Is time dilation applicable to different parts of the same object? (Related to figuring out speed of light in one direction)

Question

I understand that same object is a bit of a vague and ambiguous term, but hear me out. Like many other people here I got an idea too for measuring the one way speed of light, after watching the Veritasium video, but in a different and less practical approach.

Let's say I have a really long plank, one which extends to over a kilometre, which is the distance between two clocks that I have placed. In other methods, all answers I saw used a signal caused by something like light itself, or sound. In my method, I aim to synchronise the starting time of the clocks by pushing this plank from the centre to prevent any rotation and ... Then, by placing a laser in between or at any one of them, and rigging it to hit both the clocks, I wish to compare the time difference to find out if truly the speed of light is same in all directions. Refer to the diagram I have shared just to picture it better, since it's probably hard to comprehend what I have written

So now my real question is would the plank's right end not be reaching at the same time as the left end. If that's true, that would mean that the effect of forces is also dilated, if my grammar is right? And by same object, I meant an object which has strong internal binding forces, which as we know it, moves with the same speed if force is applied at the Centre of Mass of it.

Thanks in advance,

Ravi

Answer 1

Your proposed experiment assumes that when you push the centre of the plank it transmits the impulse to the clocks at either end simultaneously. Since the transmission of the impulse along the plank is mediated by electromagnetic forces between the molecules that form the wood, you are effectively assuming that those forces operate at the same speed in both directions, which in turn means you are already assuming that the speed of light is the same in both directions.