« on: 26/04/2021 19:45:03 »
(my post #41)
In contrast, in my method their separation doesn't instantaneously change [when he changes is velocity from 0.57735 ly/y to -0.866 ly/y]. Instead, it decreases linearly with a slope of -2.047 from its peak at 18.86 until his age reaches 38.85 years old, and their distance reaches 6.188. (That endpoint corresponds to when he receives a light pulse that she sends at his turnaround).
I have just verified that the above segment is indeed a straight line. The verification is similar to what I did for the linearity of the middle segment in the age correspondence diagram (the "ACD"), which I described in Section 8, titled "Pulses Partly in Both Halves of the Minkowski Diagram", of my monograph.
On the Minkowski diagram, first find the vertical line descending from the traveler's (his) worldline at his turnaround point, down to the horizontal axis (her worldline). Mark the half-way point on that vertical line, and call it "point Q". Then draw a light pulse being sent by her, at such a time in her life that the pulse passes through that half-way point, and continues on until it reaches his worldline. Mark that point on his worldline as point R. His age is 35.75 then.
According to her, their separation at the turnaround is 23.094 ly. And according to her, that half-way point is at distance 11.547 ly from her. According to a perpetually-inertial observer traveling at 0.57735 ly/y (with gamma = 1.2247), that distance is 11.547 / 1.2247, or 9.43 ly from her. Similarly, a perpetually-inertial observer traveling at -0.866 ly/y (with gamma = 2.0), concludes that that pulse travels a distance 3.09 ly from point Q until it reaches the traveling twin at point R. So the traveling twin (he) then concludes that the distance between him and her at the instant he receives that pulse is 9.43 + 3.09 = 12.52 ly. If, on the SAAOD (Separation According to the Accelerated Observer Diagram), you plot the separation 12.52 ly when he is 35.75 years old, you will see that it does indeed lie on the midpoint of the previously described straight line.