← Theory of RelativityPart 0 — Foundations · 01

How Speeds Normally Add

▶ DRILL

Vika walks toward the front of a moving train. To George on the platform, she's going the train's speed plus her walking speed — and if she turns around, the train's speed minus it. Speeds just add up. It's so obvious nobody ever questions it, which is exactly why light — which flatly refuses this rule — comes as such a shock later. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words, names & pictures
🚆 TRAIN SPEED40 km/h
🧍 VIKA WALKS+5 km/h ▶
SLOW-MOnormal
▶VikaGeorgehow fast George sees Vika:train 40walk +5 km/h45 km/h
🚆 THE TRAIN
carries everything inside it along at 40 km/h.
🧍 VIKA WALKS
walks forward at 5 km/h inside the train.
🧑 GEORGE SEES
Vika moving at 45 km/h — the train's speed plus her walking.

The big idea — to find how fast George sees Vika go, you just add the train's speed and her walking speed (or subtract, if she walks the other way). Everyone does this without thinking. It works perfectly for trains, balls, planes — everything you'll ever throw or ride. But there's exactly one thing in the universe that breaks it: light. Hold onto this rule — the surprise comes when we try it on a beam of light.

# formulaw = v + u — the ground speed is the train's speed plus the walker's speed (Galilean addition)
# setuptrain v = 0–60 km/h · Vika walks u = −6…+6 km/h (forward or backward) · George measures v + u
# scaleeveryday speeds in km/h — no relativity here; the exact rule (u+v)/(1+uv/c²) differs by ~1 part in 10¹⁶ at these speeds
# nexthold onto this rule — The One Speed Everyone Agrees On shows the one thing that breaks it