The relativity of simultaneity is captured by the example of the treaty signing ceremony: from the perspective of those on the train, the presidents both sign at the same moment while from the perspective of those on the platform, President Forwardland signs first. Nevertheless, it is easy to get confused regarding what this really means. The asynchronous nature of clocks in a moving frame provides a good way to gain clarity.

To that end, imagine that the UN Secretary General, to commemorate the historic ceasing of hostilities, has given each of the presidents an identical watch, both identically set to New York time, which they both wear as the signing ceremony gets underway. The light bulb goes off. Each president receives the signal and signs the treaty. According to those on the train, each president’s watch reads exactly 2:00 PM when they signed the treaty. You are stationary on the platform. Let’s analyze this from your perspective.