A variation of the train-and-platform demonstration of relativity of simultaneity

Question

Suppose one observer is midway inside a speeding train and another observer standing on a platform as the train moves past. A flash of light is given off at the center of the train just as the two observers pass each other $t_0$.

Additionally, there are two clocks, one in the front end of the train, and one in the back end. Both observers agree that the clocks are synchronous at $t_0$ (is this assumption the source of the problem?). The clocks are programmed to freeze immediately once they receive the light from the flash. Will the observers disagree on the time the frozen clocks are showing?

Answer 1

No, both observers will agree on what the clocks say. The reason for this is that Lorentz transformations don't change clock faces. What they won't agree on is everything else:

On the train, both clocks are synchronous--the light pulse is emitted and simultaneously stops both clocks, which read the same value (12:34 56s)

On the platform, the clocks don't show the same number at the same time (so they aren't synchronized). The light pulse is emitted, the clock in the back is hit, and stops at 12:34 56s. Time passes with the forward clock continuing to tick forward slowly (time dilation). The light pulse hits it, and it stops, also at 12:34 56s.