twin paradox

One twin boards a fast rocket, races out to a distant star and back, while the other stays home on Earth. When they reunite, the traveller is genuinely younger; less time has elapsed on her body and her clocks. The puzzle, the 'paradox', is that time dilation is supposed to be symmetric, so why does only one twin come back young instead of each finding the other younger?

The resolution is that the two situations are not actually symmetric. The stay-at-home twin remains in a single inertial frame the whole time, never feeling any push. The travelling twin must fire her engines to turn around, and during that turnaround she changes frames and feels real acceleration. That broken symmetry is what makes one path objectively different from the other; the naive 'each sees the other slow' argument quietly assumes a symmetry that the turnaround destroys.

Seen through spacetime geometry, the answer is clean and needs no acceleration formulas at all. Between two events, the straight, unaccelerated worldline accumulates the most proper time, and the traveller's bent, out-and-back path is shorter in this special sense. So she simply ages less, for the same reason a dog-legged route covers less 'time-distance' than the direct one. It is not a paradox once you accept that spacetime measures elapsed time along a path, not along a single universal clock.

This is settled experimental fact, not a thought experiment frozen on paper. Particles whipped around storage rings live measurably longer than their resting kin, exactly as the bent-path picture demands, and precise atomic clocks flown around the world have come home reading slightly behind clocks left on the ground. The traveller really does return younger; the only illusion was ever calling it a paradox.