The special theory of relativity (STR) has successfully predicted that proper clocks run more slowly as their speed relative to an observer on the Earth's surface increases. A straightforward means of  describing this phenomenon is to assume that the unit of time varies from one inertial system to another. A key theoretical assumption that has been verified by means of experiments with airplanes and satellites is that all clocks in a given rest system slow down in exactly the same proportion (R) when they are accelerated, thereby making it impossible to observe any change in their rates on the basis of exclusively in situ measurements, consistent with the relativity principle (RP). The same line of argumentation leads to a similar conclusion for in situ length measurements, since any change in the distance between two objects co-moving with an observer must be matched by a strictly proportional change in the standard device employed to measure it. It is argued on this basis that the unit of length must vary with the state of motion in the same proportion R as that of time in order for the speed of light to be constant for all observers (Einstein's second postulate of STR). The use of such a rational set of units in each rest frame requires that a different space-time transformation (alternative Lorentz transformation, ALT) be introduced into relativity theory than that given by Einstein in his original work. Moreover, the unit of energy must also vary in exactly the same manner as that of time (R). since the energies of accelerated objects are known to increase in direct proportion to their lifetimes, even though in situ measurements are again incapable of detecting such changes because of the RP. The latter conclusion indicates that the ratio of the energy of Photons to their frequency (Planck's contand h) varies as R² with the state of motion of the ligt source relative to the observer, and an experiment involving the photoelectric effect is suggested to test this prediction. More generally, the ratio of the units of any other mechanical quantity must vary as Rⁿ between the same two rest frames, where n is determined from the composition of this quantity in terms of the basic units of energy, time and length.