What wrong with Lorent transformation here?

[AlienUFO]

Say we build a train that can travels revolve Earth continuously. And inside the train there is another smaller train that also revolves Earth but travels in opposite direction with the bigger train.

The problems is: relative to observer on earth, the bigger train is under L.transformation but not the smaller one. Hence the time in bigger train seems slower but not the smaller train. But for the observer on the bigger train, the smaller train is undergo another L.transformation, hence the smaller train's time should be slower.

The speed of the smaller train should cancel the L.transformation relative to earth, hence where the time clock of the train should I refer to?

Is there something wrong?

 

[Hootenanny]

Let me get this straight. We have two trains, a larger train traveling with a constant velocity (relative to the Earth's surface) anti-clockwise around the Earth (for the sake of argument); and a smaller train, inside the larger train, traveling at the same velocity (relative to the larger train) but in the opposite direction to the larger train. Is this correct?

 

[AlienUFO]

Yup. Thank you Hootenanny, my english is just...

 

[HallsofIvy]

I don't see a problem. Without the "inner train", an observor on Earth would see time running more slowly on the train while an observor on the train would see time running more slowly on the earth. Adding the "inner train" doesn't present anything new- it's just part of the Earth fram of reference.