The concepts underlying the Lorentz transform for time dilation and length contraction are presented. The notion of a rest frame is introduced and its usefulness discussed. The rest frame of the CMB (the Hubble frame) is proposed as the correct candidate for the rest frame in the Lorentz transform, and an equation developed to compute the relative time dilation between inertial frames based on this assumption.

Abstract: The assumption that time dilation must be computed using velocities relative to the local Hubble Frame has important consequences for cosmology. Four such consequences are described: (1) the impact on redshift calculations, (2) an alternate explanation of the apparent accelerated rate of expansion of the universe, (3) a reinterpretation of the period of inflation following the Big Bang, and (4) reevaluation of the computation of time dilation experienced during space travel, such as that postulated in the Twins Paradox.