According to the principles of special relativity, the scenario you described involving entangled particles and their measurement is subject to the relativistic effects of time dilation and length contraction. These effects can lead to apparent discrepancies in observations made by different observers in relative motion.
Let's consider the scenario from two perspectives: the stationary observer and the observer on the moving train.
From the perspective of the stationary observer: When the entangled particles are observed by the stationary observer, their states become correlated or entangled. The measurement of one particle's spin instantaneously determines the spin of the other particle, regardless of the distance between them. This phenomenon is known as quantum entanglement.
From the perspective of the observer on the moving train: According to special relativity, when an observer is moving at near-light speed relative to the stationary observer, they experience time dilation and length contraction. Time dilation means that the moving observer perceives time passing more slowly compared to the stationary observer. Length contraction implies that the moving observer sees distances along their direction of motion appearing shorter.
In this scenario, if the observer on the train measures the spin of one particle, they will observe it to be determined. However, due to the time dilation and length contraction effects, the observer on the train would also perceive the distance between the entangled particles as contracted, and the information about the measured spin would take longer to reach the other particle.
As a result, from the perspective of the observer on the train, it would appear that there is a delay between the measurement of one particle's spin and the determination of the other particle's spin. This delay is consistent with the principles of special relativity and does not violate the theory's limitations on information transfer faster than the speed of light.
It's important to note that the concept of entanglement and its interpretation in different reference frames can be complex and has been the subject of ongoing scientific discussions. However, the description provided here captures the essence of how relativity affects the perception of entanglement in the context of observers in relative motion.