Hi, Burt.

Thank you for this and for your invaluable help. The exercise of changing from a class of transform that allows changes scale (a causal transform) to a class of transform that preserves scale (a Lorentz transform) was very useful to me. The scale change doesn't matter for my argument, but keeping the scale constant is more customary. I learnt a bit having to do a Euclid-style straight-edge-and-compass construction for the Lorentz transform. It is to do with the geometry of the hyperbola, just a bit more complicated than the geometry of a circle.

You write:

"an inertial observer present at two events will always observe a shorter time interval between the two events than any inertial observer not present a both events. 'Observe' here obviously means compensating for light travel time.

"In the twin's case, the traveling twin is the only one present at the turn-around event and hence will observe a smaller outbound time."

These matters are obviously so familiar to you that what seems immediately obvious to you is far from obvious to me who is less familiar with them. Your two maxims here are so compressed into few words that your familiarity gives you an advantage. As I am reading the two above maxims of yours, they seem quite baffling. I am not saying they are not right, just that I have the impression that you find them obvious, while I don't. You seem to have access to some logic that isn't apparent to me. Can you expand a little on your two maxims, to show why they seem obvious to you, that is to say, reveal your logic that underpins them?

Christopher