A Lorentz variant theory that passes fundamental tests of special relativity and makes diverging, testable but as of yet untested predictions

Background Tests of special relativity have been conducted over the past century with increasing accuracy and none have showed violations of Lorentz invariance. In this paper we will examine whether these tests are together sufficient to rule out theories that violate observational symmetry. Methods A variant theory is outlined where relativistic effects such as length contraction and time dilation are purely local consequences of the relative velocity between a system and its medium. The outlined theory is tested against the fundamental tests of special relativity. Results It is found that although this alteration does not align with the principle of relativity, it quantitatively aligns with the experimental results of the fundamental tests of special relativity and their modern variations, and makes diverging, testable but as of yet untested predictions concerning Doppler shift and time dilation. Conclusions These results warrant a closer theoretical inspection of the outlined theory, and could provide a direction to test for new physics. A modified Ives-Stilwell experiment is proposed to test between this model and special relativity.