Lorentz Transformation --- Exponential factor, why not Proportional? When using the Lorentz Transformation, the increase in mass, or the decrease in space-time is an Exponential, why can't it be Proportional? What is the logic behind that? For instance, if SR had a proportional decrease in time, then if you traveled .5c, time would be cut in half (t=(t/2)). But, according to the Lorentz Transformation, to cut time in half, you have to travel about .86c, why is that? Why can't v = .5c, then time = .5t? Is this just how nature works, or is there an actual reason?