[A-wal]

I'm not sure why this topic is in new theories, but I've only read this page.

Here's the space-time diagram of this signal exchange between stationary twin and travelling twin, according to Lorentz' theory of relativity.

You are perfectly free to posit an ether frame that defines motion relative to it and everything still works in exactly the same way but there is no preferred ether frame, you're free to use any frame you like. That's not a different model, that's just special relativity using one arbitrary coordinate system for every observer.

In standard explanation for the twin paradox, the stationary twin observes the travelling twin ages less than himself. He perceives that travelling twin experiences time dilation.

On the other hand, the travelling twin observes the stationary twin ages more than himself. He perceives that stationary twin experiences time contraction. It's simply the antonym for dilation. Do you have a better terminology?

Other way round! Less time passes for the more accelerated twin so the more accelerated twin has been time contracted with respect to the less accelerated twin (what you called stationary) and the less accelerated twin has been time dilated with respect to the more accelerated twin.

The whole time dilation length contraction terminology is an absolute mess. Length, wtf is that? So there's no lengths of time then? Length doesn't exclude a duration. It's the contraction of space with respect to bodies in motion relative to the observer.

But then time dilation is the extended time on the observer's own clocks with respect to bodies in motion relative to the observer, you don't see your own clocks as dilated! You see clocks in motion relative to you as contracted so why frame in in the context of unobservable dilation?

That's why I use space contraction and time contraction, time dilation is reserved for the observable speeding up of clocks that the observer is accelerating relative to which is officially called a simultaneity shift.

This time dilation is the only thing responsible for the age difference in the twin paradox because unlike space contraction and time contraction, observable time dilation is non-reciprocal in that it only applies to bodies that you accelerate relative to.

It's caused by but not proportional to acceleration so acceleration is the cause but not the direct cause. It's proportional to the change in relative velocity scaled by the distance between the observer and the clock that the observer is accelerating relative to.

two observers are both traveling at velocity v in the same direction

is meaningless unless there is such a thing as absolute velocity, which there isn't, or a third observer, which isn't stated or relevant to the question.

The only fact is that one of the observers has undergone an acceleration from 0 to v/2 relative to the other.

It only means that their relative positions don't change with time. This can be determined even when there is no absolute velocity.

So they're at rest relative to each other then, so the question is just: How does each observer measure the tick rate of the other observer's clocks if two observers are at rest relative to each other and one of them then accelerates relative to the other? Which of the two observers experiences time at a slower rate after the acceleration?

The answer is that after the acceleration when they are in constant motion relative to each other each sees the other clock as time contracted (running slower than their own clock) by T = t(√((c^2−v^2)/c^2)). During the acceleration the observer that is accelerating relative to the other observer sees the other observer's clock as time dilated.

This is caused by changing to a frame in which the distance between the observer that they're accelerating relative to and other bodies at rest relative to that observer become shorter in their new frame so it takes less time to travel those shorter distances.

If you like I can post a screenshot of the general formula I derived that works for simultaneity shifts of any acceleration profile regardless of how unsmooth it is.

[paul cotter]

This topic is in "New Theories" because it is an exercise in confusion.

[A-wal]

There's no need for any confusion.

An ether frame works but it works for any frame, so if there's no preferred ether frame it's just special relativity using the same frame for every observer.

The confusion for terms like time dilation is the fault of the official terms being very misleading, so clarity about the context is important.

The twin paradox time difference is caused by the traveling twin accelerating to a frame in which the distance between the Earth observer and the turnaround point becomes shorter while the traveling twin is in motion relative to them so it takes less time to travel that shorter distance.
This causes a non-reciprocal time dilation (speeding up) of Earth's clocks from the perspective of the accelerating twin but only at the turnaround point, not the initial and final accelerations because simultaneity shifts are proportional to distance.

[paul cotter]

I know there is no need for confusion but this particular thread is bedevilled with utter confusion.