According to the special theory of relativity (STR) the rates of clocks and energies of objects should change in direct proportion as their state of motion is varied. The rates of clocks should slow down by a factor of γ = (1-v2/c2)-0.5 when they reach a speed of v relative to the observer (c is the speed of light in a vacuum) and the energies and inertial masses of objects should increase by the same factor. There is ample experimental evidence for both predictions of STR, but there is another aspect of the theory that has yet to be verified conclusively. According to the Lorentz transformation (LT) of STR, a symmetry principle must exist whereby two observers in relative motion each think that it is the other’s clock that has slowed down or that it is objects in the other’s rest frame whose energy has increased.
Probably the most credible evidence for this symmetry principle is found in the measurement of kinetic energies in elastic collisions. Measurements of the rates of clocks onboard airplanes are not consistent with this principle, however, and one is forced to explain this negative result by restricting the validity of the LT to inertial systems, even though no comparable restriction appears to be necessary in the case of measured kinetic energies. A plausible explanation for this apparent distinction between the relationships of measurements of clock rates and kinetic energies for different observers is discussed in the present work. 
Finally, an alternative relativity theory is presented that is consistent with the latter results and also requires strict adherence to the principles of simultaneity of events and the rationality and objectivity of measurement.