LIGHT CLOCK
One postulate, one right triangle — and time itself gives way. γ = 1.25, bitwise.
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
Two identical clocks made of nothing but light: a photon bouncing between mirrors, one tick per round trip. One sits still; one glides past at a good fraction of c. Then the single strangest sentence in physics: both observers measure the photon at exactly c.
Pythagoras
Seen from the ground, the moving photon travels a diagonal — a longer path — but refuses to exceed c, so the tick must take longer. Solve the right triangle and time dilation falls out in one line: t = γt₀. No machinery in history has derived so much from so little.
The factor
γ prices everything. At β = 0.6 it is exactly 1.25 — five rest ticks for every four moving ticks — and the same bargain shortens lengths: a rod along the motion measures d/γ, because a sideways light clock only keeps time with its upright twin if it shrinks.
The race
Both photons fly at exactly c — watch them. The moving one zigzags, and its counter falls behind on a precise schedule: the tick ratio is γ to the last digit. Nanoseconds, honestly slowed; no gears, no trick — geometry alone is doing this to time.
Audit
Audited to zero residual: the photon’s triangle closes exactly, the interval c²t² − x² is identical in both frames — and the crown, Michelson–Morley resolved: the longitudinal arm ticks in step with the transverse arm only if it contracts by γ. The 1887 null result, reproduced as an identity.