A special point in special relativity

[Dale]

All clocks should show the same time, or I’m wrong.

You are wrong. See post 24.

The key is understanding the relativity of simultaneity.

 

[Chestermiller]

When the train is at rest with respect to the ground (prior to its initial acceleration), its clocks can be synchronized with one another and with the clocks on the ground. But, during the acceleration of the train, the clocks on the train will fall out of synchronization with one another (and with the clocks on the ground). This is analogous to the gravitational time dilation effect.

After the acceleration is complete, and the train is now traveling at constant speed, its clocks can be resynchronized with one another. At this point, the locations on the train and the clock times on the train can be related to those on the ground by the Lorentz transformation. But, when the train next decelerates down to zero speed relative to the ground, its clocks will again fall out of synchronization, so that when it stops, they will again have to be resynchronized with one another and, if desired, with those on the ground. If, after the initial acceleration, the clocks on the train are not resynchronized with one another, then my guess is that, after the final deceleration down to zero speed, the clocks on the train will again be in synchronization with one another and with those on the ground. However, I am not sure of this, since I have not analyzed the problem in detail. Maybe another responder with more experience than I could address this.

Chet