Illustrated Physics
physics, drawn
Concept

Clock — where it appears

A device that counts the cycles of a periodic process to measure time, from a swinging pendulum to an atomic transition. Its accuracy is set by how little the period depends on anything but the process itself, and comparisons between clocks are how relativity's effects on time are measured.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The height a clock can see. The fractional difference in rate between two clocks against how far apart in height they are, on logarithmic axes — a straight line of slope one, since the shift is gh/c² and comes to 1.09e-16 per metre near the ground. a caesium fountain, good to 1e-16, resolves 91.6 cm; an optical lattice clock, good to 1e-18, resolves 0.9 cm; the best clocks built, good to 8e-19, resolves 0.7 cm. The caesium fountains that define the second reach about a metre. The optical clocks that will replace them reach a centimetre, and the best of them a few millimetres. That is the whole of why this has stopped being a test of relativity and become a way of measuring the ground. A shift once so small that it took a Mössbauer experiment in a tower to see at all is now large enough to be a nuisance: two clocks in the same building disagree, and the disagreement has to be corrected for before either can be used to keep time.

The clock that measures a height

A clock a metre higher runs faster by a part in ten thousand million million million. That was once so small it took a tower and a Mössbauer source to see; the best clocks now resolve a centimetre of height, at any distance, without a line of sight. What began as a test of general relativity has become a surveying instrument that measures the quantity surveying actually wants.

astrophysics · Gravitational redshift Where a kick lands decides whether the clock gains. A pendulum's state as a point on a circle: horizontally its angle, vertically its angular speed, both scaled by the swing, so that undisturbed it goes round the grey circle clockwise once a period and its phase is the angle round the circle from the top. An escapement's kick raises its speed: an upward jump. Kicked at the bottom of the swing (top of the circle), the point jumps straight outward — a bigger swing, phase unchanged. Kicked 42° of phase before the bottom, the jump also carries it forward round the circle, by 9.8°, and the pendulum arrives early; kicked the same amount after the bottom, it is set back by 9.8° and arrives late. The kick is exaggerated here to 0.32 of the top speed to make the angles visible.

The kick that does not change the beat

A pendulum clock has to push its pendulum, or friction would stop it within minutes, and every push risks disturbing the very period the clock exists to keep. In 1826 George Airy worked out exactly when a push does no harm: at the bottom of the swing, where the pendulum is moving fastest, an impulse changes how far it swings and leaves the timing untouched. A push before the bottom makes the clock gain; after it, lose. Three centuries of escapement design are a search for a mechanism that pushes where Airy said — or that pushes in the wrong place in a way that cancels some other error.

mechanics · Pendulum

Named alongside it

The objects these essays reach for when they reach for this one.

CalibrationCircular errorEquivalence principleEscapementFrequencyGeodesyGravitational redshiftImpulseIsochronismMeasurementPendulumPhase

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