 Just after turnaround, if he recalculates, he will measure the interval from the origin to the lower red line.In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the Earth-based twin.When one transfers from the outgoing inertial frame to the incoming inertial frame there is a jump discontinuity in the age of the Earth-based twin (6.4 years in the example above).