Time Sync Problems: Answers to Questions on Moving Train Synchronization

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whereisnomar
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http://galileoandeinstein.physics.virginia.edu/lectures/synchronizing.html" the website talks about synchronizing clocks on a moving train. But I have a few questions about it:

1) Why are you allowed to add ct+vt on the left-hand side of the first equation below the picture of the train? I thought one of the main tenants of Special Relativity was that you can't add velocities (or I'd assume distances) without taking into account the dilation/ contraction of that quantity.

2) What would happen if you stopped the train, and then looked at what the clocks say? Would they be synchronized or not? I understand that the train would enter a noninertial reference frame, which would change how they behave, BUT wouldn't both clocks be affected equally... so who is right once the train is stopped- the person who says they're synchronized, or the person who says they're not?

THANK YOU SO MUCH!
 
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whereisnomar said:
http://galileoandeinstein.physics.virginia.edu/lectures/synchronizing.html" the website talks about synchronizing clocks on a moving train. But I have a few questions about it:

1) Why are you allowed to add ct+vt on the left-hand side of the first equation below the picture of the train? I thought one of the main tenants of Special Relativity was that you can't add velocities (or I'd assume distances) without taking into account the dilation/ contraction of that quantity.

2) What would happen if you stopped the train, and then looked at what the clocks say? Would they be synchronized or not? I understand that the train would enter a noninertial reference frame, which would change how they behave, BUT wouldn't both clocks be affected equally... so who is right once the train is stopped- the person who says they're synchronized, or the person who says they're not?

THANK YOU SO MUCH!

It didn't say that velocity is added, ct+vt is the distance which had been through a length contraction.

Though I didn't learned much of it, I don't think that the clock would be synchronized. Because according to the rest frame it is not synchronized even when the train is still moving, for different frames have different synchronization.
 
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So at what point would the person on the train see them leave synchronization, then?
 
schaefera said:
So at what point would the person on the train see them leave synchronization, then?

I think just when the train changes speed. Look at the time of rear and front, they depend on c+v and c-v, so when v changes time would change. Synchronization means when the two times are equal, but if they are equal at one v they got to be different when v changes.