(7) The limit is not taken in E=γmc² (m is the invariant mass) but in E² = (pc)² + (mc²)². If m=0 then E=|p|c: the ratio between the magnitude of the speed '|v|' and the speed of light 'c' is given by (|p|c)/E, so |v|=c. There is no discontinuity: these formulas can be found on every basic relativity textbook. | (7) The limit is not taken in E=γmc² (m is the invariant mass) but in E² = (pc)² + (mc²)². If m=0 then E=|p|c: the ratio between the magnitude of the speed '|v|' and the speed of light 'c' is given by (|p|c)/E, so |v|=c. There is no discontinuity: these formulas can be found on every basic relativity textbook. |