Alice, Bob and Charlie (A, B and C) are all purely inertial "movers" in free space, each carrying a perfect clock. Since they are moving relative to each other, their clocks are not synchronized, but as Bob flies past Alice, they both set their clocks to zero. Let their relative speed by 0.8660c, so that relative time dilation is exactly 1:2, i.e. each perceives the others clock to run at half the rate of his/her own clock.

When Bob's clock reads exactly 2.0 years, Charlie happens to fly past Bob at high speed, but he succeeds to set his clock at 2.0 years at the moment they were next to each other. This is the "time handoff event" in the diagram (t

_{B}=2, t

_{C}= 2). Say Charlie is now approaching Alice at 0.8660c, i.e. the reverse of Bob's speed as seen by Alice.* When Charlie eventually passes Alice, they read each others clocks and find: t

_{A}= 8, t

_{C}= 4 years.

This is the same as the classical twins paradox solution and there is no disagreement between Gray and myself on the result. What we disagreed on previously is the answer to this question: what was the time on Alice's clock when the "time handoff" between Bob and Charlie took place?** I maintained that it is not known in any absolute sense, but if I had to put a time on it, I would choose 4 years. Gray argued for either 1 year or 7 years, depending on who looked at it from where: 1 year per Bob and 7 years per Charlie.

Now this I could also agree with, kind of, because it is a coordinate dependent observation. The problem came in when I asked Gray by how many years Alice aged between the time that Bob flew past her and the time of the hand-over event. Grey used all sorts of Lorentz transformation arguments to claim that she have aged only 1 year from Bob's perspective. The problem is that from the handover event until Charlie's eventual fly-by, the same argument is that Alice could have aged only one year from Charlie's perspective.

You can see all the elements for a paradox here. Any bets on what will happen this time around?

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Regards

Jorrie

* Bob and Charlie pass each other at a relative speed of 0.9897c (by the parallel relativistic addition formula).

** This where the title "half-twins paradox" comes from, because the full scenario is essentially stopped at the half-way mark and the situation analyzed.