the usefulness of this is very questionable. It would take 16,000 years to reach even alpha centauri.