Light-Based Length Measurement in Relative Motion: A Classical Approach and Its Relation to Special Relativity

In this article, length measurement is analyzed using an explicit light-based measurement procedure.An idealized rod is considered in an inertial reference frame (IRF), in which it is at rest, and in a reference frame IRF′ that moves with constant velocity relative to IRF. The length of the rod is determined in both cases exclusively from calculatedreturn times of light signals and fixed geometric relations between selected points.The analysis is carried out entirely within a classical-physics framework, in which light is described as a signal propagating in vacuum with speed c. It is shown how the same geometric length can be reconstructed from measurements performed in IRF and IRF′ , and how the difference between the return times is related between these reference frames within the framework of the specified measurement procedure.The results highlight the central role played by operational assumptions in the measurement of length in situations involving relative motion. A numerical comparison shows that the present analysis and SR agree to 7 decimal places at the Earth’s orbital speed, which explains why SR is consistent with experimental measurements despite being based on different operational assumptions.