Twinne & Twynne: Twin Paradox
Relativity & Gravity arc, page 29 of 193. Back to The Pixelated Physics Universe
Who they are
Twinne stays home. Twynne flies out at 0.8c and back. They meet again 20 years later for one of them and 12 for the other.
Twinne & Twynne is a character of the Relativity & Gravity arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Each clock records the proper time along its own path through spacetime. The traveller's path is shorter in proper time, so at 0.8c a 20-year round trip on Earth lasts 12 years for the traveller. The gap comes from the geometry of the two paths, not from acceleration itself. Einstein predicted the clock effect in 1905, and Paul Langevin recast it as a human traveller in 1911.
$$ \begin{gathered} \tau = \int \sqrt{1 - \frac{v^{2}}{c^{2}}}\;dt \\ v = 0.8c,\ \ \gamma = \tfrac{5}{3}: \quad 20\ \text{yr (Earth)} \ \to\ 12\ \text{yr (traveller)} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\tau$ | proper time recorded by a clock along its path | s |
| $v$ | speed of the clock in the Earth frame | m/s |
| $c$ | speed of light, 299 792 458 m/s (exact) | m/s |
| $t$ | time in the Earth frame | s |
| $\gamma$ | Lorentz factor 1/√(1 − v²/c²) | 1 |
Sources
- Einstein (1905) Zur Elektrodynamik bewegter Körper, Ann. Phys. 322, 891
- Langevin (1911) L'évolution de l'espace et du temps, Scientia 10, 31–54 (English translation on Wikisource)
- Pesic (2003) Einstein and the twin paradox, Eur. J. Phys. 24, 585
Crossovers
Twinne & Twynne meets Jetlagga (Clocks Around the World 1971). Twinne and Twynne predict that the travelling clock records less proper time. Jetlagga carried real caesium clocks around the world in 1971 and measured differences, east versus west, that combine motion and gravity as relativity predicts.
Twinne & Twynne meets Tethra (Bell's Spaceship Paradox). Twinne and Twynne show that clocks disagree. Tethra shows that lengths do too: two identically accelerating rockets keep their launch-frame gap, so in their own frame the thread between them is stretched until it snaps.
Twinne & Twynne meets Sir Aetheron (Luminiferous Aether and Michelson–Morley). Sir Aetheron's null result fits Twinne and Twynne's world. If light's speed is the same in every inertial frame, there is no aether wind to detect, and clocks on different paths must disagree.
Wear the lore
- Twinne & Twynne – The Twin Paradox Physics T-Shirt
- Related infographic poster: Ives–Stilwell – Plate 027 Physics Poster
Concept keywords: Twin Paradox, Twinne & Twynne, Relativity & Gravity, physics lore, Pixelated Physics