← Theory of RelativityPart 1 — Special Relativity · 08

Why You Can't Add Velocities

▶ DRILL

Vika's ship flies at half light-speed and fires a probe forward at half light-speed. The everyday rule from How Speeds Normally Add says just add them — a whole light-speed. But George measures only 0.8c: speeds don't simply add. The real total is always squished to stay under light-speed, and firing actual light gives exactly c — the same answer everyone gets. That's why nothing can outrun light. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words, names & pictures
🚀 SHIP SPEED0.50c
🎯 PROBE SPEED0.50c
SLOW-MOnormal
🚀 Vika fires a probe — how fast does George measure it?George0light-speedimpossible — nothing goes herejust add: 1.00creally: 0.80c
➕ JUST ADD THEM (drill 01)
0.50c + 0.50c = 1.00c
✅ WHAT GEORGE REALLY MEASURES
0.80c — squished to stay under light-speed.

The big idea — you can't just add speeds when they're huge. Adding would push things past light-speed, and nothing ever goes that fast — so the real total gets squished back under light. At everyday speeds the squish is so tiny you'd never notice (that's why drill 01's "just add" works perfectly for cars and trains). And fire light itself, and everyone measures plain light-speed — exactly the light drill. This is the reason nothing can outrun light, which is a whole drill of its own.

# formulaw = (u + v) / (1 + uv/c²) — the relativistic sum; never exceeds c, and equals c when u = c
# setupship v = 0–0.99 c · probe u = 0–1 c (u = 1 fires light) · George measures w; "just add" shown for contrast
# scalereduces to drill 01's v + u at low speed (correction ~1 part in 10¹⁶ at car speeds); recovers drill 06's c for light
# nextbecause the sum can never reach c, nothing can outrun light — coming up in Part 1