How to send a spaceship to the closest star using lasers

The StarShot program wants to accelerate mini-spaceships by means of laser bombardment to a velocity of one-quarter the speed of light so that they can reach our neighboring star, Proxima Centauri, within the foreseeable future. The technology sounds feasible, but still must overcome a few hurdles.

Imagine you had to keep a ball floating in the air using a hairdryer. You will automatically think of a ping-pong ball floating a few inches above a fan. But could you accomplish this feat with a s...