Reinterpreting the famous train/embankment experiment of relativity

Einstein’s well-known train/embankment experiment, frequently used to introduce the relativity of simultaneity, is revisited. Though present in numerous textbooks, the traditional analysis is shown to be incomplete and inadequate to demonstrate that simultaneity is relative. Completing the analysis produces not the relativity of simultaneity in its usual form but rather a new contradiction. It is shown that, under the conditions of the experiment, a simultaneity in one inertial frame does indeed hold in another inertial frame but is perceived as a non-simultaneity by an observer outside the given frame. The source of the paradox is traced to the experiment itself, which is posited in Newtonian space–time but under Einsteinian postulates. Though crafted as an introduction to relativity, the experiment is seen, ironically, to require relativity to analyse it. The contradictions are resolved by a relativistic analysis.