September 3, 2020
special relativity, time dilation, length contraction, universal speed
If there is no time dilation and no length contraction in passage from one inertial frame (IF) to another, then velocities add like vectors and no velocity can be invariant. We are in Newton’s realm. In 1905, Einstein postulated the universality of the speed of light in vacuum. This implies time dilation and length contraction between IF’s. We shall show that conversely, time dilation or length contraction alone implies the existence of a unique universal velocity. In the proof we obtain the one-dimensional Lorentz transformation as a byproduct.