I set up a Twin Paradox scenario and accompanying spacetime diagram to help better understand the resolution, but I had a question about the diagram I was hoping someone here could help answer. Please excuse the hastily drawn diagram!(adsbygoogle = window.adsbygoogle || []).push({});

(Note: the ' frame corresponds to the outbound trip, the '' frame to the return trip. I mistakenly jotted down t_{D}as 6 yr when it should actually be 16yr. My bad!)

A traveler is making a 6 lightyear voyage to a distant star at a constant speed of 0.6c. His twin remains on Earth. In the traveler's frame, the 6 ly distance is contracted to 4.8 ly (γ = 1.25). I have drawn lines of simultaneity on the diagram, as well as incoming and outgoing information at the point at which the traveler reaches his destination. Once he does, he immediately turns around and goes home at the same speed. I know that if the traveler and his twin are exchanging timestamp information, that the twin on Earth sees the traveler's clock read 8 years upon reaching the star, while his own reads 16 years. The traveler sees his own clock read 8 years upon reaching the star, while his twin's reads only 4 years. I have t_{A}= 4 yr in the diagram and t_{D}= 16 yr (note errata).

I understand that the magic of the twin paradox scenario happens when the traveler changes his reference frame and heads home. The geometry of the spacetime diagram suggests that there is an immediate shift in the lines of simultaneity between the traveler frame and the twin frame. This feels pretty reminiscent of the Doppler effect. What I don't know is how to calculate t_{B}and t_{C}, that is, the time on Earth the moment before and the moment after acceleration of the traveler back toward Earth, respectively, and how to interpret that result. Am I to understand that the traveler's acceleration corresponds with an IMMEDIATE jump in the simultaneous time on Earth? How big is this jump (t_{c}-t_{B})? Why does this occur, and why is it independent of any details of the acceleration (except initial and final velocities)?

Thanks for any insight!

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# I Lines of simultaneity in Twin Paradox spacetime diagram

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