[paul cotter (OP)]

An acquaintance on another forum has suggested a possible violation of the conservation of momentum. I am sceptical but don't feel competent to analyse the scenario rigorously. The setup is quite simple: two half wave dipoles are physically separated by a quarter wavelength spacing and fed with two signals with 90degree phase difference, at the resonant frequency. The argument is as follows: the electrostatic field from A arriving at B will be in phase and cause repulsion while the field from B arriving at A will cause attraction in the same direction as the repulsion occurring at B and hence a net force in one direction without reaction. Any thoughts? 

[Bored chemist]

Is this a violation of com?
no
https://en.wikipedia.org/wiki/Noether%27s_theorem

[paul cotter (OP)]

Yes BC, I know all that. What I was looking for was a refutation on first principles. This acquaintance of mine is certainly no crank. Personally I think Emmy Noether is unassailable.

[Bored chemist]

He seems to have neglected the momentum carried off elsewhere by the EM radiation.

[hamdani yusuf]

the electrostatic field from A arriving at B will be in phase and cause repulsion while the field from B arriving at A will cause attraction in the same direction as the repulsion occurring at B and hence a net force in one direction without reaction. Any thoughts?

The electrostatic force is not the only thing we need to consider. There's also electrodynamics force produced by electrons moving in the antennas.