If I put a wire near solenoid/electromagnet and put DC current in proper direction (Fig 1), then there will be force going up which will pull the wire up. But according to 3rd law of Newton there will be force going down, from wire magnetic field to current in solenoid. Solenoid and wire are mounted on the same platform, they are hardly connected. In this case total average force will zero. It will be the same if I pull myself for my hair up. Nothing will happen. I also assume there is no external magnetic field, like Earh field etc.
If I put AC current and sync it properly between wire and solenoid, then it will be the same, force up to wire and down to solenoid.
Now if I replace solenoid with powerful radio waves source (magnetron, etc). It will look like Fig 2. Wire and radio waves source hardly connected as well. And I make radiowave like parallel beam and put the wire in a long distance like 10-100 wavelength from radio waves source. And I sync it properly, AC current in the wire and radio waves frequency/phase. In this case there will be no force from wire to waves source and there will be only one force to the wire up. And it should fly.
Question is why it will not fly (where is mistake in my thinking)? If it would work it would be implemented 50 years ago.
Fig 2 +/- means at one specific moment, current is AC.
P. S. It is highly theoretical question. Please do not spend your time with very practical things like wire resistance etc, if influence is less than 20%.