Two myths about special relativity

Q. Does the Lorentz transformation reduce to the Galilean transformation when the ratio v /c is small? A. No. At least two routes are available to substantiate the negative response. I will first give a direct, algebraic route and then a more sophisticated indirect route. Consider the usual pair of inertial reference frames, the primed frame moving with speed v along the x axis of the unprimed frame. To avoid any spurious dependence on the origins of coordinate systems, consider a pair of physical events. The Lorentz transformation for the time interval between the events takes the form