PS note that an accelerating train would have an internal time dilation similar to gravitational time dilation. A clock at the front of the train would run faster than a clock at the rear, as observed from onboard the train. That's essentially why clocks don't stay in sync in an accelerating reference frame.
I thought the train was in constant motion in this thought experiment.
Yes. It doesn't matter how the clocks are synced. In reference to your diagram in a later post. You have a device with two arms attached to it. When the device triggers the two arms press the buttons on the clock. However, you are assuming that the triggering of the device and the pressing of the buttons are simultaneous in the device's own frame, and they are not. The impulse generated at the trigger can't travel down either arm faster than the speed of sound for the material the arm is made of. Let's call this "S". In the platform frame, the speed of those impulses relative to the platform is subject to the relativistic addition of velocities.Thank you. I will look into that.
Okay. Let's say that the clocks are synchronised inside the train when the train is in constant motion. But let's say they were synchronized MECHANICALLY, by a very precise machine that pressed the "start" buttons of both clocks at the exact same time.
Now, would the clocks still appear to be out of sync to the platform observer?