Twin paradox in special relativity: length contraction

Can the concept of twin paradox be applied to length contraction as well? meaning that the twin which is in spaceship will have its meter rod "actually" contracted while he will see his brother's meter rod contracted which is in fact will be an "apparent" effect.

Despite their superficial similarity Lorentz contraction and time dilation are different things and this is why there isn't a distance version of the twin paradox.

To see the difference you need to understand that a clock is a form of odometer. Suppose you start at the origin and travel 100 metres, then the odometer you carry will show the total distance you've moved in space i.e. 100m. Suppose you are also carrying a clock, which you set to zero at the moment you start walking, then after you've finished the walk your clock will show some time $t$. This time $t$ is the distance you've moved in time, just like the odometer shows the distance moved in space.

The twin paradox is that the two twins end up having moved different distances in time. That is, they both start at the same point on the time axis $t = 0$ but when they meet again they find have travelled different distances in time so their clocks show different times. (At this point we should issue the obligatory statement that the twin paradox isn't a paradox.)

If there were a distance version of the twin paradox it would be that on their return each twin observes the other twin to have moved a different total distance in space. Actually this is indeed the case, though since moving at different speeds in distance isn't as interesting as moving at different rates through time the distance version of the twin paradox has yet to catch on.

But when we talk about Lorentz contraction we normally aren't talking about the distance moved in space. Instead we consider some object, like a metre ruler, and calculate how the length of that object decreases with velocity. While length contraction is a real effect, what actually happens is that the metre ruler rotates in spacetime. As viewed by the static observer the proper length of the ruler remains constant, but the two ends of the ruler shift to slightly different times. In the case of our twins each twin would see the other twin's ruler rotated in spacetime by equal and opposite amounts, so actually the situation is perfectly symmetrical.

• It might be worth clarifying that the contraction only happens in the direction of motion, so if the one twin is moving directly away from or toward the other, length contraction only happens in that direction, which could make it hard to see (aside from the contraction of space between them for the traveling twin). If the traveling twin instead flies by his sibling, it’ll be much easier to see and measure the contraction of meter sticks and everything else. Commented Mar 28, 2022 at 20:02

This might or might not be responsive to the question you intended to ask:

Suppose you've got a meter stick. Over a period of time, I apply identical forces to the front and back ends of that meter stick, causing them to accelerate in the same direction. Therefore the entire stick, being a rigid body, accelerates in that direction. After a while, the forces stop, so the stick is now moving at a fixed velocity.

In your frame (the frame the stick was in to begin with), the length of the stick can't change, because we applied identical forces to the front and back, so the distance between the front and the back can't change. On the other hand, the Lorentz contraction tells you that the (now-moving) stick is shorter in your frame than it is in its own frame. This means the moving stick, in its own frame, is now more than a meter long. It has stretched.

(In its own frame, the moving stick says that it has stretched because the front started accelerating before the back did.)

But there is a limit to how far you can stretch a stick. So if you get the velocity high enough (no matter how gently you accelerate it to that velocity) the stick must snap. And of course all observers must agree that it has snapped. I think we can count that as a real effect, which no observer can dismiss as merely "apparent".

I'm still a little unclear on whether we can give a completely non-relativistic explanation of why the meter stick snaps. I once asked a closely related question here.