According to the principles of special relativity, time dilation occurs when there is relative motion between two observers. Time dilation means that the passage of time appears to differ for observers in different reference frames.
In the scenario you described, where you're traveling on a train in the same direction as Earth's rotation, your relative velocity with respect to an observer on the Earth's surface would increase. However, the difference in velocity between you and the observer on the surface of the Earth would be relatively small and not significant enough to cause a noticeable time dilation effect.
To experience a noticeable time dilation effect, you would need to travel at speeds close to the speed of light, which is about 299,792,458 meters per second. At such speeds, time dilation effects become more pronounced. For example, astronauts on the International Space Station, which orbits the Earth at a high speed, experience a slight time dilation compared to observers on the surface of the Earth, but the difference is extremely small and not perceivable in everyday life.
In summary, traveling on a train in the same direction as Earth's rotation would not cause a significant time dilation effect. The relative velocity difference between you and an observer on the Earth's surface would be too small to result in a noticeable change in the passage of time.