Hi all, I'm in a modern physics course and am surprised by how confused I am about special relativity. I know multilinear algebra quite well, and so I thought it would be pretty easy, but I'm having some conceptual difficulties. Any help would be greatly appreciated! 1. Why is a special formula needed for the addition of velocities? Aren't velocities 4-vectors, which transform via Lorentz Transformations? Are there situations in which you would simply add or subtract two velocities? I have in mind when you want to compute the relative velocity of two objects in a third object's rest frame. 2. What does it mean for an object's mass to increase with increased energy (but not an increased net momentum)? Does this mean that the same applied force will accelerate it less strongly? Or is it just an issue of conservation? 3. Why is it that the energy in the motion of a bunch of moving particles with no net momentum adds mass to the collection of particles? If you considered an individual particle, wouldn't it have a net momentum and thus no increase in mass? Where does this mass exist?