Yes, time dilation can be experimentally demonstrated using a moving train and an atomic clock. This type of experiment is known as the "clock paradox" or the "twin paradox."
In the thought experiment, let's say we have two identical atomic clocks: Clock A on a stationary platform, and Clock B on a train that moves at a significant fraction of the speed of light. Clock A remains at rest, while Clock B travels away from it and then returns.
According to the theory of relativity, as Clock B accelerates and moves at high speeds relative to Clock A, time dilation occurs. Clock B, which is in motion, experiences time passing more slowly relative to Clock A, which is at rest.
When Clock B returns to the stationary platform, it is found that Clock B has registered less elapsed time compared to Clock A. This result confirms that time dilation has occurred. Clock B, due to its relative motion, has experienced a slower passage of time compared to Clock A.
This thought experiment demonstrates the principle of time dilation as predicted by the theory of relativity. In practical experiments, atomic clocks have been used to verify this effect by comparing clocks that have been placed on moving platforms, such as airplanes or satellites, and comparing their time measurements to clocks on the ground.
It's worth noting that time dilation effects become more pronounced as the relative velocity approaches the speed of light. For everyday speeds encountered in our daily lives, the effects of time dilation are extremely small and not noticeable. Nonetheless, experiments involving high-speed or high-precision clocks have confirmed the existence of time dilation as predicted by the theory of relativity.