# Role of an Objective Rest System to Determine Energy and Momentum Relationships for Observers in Relative Motion

The energy-momentum four-vector transformation of relativity theory is derived from Hamilton’s equation for the change in the energy of an object that is produced by an applied force. Einstein pointed out in his original work that two clocks in relative motion can be distinguished when one of them has been accelerated with respect to the other, and he used this as justification for his prediction of time dilation. An example is presented in which two airplanes are subjected to the same degree of acceleration so that they both attain the same speed relative to the ground while traveling in opposite directions. The experiment with circumnavigating airplanes carried out by Hafele and Keating shows that, for a hypothetical non-rotating planet, their respective onboard clocks will be running at the same rate despite the fact that they are in relative motion (Triplet Paradox). It is argued that this result is consistent with the fact that neither clock has been directly accelerated with respect to the other in this example, but rather each with respect to the surface of the non-rotating planet. It is concluded that the conventional energy-momentum transformation does not hold under these circumstances , and therefore that the corresponding invariance relation (E2 –p2c2 = E’2 – p’2c2) is by no means of general validity. The concept of an objective rest system (ORS) from which objects are accelerated is employed to define a rational set of units for energy, time and mass for different inertial systems. Accordingly, two observers must always obtain measured values for these properties that are in the same proportion for any object. This procedure allows for a resolution of the Triplet Paradox consistent with Einstein’s original conjecture, while avoiding the contradictions that arise when the above invariance relation for energy and momentum is assumed to be of general validity.