# A special point in special relativity

Dale
Mentor
2020 Award
And the train will be ripped into parts, correct?
Or crushed, depending on the details. Unless, of course, it is sufficiently elastic.

ghwellsjr
Gold Member
Or crushed, depending on the details. Unless, of course, it is sufficiently elastic.
The detail being which frame we say the train stopped simultaneously in, correct? And if we assume n_ktt meant the train's rest frame, then we have that detail, correct?

Dale
Mentor
2020 Award
Correct. But off the top of my head I don't know which way it winds up going, I would have to work it out. Either way, it would be messy for anyone on the train!

ghwellsjr
Gold Member
Well, off the top of my head, there is no difference between acceleration and deceleration and applying brakes on every car of the train is the same as rockets being fired on every car and the latter would be like Bell's Paradox which results in the string breaking so I would think all the couplers would break at a minimum.

But still the question can't come out of my mind about the time in all cars after their stop.
Even if the couplers are broken, the cars eventually stops.
The engine driver, after stopping, goes along all the cars and looks at the clocks in the cars.
All clocks should show the same time, or I’m wrong.
So the question is what is the time shown by all the clocks in the cars?

Dale
Mentor
2020 Award
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
Mentor
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