The Lorentz transformations are not true coordinate transformations as Einstein derives them. That is, they do not represent a one-to-one mapping of a single set of coordinate values in one coordinate system onto another set in an identical coordinate system moving at a constant velocity relative to the first. Rather, they represent a mapping of an average of two sets of coordinate values from the first coordinate system onto a single set of values in the second. If the measurement system used in an experiment is inconsistent with Einstein’s averaging method, then the Lorentz transformations will give incorrect results. A simple example is given of a photon-emitting clock moving at a constant velocity, v, in a straight line between two photon detectors. The time of travel of the clock between detectors measured by the front detector would be t = τ, and by the rear detector would be t = τ (1-v/(c+v)). The Lorentz transformation gives a value of t = τ / √(1-v2/c2) for both detectors. It is also noted that the Lorentz transformations give results inconsistent with the coordinates of photons in a light pulse of the form c2t2-x2-y2-z2=0, when measured in an inertial reference frame different from that of the source.