MUONS
One in ten billion should arrive. A hundred do. The sky votes for relativity.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Fifteen kilometers up, cosmic rays mint muons — heavy, unstable cousins of the electron that live 2.2 microseconds and then vanish. They fall toward the ground at very nearly the speed of light, and the sky repeats this experiment, everywhere on Earth, every second.
The sentence
The classical arithmetic is a death sentence: the trip takes some fifty microseconds — more than twenty lifetimes — so survival should be one in ten billion. Essentially none should arrive. Yet detectors at sea level count muons by the hundreds per square meter per second. Either the clock is wrong, or the map is.
Two stories
Earth’s story: the muon’s clock runs slow — its lifetime stretches by γ. The muon’s story: its clock is fine, but the atlas exaggerates — the atmosphere is only h/γ thick. Slow clock or short sky: two incompatible-sounding narratives whose survival arithmetic comes out identical, to the last bit.
The descent
A thousand muons fall, and the counter runs the closed-form exponential — no dice, no simulation, just N = 1000·e^{−t/γτ} evaluated live. Around a hundred touch the ground, against a classical forecast of essentially zero. Rossi and Hall measured exactly this in 1941: relativity’s first everyday confirmation.
Audit
The audit is the principle of relativity itself: the Earth-frame exponent t/(γτ) and the muon-frame exponent (h/γ)/(βcτ) agree at machine epsilon — because the survival count is a fact, and facts are frame-invariant. Time dilation and length contraction are not two effects; they are one bargain, seen from two chairs.