In Star Wars, 8 laser beams fired by the death star merge into one large beam. Is this possible? It seems intuitive if you replace the laser beams with something like a bunch of baseballs (momentum in opposing directions cancel assuming your collisions are inelastic, leaving you with momentum in only one direction), but can the same thing happen with photons? What about sub-particles, like protons or neutrons?
Visible-light photons (like the photons that make up the Death Star's laser) don't collide with each other and scatter like baseballs do. They simply pass through each other. Other particles, like protons and neutrons, do scatter off of each other.
To make the Death Star laser-merging system work, you would have to have the laser beams focused on some sort of object that would interact with the laser light. The object could either absorb and re-emit the light in one direction (like using the eight lasers as the power source for an even more powerful laser positioned at the original lasers' intersection point) or refract the light (using some sort of extremely long focal-length lens). Either way, you would need some object positioned at the intersection point of the original lasers.
Photons with energies much higher than visible-light photons occasionally do scatter off of each other, in a process known as "light-by-light scattering," but this is very rare, and you'd be hard-pressed to manipulate it in a way that would result in a particularly strong beam.
Yes. But it isn't as easy as just bringing the lasers together. The must be in phase with one another or else you won't get a sharp beam coming out. This is just what they are planning to do for breakthrough starshot.