Measuring Velocity Using Moving Clocks—The Surprising Test of Tangherlini’s Theory

Motivated by the work of Matsas et al. (2024), which demonstrates that time can serve as the fundamental unit for physical quantities—obviating the need for traditional Length-Mass-Time (LMT) dimensions—this research evaluates the operational resolution of velocity within relativistic frameworks. Utilizing a Lorentz transformation matrix approach, we first validate the Matsas three-clock protocol, confirming the derivation of distance as a function of three proper clock times in Minkowski spacetime and uncovering two novel velocity expressions derived solely from these temporal intervals. The investigation was extended to Tangherlini’s 4D spacetime framework (1958) to test the hypothesis that absolute velocity could be resolved through subluminal signaling. While the initial three-clock scenario resulted in the systematic cancellation of the Base system's absolute velocity, a breakthrough was achieved by applying the Relativistic Doppler Effect within the Tangherlini metric. This approach effectively circumvents the mathematical cancellations prevalent in standard relativistic "null" experiments. The findings reveal that the Tangherlini and Minkowski frameworks are intimately related; the former serves as a necessary complement to the Special Theory of Relativity (STR) rather than an antagonist. This theoretical advancement suggests a plausible methodology for the measurement of absolute velocity without the requirement of instantaneous signals. By resolving the longitudinal Doppler shift within a preferred-frame geometry, this research provides fresh impetus for the historical debate on absolute motion initiated by Poincaré and Einstein.