Derivation of the Lorentz Transformation Accounting for Two-Way Speeds of Light in the Moving Inertial Reference Frame

Einstein’s “universal constant” speed of light has been the keystone in derivations of the Lorentz transformation up to the present time. This assumed universal constant is discretionary within the empirical/time-averaged unequal two-way speeds of light. Einstein’s (assumed) universal constant may accordingly be replaced by the (empirical) two-way universal constant. (i.e., c becomes c⁺ and c^- in all moving IRFs). Here the Lorentz transformation is operationally derived given (unequal) two-way light-speeds in the moving frame. The two-way transformation exhibits space-time details in the moving frame that are absent in the overarching one-way transformation. Time continuity during the (operational) derivation is one such detail, where any one-way transformation sets-aside (e.g., atomic clock) tracking or following how the moving IRF state is achieved, whereas the procedure is explicit in the two-way light-speeds transformation. Einstein’s same-motion transformation plays a key role in the (novel) derivation. This mathematical development within the IRF system reveals extreme photonic behavior—in particular, the development admits or allows assumed near-infinite incoming light-speed—that helps, together with the Hubble expansion, to explain ongoing challenges—e.g., the dark sector.