← Theory of RelativityPart 1 — Special Relativity · 11

The Twin Paradox

▶ DRILL

Twins Liza and Vika are both 10. Vika rockets out to George's distant star and back at near light-speed; Liza stays home. When Vika lands, she's younger than her twin — her moving clock ran slow the whole way. The catch everyone trips on — doesn't each twin see the other's clock run slow? — is settled by the turnaround: only Vika switches frames, so only she comes back younger. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words, names & pictures

VIKA'S SPEEDvery fast

comes home ~6 yr younger

SLOW-MOnormal

👧 LIZA — stayed home

ages the full 15.0 years of the round trip — she never changed direction, so her clock is the "normal" one.

👧 VIKA — travelled

ages only 9.0 years — she comes back 6.0 yr younger than Liza.

The big idea — the twin who travels fast and comes back is younger than the twin who stayed home. Her moving clock ran slow the whole trip. "But wouldn't each say the OTHER is the slow one?" On each straight leg, yes — that's the puzzle. The tie-breaker is the turnaround: only Vika flipped around and switched frames, so only she comes back younger. This is real — scientists flew atomic clocks around the world and the flown one really did fall behind.

# formulatraveller's time τ = (2D/v)/γ < Earth time 2D/v — she ages less by the factor 1/γ

# setupstar at D = 6 light-years · speed v = 0.1–0.99 c · both twins start at age 10; faster → bigger age gap

# resolutiontime dilation is reciprocal only between inertial frames; the traveller accelerates at the turnaround, breaking the symmetry

# realHafele–Keating (1971) flew caesium clocks around the world; the travelled clocks really fell behind