Application of the Lorentz transformations from an intrinsic reference frame of noninertial clocks

Abstract

Accelerated motion is considered as a successive presence of an observer in accompanying inertial reference frames (AIRF) with jumps between them. A formula comprising two terms has already been derived to explain the twin paradox. The first term of this formula describes the time dilation in the reference frame associated with the twin at rest, while the moving twin is in the chosen AIRF. The second term describes a jump of readings of the clock of the twin at rest observed by the accelerated twin who jumps in the next AIRF. In the present study, this formula is used to derive the relative velocity and the distance passed by the accelerated twin by the scale associated with the twin at rest from a noninertial reference frame (NRF). Uniformly accelerated motion followed by uniformly decelerated motion to the stop in the initial inertial reference frame is examined. Readings of any clocks at rest, including clocks of the twin at rest, are derived from the NRF.