Twin paradox with three inertial frames and symmetric accelerations

[edpell]

In this story we will have three inertia frames. Frame F_i where both twins start together and at rest with respect to each other. Frame F_L moving at a speed v in the negative x direction and Frame F_R moving at a speed v in the positive x direction.

Both twins zero their watches and start accelerating away from each other with acceleration -a and +a respectively. They do this until one year elapses on their local clock. They then coast for one year on their local clock. They then accelerate with rate +a and -a respectively for one year on their local clock. Then they accelerate with a rate of +a and -a respectively for one year local time. They then coast for one year local time. They then accelerate with a rate -a and +a respectively for one year local time. They are now at the same (almost the same, not exactly on top of each other) place. They both read six years on their own clock and they both read six years on the others clock.

Yes?

 

[tiny-tim]

Hi edpell!

(i don't see where the three frames come into it, but anyway …)

… They both read six years on their own clock and they both read six years on the others clock.

Yes?

Yes.

 

[mgb_phys]

Yes, but that's not really the point of the twins paradox

The paradox is that one twin comes back younger but the twin on Earth says, "I believe I was traveling and you were stationary = so I should be younger than you" The solution is that the one in the spaceship accelerated an turned round, he could detect these events and so prove he had travelled.
The cases aren't equivalent

 

[edpell]

Yes, but that's not really the point of the twins paradox

This is the NOT paradox twins. I agree this has nothing but part of the name in common with the other.

 

[edpell]

(i don't see where the three frames come into it, but anyway …)

You are right, it just clutters up the story.