How Do Clocks Keep Time? Find Something That Repeats and Count It

Early timekeeping measured a flow rather than counting a repetition, which is why it was so poor. A sundial reads the sun's position directly, which is accurate in principle and useless at night, in cloud or in winter at high latitude, and it measures local solar time, which differs between any two places east or west of each other. Water clocks, used in Egypt, Greece, China and the Islamic world, measure the flow of water through an aperture, which changes with temperature, with pressure as the vessel empties and with mineral deposits, and elaborate designs including compensating reservoirs improved them without fixing the principle. Candle clocks, incense clocks and sandglasses share the problem. The best of these were accurate to perhaps fifteen minutes a day, which was adequate for monastic offices and useless for navigation or science.

Galileo observed around 1602 that a pendulum's period depends on its length and, for small swings, not on the size of the swing, which is the property that makes it a usable oscillator. Christiaan Huygens built the first pendulum clock in 1656 and it immediately improved accuracy from around fifteen minutes a day to about fifteen seconds. Three refinements followed over the next century: the anchor escapement, which lets the pendulum swing in a smaller arc where the isochronism holds better, temperature compensation using combinations of metals with different expansion rates so that the effective length does not change with the seasons, and careful suspension to reduce friction. The best regulator clocks of the early twentieth century, kept at constant temperature in a vacuum tank in an observatory basement, reached about a hundredth of a second a day, which is where mechanical timekeeping ended. The pendulum also has a fundamental limitation: it depends on gravity, so it cannot work on a moving ship.

Finding latitude at sea is straightforward from the height of the sun or the pole star. Longitude requires knowing the time at a reference place while observing local noon, since the Earth rotates fifteen degrees an hour, so a clock that keeps reference time through a voyage solves it. The British Parliament offered a large prize in 1714 after a naval disaster caused by a navigational error killed around fourteen hundred men. The prevailing opinion favoured an astronomical solution using the moon's position, and John Harrison, a Lincolnshire carpenter, spent decades building marine timekeepers instead, solving the problems in sequence:

• •A gridiron pendulum and later a balance mechanism compensating for temperature
• •Bearings requiring no lubrication, since oil thickens with cold and changes the rate
• •A drive that continues turning while the mechanism is being wound
• •A design immune to the motion of a ship, achieved by abandoning the pendulum entirely for a balance wheel with springs
• •His fourth timekeeper, completed in 1759 and the size of a large pocket watch, lost about five seconds on a voyage to Jamaica, well within the prize requirement, and he was paid only after prolonged obstruction and an appeal to the king

The next oscillator came from physics rather than from mechanics. A quartz crystal deforms when a voltage is applied and generates a voltage when deformed, and a crystal cut to the right shape vibrates at a very stable frequency when driven by a circuit. The first quartz clock was built in 1927, and by the 1970s the technology was cheap enough for a wristwatch, which is why almost all mechanical watchmaking collapsed within a decade in what the Swiss industry calls the quartz crisis. A standard watch crystal runs at 32,768 hertz, chosen because it is two to the fifteenth power and a simple chain of circuits dividing by two fifteen times produces exactly one pulse a second. Atomic clocks go further by using the fixed energy difference between two states of an atom: microwaves are tuned until they cause a transition in caesium atoms, and the frequency at which that happens is a property of the atom rather than of any manufactured object. Since 1967 the second has been defined as 9,192,631,770 of those oscillations, which means the definition of time itself is now a count.

Extreme accuracy sounds like an end in itself and is load-bearing infrastructure. Satellite navigation works by measuring the travel time of signals, and since the signals travel at the speed of light, an error of a billionth of a second is an error of thirty centimetres, so the satellites carry atomic clocks and the system corrects for the fact that time runs measurably faster in orbit, both because the satellites are higher in the gravitational field and, opposingly, because they are moving. Financial markets timestamp transactions to microseconds and regulators require synchronisation. Telecommunications networks depend on it. The current generation of optical clocks, which use a laser to drive transitions in strontium or ytterbium at frequencies a hundred thousand times higher than caesium, are accurate to within a second over the age of the universe, and they are precise enough that raising one by a few centimetres changes its rate detectably, which makes them instruments for measuring gravity and, potentially, the shape of the Earth.

A clock needs something that repeats steadily and a mechanism to count it, which is why sundials and water clocks, which measure flow, were so poor. The pendulum, adopted by Huygens in 1656, cut error from fifteen minutes a day to seconds, could not work at sea, and was replaced there by Harrison's balance-wheel marine timekeepers that solved longitude. Quartz crystals vibrating 32,768 times a second replaced mechanical watches in a decade, and the second is now defined as a count of caesium oscillations, a precision that satellite navigation depends on directly.