Symmetry groups of the special theory of relativity with correspondence principle

Abstract:
The correspondence principle was taken as the guiding principle to discoveries in the old quantum theory but it has not been properly used as a heuristic principle in special relativity theory. In the present work, we apply the correspondence principle to special relativity (correspondence to classical mechanics in the limit of small velocities is meant) to derive the coordinate transformations between different inertial frames using the Lie group theory apparatus. It enables us to derive the Lorentz transformations without assumption of linearity. It also provides a basis for discovering some unknown consequences of postulating an anisotropic propagation of light ("non-conventional synchronization") in the theoretical context of special relativity - the topic that is quite widely discussed in the literature (see, e.g., [1]). In particular, applying our approach together with an assumption of anisotropy in the velocity of light yields nonlinear coordinate transformations between different frames.

References
[1] Rizzi, G, Ruggiero, M.L., and Serafini, A. Synchronization Gauges and the Principles of Special Relativity. Foundations of Physics, 34, No. 12, 1835-1887, 2004