Use of an Objective Rest System to Determine Energy and Momentum Relationships for Observers in Relative Motion
2018-01-22
Relativity and Gravity Publication - No. 14
Buenker
Robert J.
Prof. Dr.
Buenker, Robert J.
aut
de
<p> 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 their respective
onboard clocks can 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. It is concluded that the
conventional energy-momentum transformation does not hold under these circumstances,
which shows that the corresponding invariance relation (E<sup>2</sup>-p<sup>2</sup>c<sup>2</sup>= E'<sup>2</sup> - p'<sup>2</sup>c<sup>2</sup>) 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.
2018-01-22T10:45:47.727Z
2018-01-22T11:42:21.426Z
published
Pub