Can you use light to push light?
No, you can't. Photons, the particles that light is made from, transmit a force known as the electromagnetic force. This is the force that causes positive charges and negative charges to attract each other. It turns out that, while they transmit the electromagnet force, photons themselves do not feel the electromagnet force. A photon has no way to exert a force on another photon. If it can't exert a force on another photon, there is no way that it can push one.
Steve Gagnon, Science Education Specialist (Other answers by Steve Gagnon)