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'The Elegant Universe' and 'The Fabric of the Cosmos' I liked them both. They are funny in that some ideas are over simplified and other ideas (which I consider hard) are left with no attempt at simplifying. Well, maybe they are simple and it was just me.
Ok. There are math notes for the chapter in the back of the book. Will post a picture here later. Chapter 2 Math notes on page 392 for those with a copy. Here's the pic, sorry it's so big. Please Register or Log in to view the hidden image! I'm now thinking the slowing of time would shorten the world line of the object in spacetime??
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t_B is defined in my post called: "Constructing Time from Four Axioms". The minus is an error it should read speed-in-time = c m/s. If one need clock B to check clock A, one could equally well search for clock C to check clock B and so on until reaching a stage where there are no further clocks.