It is likely that it "could" be done. But not currently practical.
Here is an address for an interesting article on a laser powered aircraft.
http://diydrones.com/profiles/blogs/laser-powered-quadrotor-sets
Yes, but then so could a torch or a jet of urine.
The thrust would be very small, although of course it could be increased by chucking it out the back.
Del
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There are science toys that look like a light bulb with a black and white rotating device suspended in them. Shine a laser on the black part and see if it speeds up, that will answer your question. For every action there is a reaction, but the laser has very little mass, so the push is slight.
If you can add enough power, you may have something. I would expect at high thrust, the laser will be consuming something. It's gotta have something to spit out, at that point it is called ion drive, I believe.
"I'm giving it all I've got, Captain Kirk, but it's just not enough" (Scotty).