It's impossible to arrive at a non-zero net Force with classical electrodynamics. It's theoretically proven that it conserves momentum.
Very possible reasons for measuring non-zero force:
> Systematic measurement errors.
> Leaking EM field carrying momentum.
> Energy channel from outside carrying momentum (failing measurements including battery mentioned in comments)
Unlikely explanation: All currently used theories of electrodynamics are wrong.
But explaining non-zero force from classical ED is simply impossible.
Also note that breaking conservation of momentum + relativity means that conservation of energy is broken as well.
edit: typo
edit 2:
I mean the theoretical approach presented in the paper makes obvious mistakes. I'm not arguing that breaking conservation of momentum is impossible (although I think it's really unlikely), I argue that even if it would happen it couldn't be described by classical electrodynamics (or even QED). We would have to come up with better laws for electrodynamics.