Electromagnetic thrust force 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%.
 A: 
But according to 3rd law of Newton there will be force going down,
  from wire magnetic field to current in solenoid. And total average
  force will zero. It will be the same if I pull myself for my hair up.

It would be the case and a fair comparison, if the wire and the solenoid were mechanically connected to each other, i.e, were parts of the same body, like your arm and your head. Then, the two forces would be internal to the body and would not be able to move it (or, more precisely, its center of mass).
Since, in the setup you've described the wire and the solenoid are not linked together, they could move relative to each other, if the electromagnetic forces are sufficient and if they are not bolted to the table (in which case they would be, again, parts of the same body, along with the table).

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.

If the fields are very strong and the wire is light, and everything is synchronized, it might fly, but it would not be a very efficient system, since the fields decrease with distance. But, as discussed earlier, the forces won't cancel each other even at close range and that's why this kind of interaction is used in various electromechanical devices, like relays, which do not fly, but do other useful things. I was going to list motors, but, since most common motors spin, their COM does not change, so it would not be a good example.
