Imagine a universe in which space has the shape of a circle (consider one dimension of space for simplicity, as we often do). Then notice that for Gracie to come back to George she does not need to stop, turn around and head back to Earth. Instead, she just keeps on going and because of the circular shape of space she subsequently passes by George (somewhat as traveling on the Earth’s surface in one direction ultimately takes you back to your starting point). That is, neither observer needs to relinquish constant velocity motion; each (apparently) can rightly claim to be at rest. So, in this example, how do you think the Twin Paradox works out?
Update: In this example, I’m imagining that space itself has a circular shape, not that Gracie is traveling along a circular track within space. If you’d like, think of space like a video game screen that “wraps around”: when you reach the right edge of the screen you reappear on the left edge, and so on. The point, then, is that Gracie does NOT accelerate/decelerate to return to George. She maintains constant velocity throughout the journey.
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