But those two intervals of 3.2 seconds do not cover the entire length of Bob's worldline between the two meeting events; i.e., they do not cover the the entire length of the third side of the triangle in spacetime (see below). There is a gap in between them, 3.6 seconds long, corresponding to the change in simultaneity conventions between the outgoing and ingoing legs of the traveling twin's trip (or between Lucy and Betsy, if you look at it that way).Each of them sees Bob's clock ticking 3.2 seconds while their own ticks 4 seconds.
Sure we can. Each 4 is the length of one side of a triangle in spacetime. Adding the two together gives the combined length of the two sides. This can then be compared with the length of the third side (10). It's just geometry.But we can't just add 4+4 to get 8,
A calculation comparing the sum of the lengths of two sides of a triangle in spacetime with the length of the third side, as above. Again, it's just geometry.What kind of calculation would you be doing where it's appropriate to add his four second to your four seconds?
Physically, the sum of the lengths of the two sides gives a very good approximation to the proper time experienced by a traveling twin who turns around very sharply at the vertex of the triangle between the two sides of length 4. Understanding that this calculation is just geometry, and doesn't depend on your choice of coordinates, can help to drive home the point that the traveling twin will be younger than the stay-at-home twin when they meet up again, and that that fact is independent of your choice of coordinates; it's an invariant fact that arises from the geometry of spacetime.