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Twin paradox (introductory)

Foundations · Physics

Study notes

Worked example: Twins, one stays home, one visits a star 3 light-years away at v = 0.6c and returns. What are their ages at reunion if both were 20 at departure? Step 1: γ = 1/√(1 − 0.36) = 1.25. Step 2: Earth frame: one-way time = 3 ly / 0.6c = 5 years; round trip = 10 years. Earth twin's age = 30. Step 3: Ship frame: contracted distance each way = 3 / 1.25 = 2.4 ly; time each way = 2.4/0.6 = 4 years; round trip = 8 years. Traveller's age = 28. Step 4: Difference = 2 years. The traveller is younger, and both agree because they compare clocks side by side at reunion. Conclusion: the 2-year gap is real and measurable — acceleration at the turnaround makes the traveller's frame non-inertial, breaking the symmetry.

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