Authors: Richard Kaufman
Einstein’s train—lightning thought experiment is commonly used to illustrate the relativity of simultaneity, yet many textbook treatments leave implicit a modeling choice: observers typically analyze the scenario as though their own inertial frame were at rest. This assumption is not required by the postulates of special relativity, which permit an observer to adopt any inertial frame as at rest and itself as moving relative to it. This paper develops an operational method that makes this choice explicit by treating the rest frame of the light sources as the reference for assigning propagation distances, with the sources understood as lightning in ground air or as bulbs fixed to the track. Working in the train frame, and using only the train’s proper length, the relative velocity v, and the invariance of the speed of light c, the observer computes the propagation times and infers simultaneous emissions. The choice of source frame is an operational decision tied to the physical configuration of the emitters and does not introduce an absolute rest frame or imply any dependence of c on source or observer motion. The analysis does not replace the conventional interpretation but complements it by making explicit the operational choices involved in simultaneity judgments. Because the train—lightning experiment is almost universally presented as requiring the train observer to infer non-simultaneity, the analysis highlights how that conclusion depends on an implicit operational modeling choice while remaining consistent with special relativity. For completeness, Appendix A applies Selleri synchronization to Einstein’s original thought experiment, illustrating how admissible synchronization conventions affect simultaneity assignments.
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