Reconstructing simultaneity using Doppler-based inference: A frame-specific convention within special relativity

Simultaneity of spatially separated events in special relativity is not directly observed but inferred through synchronization conventions. Einstein’s method assumes light travels at the same speed in all directions, while alternative conventions—such as Selleri’s—allow for anisotropic light speeds. This paper presents a complementary approach: a Doppler-based method in which an observer—such as one aboard a moving train in the classic lightning strike scenario—uses known rest-frame emission frequencies and measured Doppler shifts to back-calculate the emission times of signals and determine whether events were simultaneous in their own frame. This method applies in scenarios—such as the one presented here—where the rest-frame frequency of the source is known (for example, if the light source—envisioned as a light bulb—was marked by the manufacturer while at rest in its own frame). Although this rest frame corresponds to the ground frame in our scenario, the train observer’s analysis remains entirely within their own frame. This approach does not assert that all observers agree on a single time of occurrence; rather, it respects that simultaneity is frame-dependent and that observers in relative motion are subject to time dilation. The method highlights that conclusions about simultaneity depend on the chosen synchronization framework—even when all frames apply consistent physical reasoning. This demonstrates that simultaneity is a frame-dependent reconstruction, consistent with Einstein’s acknowledgment that simultaneity rests on a chosen stipulation, leaving room for alternative conventions.