Another time dilation question

[PatPwnt]

Say we synchronize two clocks in a spaceship each at the opposite ends of the ship a length of x'. Now we accelerate the ship to a velocity v with respect the the initial rest frame. So now according to the rest frame. The clocks are out-of-sync by vx'/c^2. What exactly happened to the clocks when they were accelerating to make one of them ahead of the other in the rest frame? Or is this all wrong?

 

[MeJennifer]

Good but ambiguous question.

An extended object, like a space ship, cannot remain Born rigid during acceleration. To avoid confusion I would advice to rephrase the question into:

Two test masses at rest with respect to each other with a radar distance of r accelerate at the same time (using Einstein's synchronization convention) with a proper acceleration a. After this acceleration is their radar distance still r and are their clocks in sync?

 

[yuiop]

This old thread addresses exactly that question and has some equations and diagrams that should be helpful to you.

https://www.physicsforums.com/showthread.php?t=216113

As a general rule the clocks will not still be synchronised after the acceleration except under some very careful set up acceleration schemes. Born rigid acceleration does not result in the clocks remaining synchronised and as Jennefir has aluded to, extended objects would not, as a rule, naturally undergo Born rigid acceleration unless every atom of the extended object had its own carefully synchronised rocket moter.