Free 238U nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x in time t after the decay. If a decay takes place when the train is moving at a uniform speed v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger will be

The separation between the alpha particle and the recoiling nucleus is measured as x in time t when uranium atom is kept in a stationary train. If decay takes place in a moving train, the distance between the alpha particle and the recoiling nucleus is now measured, will remain x in time t. This is because the decay process and the passenger are in same time frame.

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