Graphical Derivation of the CADO Equation

You talk like I'm the only person in the world who believes that when the traveler suddenly changes his velocity at his turnaround, that he rightfully concludes that the home twin suddenly gets much older. I'm in good company: Brian Greene (previously referenced) expresses the same conclusion in his NOVA TV show (and in his book, The Fabric of the Cosmos). And so does Taylor and Wheeler, in their excellent SR book. And so does Roger Penrose, in his famous Andromeda Paradox. There are many others ... it is the mainstream view. The result given by the CADO equation is exactly the same result that is given by the Lorentz equations. But the CADO equation is quicker and easier, and the CADO terminology and variable names were chosen to reduce common errors that are frequently made when using the Lorentz equations.

The fact that I haven't changed my opinion of the proper resolution of the twin "paradox" in 2o years is a good thing ... it's got "staying power".

 

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Note though, as we saw earlier, that some of the terminology was quite badly defined, but nothing that couldn't be fixed.

Also, you have accidentally skipped post #298, and with it, post #294.

 

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On the left, Chuck is moving to the right at .9c relative to Alice.
The red line is the time dilation transformation (.44) of Chuck time to Alice time.
The green axis of simultaneity (aos) allows Chuck to assign a time corresponding to an Alice event, for a given relative velocity. It's valid until Chuck changes velocity as it does at Alice time A40, Chuck time C17.6.
As an experiment, Chuck will send blue light signals to Alice and assign a time upon the return signal (the SR clock synch method).
On the right are Chucks assigned times.
The expected reciprocal triangular path for Alice is not there.
The time dilation is correct while diverging and converging.
The middle portion is strange with two instantaneous velocity changes for Alice and a parallel path with the Alice clock running faster than the Chuck clock.
Chuck receives every signal from the Alice clock and assigns a time, contrary to the popular 'missing time' or 'time jump' explanation.
The problem is the assumption that the aos is valid for a discontinuous path. It depends on velocity, and the transition from outbound to inbound is missing.
The initial C path is not realistic motion for masses other than particles on the scale of atoms.

Truth will never be decided by an opinion poll.

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The instantaneous velocity change can be approximated arbitrarily closely by a continuous velocity change produced by a constant finite acceleration. In that case, the home twin's rapid age change is continuous ... nothing is "missing".

 

You're looking through the wrong end of the telescope! It's a real continuous motion being approximated (carelessly) by two straight lines. If you agree the curved path provides a continuous aging of the static twin, then why the need for a 'time jump'? If the spacetime graphic was drawn more accurately, the dynamic duo here would not be posting speculation about a fictitious problem. SR does not predict 'time jumps'.