Four-dimensional symmetry of taiji relativity and coordinate transformations: III. - Tests of concepts of Reichenbach, Edwards and taiji-time

Based on four-dimensional symmetry framework with Reichenbach's extended concepts of time, Edwards' weaker postulate for the speed of light and taiji-time, we analyze their test by a combination of precise Miehelson-Morley, Kennedy-Thorndike and Ives-Stilwell experiments. Hills and Hall claimed that by using these three precision experiments, one can derive uniquely the Lorentz transformation and exclude other concepts. The derivations are examined within a more general parametrization of linear transformations. We show that, with the Einstein clock synchronization convention, one gets uniquely the Lorentz transformation; without it, the three precision experiments lead to an infinite set of four-dimensional transformations with Lorentz group properties. Thus these experiments are consistent with taiji-time, Reichenbach's extended concept of time and Edwards' weaker postulate for the speed of light. Based on Wu transformations for accelerated frames, we also discuss a test of taiji-time by a generalized Ives-Stilwell experiment involving ions with constant linear accelerations.