text: Einstein showed that the following is true:\n(m^2)(c^4) = e^2 - (p * c)^2\nwhere m is mass, e is energy, p is momentum, and c is the speed of light.  (It's possible to derive this, but not without a ton of explanation and math.)\n\nFor any particle that has no mass, m = 0.  This means that:\ne = (p*c)\n\nHe also showed that v = (p * c^2) / e, where v is velocity.\n(Again, it can be derived with pain.)\n\nSo, when e = pc, you get v = c.  What this means is that when all of a particle's energy is due to momentum (and none due to mass), the velocity the particle travels HAS to be c.  That's the mathematical explanation.