I don't understand. My stated requirement involves relative motion between inertial clocks. The clocks are not stationary with respect to one another.

No, of course not, and I didn't say so. For any stationary clock, relatively moving clocks are moving, and 'tick at the rate of 1/γ'. But suppose we have two clocks moving north and south at equal speeds. They'd tick at the same rate despite their relative motion. So the validity of your requirement depends on a coordinate system in which the one clock is stationary.

In other words, if I add the words you suggest, I would not even understand the meaning of the statement anymore.

I added one word. That so bad? Other clocks don't tick slower at the rate you specify relative to a non-stationary clock. I've given a simple example illustrating the point.

Could you please connect your words and mine together in one sentence or phrase, and then tell me what you think it means? Also, please tell me stationary with respect to what?

Well, stationary wrt/ the coordinate system chosen. Without that coordinate system, such statements are meaningless, and relative to a different choice of coordinate system such statements are wrong. So to add a little more than just one word:

You want a method that satisfies the requirement that, "for all inertial clocks, relative to an inertial coordinate system in which that clock is stationary, a moving clock ticks at a rate of 1/γ = 1/gamma of the rate of the stationary clock."

That's a thin requirement, and I'm not sure if D&G or Minguzzi methods violate that since they're not necessarily using an inertial coordinate system at all when making their calculations. I'm unclear about how D&G works, but Minguzzi is definitely using a totally different sort of coordinate system than the inertial one typically used for Minkowski spacetime. In fact, in a way it resembles (and can be reduced to) the non-inertial comoving coordinate system used by cosmologists for non-local descriptions of things. I digress I think...

Yes, I agree SR lets you look at a situation from any perspective. You had mentioned earlier that it would be easier if the traveler used the stay-home frame. The correct way to do this is by transforming the coordinates from one frame to another.

Ach no! Just use the one system the whole time and don't translate anything at all. Of course Bob's going to need a clock that displays time and speed and such, but it's a digital clock hooked to an accelerometer so that shouldn't be unworkable.

So, in the traveler's frame, he is stationary & she is moving

My suggestion was to completely ignore the traveler frame.

his clock ticks at the normal rate & hers tick at a slowed rate. But he can transform coordinates from his frame to her frame. In that case she is stationary & he is moving, her clock ticks at the normal rate & his tick at a slowed rate.

He has almost no coordinates to translate since in his frame he's always 'here' and stopped. That's useless. He needs something like a speedometer and odometer, just like a car has, neither of which he would have if he used his own frame. No car attempts to use its own coordinates (I'm always here and stationary!) and then translate to a standard one. It uses the standard coordinates the whole time. Our hero is in a car and he knows it.

One does not need to select Alice's frame as the standard one. Any arbitrary frame will do, but if Alice is not stationary, she'll need a speedometer, odometer, and funny clock just like Bob.

You are mistaken if you think the reason that the traveler ends up younger is because acceleration is absolute. There is no variable for acceleration in the SR equations.

I didn't claim that acceleration was the reason, which is easily verified right here on Earth by comparing a couple atomic clocks that differ only in acceleration, but not speed. If you asked, I'd say the reason is moment-of-acceleration, but I've not mentioned that until now. It's a term not often mentioned in the articles I find, but it's explicitly computed in the CMIF method. That's not 'the' correct answer since there are several different explanations that are all correct. One simply involves computing intervals between events.

It doesn't matter that acceleration is absolute.

I brought it up because the CMIF method assumes Bob is stationary both before and after a significant acceleration, which seems to violate a different but reasonable requirement, one that the pick-a-frame method doesn't violate.

You could make something similar to the "twin paradox" in which both twins accelerate equally. Let Bob and Alice be twins born at the same time, and let Bob accelerate away from Alice and then coast away at constant speed. Due to relative motion alone, Alice says Bob's clock ticks slower than her own, and Bob says Alice's clock ticks slower than his own. After awhile, Alice accelerates in the exact same way that Bob did, and then she starts to coast in the same exact way. Now both twins are stationary with respect to one another, although they are some distance apart. Now Alice is younger than Bob, even though they both accelerated identically, albeit at different times.

Not in Earth's frame she isn't. That's why specification of frame is important, and your statement that Alice is younger than Bob omits any explicit frame. Seatmates on an airplane are stationary relative to each other but not necessarily stationary because of that. Almost all the confusion, often deliberate confusion, results from lack of frame specification when making such statements.

Oh, and thanks for picking up on the perpetual victims Alice and Bob, (and occasionally their mutual nemesis Victor).

It is not the "standard" way in SR for everyone to agree to use one frame. It is standard for everyone to use their own rest frame, and then they can transform to other frames.

Buck lack of the specification makes for ambiguous statements. I'm find with any choice of frame as long as it's explicit.

Using your example again where the traveler uses the stay-home frame, that is not standard. Because it is not standard for the traveler to think his own clock is ticking slow.

For doing local things in and about the ship, sure, but for interactions with home, neither frame is the best choice. He personally has no need of it. He cares about what age she appears now, which is whatever age she was when each photo-message was sent. She'll appear to age quite slow on the way out and stupid fast on the return leg. Both of them get that, and at the same two rates as well. Nice and symmetrical.

For example, they're talking about Betelgeuse in the news. Just google the one word. First hit today says: "

**Huge red star might explode soon and next few weeks are critical**"

That's the standard that is used, the only one with practical value. Not our frame, and not its frame (not that it's a whole lot different). They use what they're seeing now. The star is 642+ light years away but no headlines reads "Huge red star might have exploded 642.4 years ago and the weeks just before that are critical".

The only reason there appears to be discontinuities in ages of distant things is because we let the turnaround acceleration be instantaneous, which creates an undefined slope at the turnaround point,

I know. With any finite acceleration, you get a very steep slope with something like the CMIF method.