I've been doing some doppler thought experiment around the twin paradox,

(wikipedia) The paradox centers on the contention that, in relativity, either twin could regard the other as the traveler, in which case each should find the other younger—a logical contradiction.

Let's say Bob and Alice are twins who can measure each other's wavelength shift. As they move apart, they will see eachother red-shift. If you see a person red-shifted, you see them in slow motion, and if you see them blue-shifted you see them in fast forward. (Einstein thought about looking at the hands of the clock tower while moving away from them in a tram).

Scenario 1: Bob moves away and Alice stays put. Both instantaneously see eachother red-shift. At some point, Bob decides to stop and move back towards alice. Immediately Bob will see Alice blue shift. But Alice will have to wait until the light of the turnaround event has reached her, before she will see Bob blue-shift. Bob will see Alice red/blue 50% / 50% of his travel time, and Alice will see Bob more red than blue. So Bob will have aged less.

Scenario 2: Bob and Alice both move away from eachother at half the speed that Bob did in Scenario 1. Both turn around at the same time, and both will see eachother red/blue 50% of the time. They will have the same age. Both can clearly distinghuish this situation from the first, and also now they both have to agree on their turnaround timing, while in Scenario 1, Bob could decide by himself whenever he wanted to turn.

Scenario 3: Alice moves away, Bob stays put, the reverse of Scenario 1. Now Alice will instantly see Bob's color change as she reverses direction, thus making her the traveler.

It seems to me that after Bob and Alice reunite and compare measurements, it should be possible for them to figure out who was the traveler. There also seems to be no meaningful age comparison possible if the twins do not at some point reunite at the same location, because how would that work. Furthermore, can we conclude from these examples that changing course is what slows down the course-changer's clock? I would define changing course as being any change in velocity with respect to the other person. To move apart and rejoin, requires at least two course changes, so in the end: does this mean that, acceleration is the key to resolving the twin paradox? That the one who has a force acted upon her/him, will have his/her clock slowed down? If the answer is yes, it would be a relatively (no pun intended) logical direction of thought to reason that this could explain as to why gravity slows down clocks? But this raises another question: A course change requires a short time of force acted upon the traveler, if this slows down a clock, gravity seemingly exerts a continuous force on the traveler, but the clock does not keep on slowing down, or does it?

• You can trivially tell by the acceleration who is and who is not in an inertial system. What, exactly, is your question? Does relativity regard inertial and non-inertial systems equal? No. Commented Oct 19, 2022 at 3:48
• What specifically is the question?
– Dale
Commented Oct 19, 2022 at 4:13
• This can certainly be turned into a correct argument, but you have to be careful about how you say it. For example, in your first scenario, Bob's clock runs slow in Alice's frame on both his inbound and outbound journeys [and by exactly the same amount for each leg of the journey], even though what she sees through her telescope is slowed-down Bob on the first leg and sped-up Bob on the second leg. Failing to call attention to this distinction risks creating great confusion for your audience. Commented Oct 19, 2022 at 4:22
• Why do you think you are missing something? You describe the three scenarios correctly, so what's the problem? Commented Oct 19, 2022 at 6:03
• @twmen your extension to your original question is just wrong, I'm afraid. The twin paradox is a consequence of the geometry of spacetime, and has nothing to do with forces slowing down clocks. You can formulate a version of the paradox that doesn't involve acceleration or forces and the effect remains. Commented Oct 19, 2022 at 20:53