How big is our Galaxy.

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So in all cases - SR, cosmology and black holes - we have two completely separate effects: observational effects caused by Lorentz and doppler, and then we have shortening of the time-line caused by acceleration. In all cases - Twin's Paradox, cosmology and black holes - these two separate effects are totally confused, and leads to all sorts of misunderstandings.

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I like this way of thinking about things, it really clears a lot up.But if they are really completely different effects doesn't that make it a coincidence that when the twin is coming back to earth the observational effects will adjust the rate of his clock as to make it read what it should read based on the lengthening of his path through space-time?

So if I were to imagine this on a space-time diagram, with instant accelerations, it would look like a four sided polygon with two sides parallel and the others sides symmetrical. I don't if that is a good way to describe it, but I think you know what shape I'm thinking of. Then, since the the twin takes a longer route to get back to the reference frame he started at (the part of the diagram that runs parallel with the original twin), his clock will read less time compared to the twin who just stayed in his refernce frame. Is this correct?So is the maxim, "The longer the path one takes to get to a particular reference frame, the less time there clock will read compared to someone who took a shorter path to get to that reference frame."