How Atomic Clocks Keep Almost Perfect Time

By Sam Fan 樊潤璋

Why Do We Need Perfect Time?

Every time you launch Pokémon Go or other games that require the Global Position System (GPS), your phone’s GPS determines coordinates and shows your location. What if your avatar is teleporting across town or refusing to register the two kilometers you’ve walked to hatch an egg – frustrating, right? That’s exactly what happens when GPS timing drifts even for a small error.

Radio signals travel at the speed of light, which is approximately 3 × 10⁸ m/s. To determine the distance between you and a GPS satellite, the travel time of the radio signal emitted by the satellite to you is needed. By the simple velocity formula, we know that an uncertainty of just one nanosecond (10^-9 seconds) in a clock corresponds to about 30 cm of range error [1], so a timing drift can misplace your avatar enough to miss a rare resource in game. Without atomic-level precision, our smartphones’ “blue dot” on the map could drift wildly from reality.

Nature of Time

Let’s start with a fundamental question: What is time? Philosophers have long debated whether time “flows” like a river – an ever-moving present that carries us from past to future – or whether all moments exist equally, with past, present, and future represented as slices in a four-dimensional space, and many other competing perspectives [2]. While no one knows what exactly time is, one pragmatic point of view is that we can define the length of time by counting some repeatable, periodic processes.

The most common periodic processes are sunrise and sunset, caused by Earth’s rotation. We can also use gravity-driven swinging pendulums, which provide a near-constant oscillation period and form the basis of early mechanical clocks. Albeit less notably, even your body counts: You wake up refreshed and feel sleepy at night, which marks one full day (assuming your circadian rhythm stays on track). However, given that the Earth does not rotate at a perfectly uniform speed, and that the duration of one swing is slightly different from pendulum to pendulum due to manufacturing error [3], a new definition of time is needed. In 1927, a Canadian engineer, Warren Marrison, found that quartz crystals vibrate at a remarkably consistent frequency under an electric field [3]. When carefully cut into a proper shape and size, a standard quartz crystal in a clock vibrates at 32,768 Hz [3, 4]. By counting the duration for which 32,768 oscillations take, we can define that one second has passed.

Core of Cesium-Beam Atomic Clock

However, from 10 seconds per year for a mechanical clock to only one second in three years for a quartz clock [3], there was still room for improvement for the timekeeping accuracy. As a result, scientists developed more advanced timekeeping technologies. Cesium-beam clocks are just one member of the atomic clock family: Others include rubidium-beam standards, hydrogen masers, compact chip-scale clocks, and the newest optical lattice clocks. Cesium-beam designs remain the most widely used standard worldwide. In fact, the Hong Kong Observatory has been relying on cesium-beam atomic clocks to provide official time service since 1980, with an accuracy kept within 0.01 microsecond (10^-8 seconds) per day [5].

At its core, the clock does not “tick” atoms but counts the cycles of a microwave signal precisely locked to an atomic reference. The cesium atoms act as a built-in tuning fork; cesium only resonate to the frequency at 9,192,631,770 Hz within the microwave band to change between two very slightly different energy states. This happens when cesium atoms pass through a microwave cavity [6]. If the microwave frequency is above or below 9,192,631,770 Hz, fewer atoms undergo a change in energy levels. The irregularity can be detected, and the oscillator will be steered back onto the exact cesium resonance frequency, ensuring the microwave oscillator stays locked to atomic standard. Once the oscillator is held exactly at the resonance frequency, every single cycle becomes one “tick” of the clock. By simply tallying 9,192,631,770 of these ticks, the device measures one second [6, 7].

Since this shift in energy levels is a fundamental property of cesium atoms, every clock built anywhere with cesium atoms can reproduce the same resonance frequency of 9,192,631,770 Hz signal, ensuring that time is uniform around the world.

Importance of Time Synchronization

Every GPS satellite carries multiple atomic clocks and broadcasts signals with an accurate timestamp of when the signal is emitted, so that receivers on the ground can determine their distance to the satellite by multiplying the signal’s travel time and the speed of light [8]. Without the cesium or rubidium standards, minute timing drifts would quickly lead to substantial positional errors in just a few minutes due to the cumulative time error of the onboard clock.

Summary

In just a few decades, we’ve gone from pendulums and quartz crystals to atomic clocks and optical lattices that keep time to within a quintillionth of a second (10^-18 seconds), so precise that they can sense minuscule shifts in Earth’s gravity or hunt for hints of dark matter in the cosmos [9]. Although the principles behind atomic precision may seem complicated, the technologies they enable are integral to our daily lives. Every time we check our phones, play a game, look up our location, or simply glance at the clock, we tap into nature’s steady rhythms.

References

[1] Tavella P, Petit G. Precise time scales and navigation systems: mutual benefits of timekeeping and positioning. Satell Navig. 2020;1. doi:10.1186/s43020-020-00012-0

[2] Emery N, Markosian N, Sullivan M. Time. Stanford Encyclopedia of Philosophy. Updated November 24, 2020. https://plato.stanford.edu/entries/time/

[3] Smithsonian National Museum of American History. Splitting Seconds. On Time: How America Had Learned to Live by the Clock. https://americanhistory.si.edu/ontime/expanding/seconds.html

[4] Lombardi MA. The Accuracy and Stability of Quartz Watches. Horological Journal. 2008. https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50647  

[5] Chee SC. Network Time Service – Past and Future. Hong Kong Observatory. Updated April, 2022. https://www.hko.gov.hk/en/education/astronomy-and-time/time-service/00669-Network-Time-Service-Past-and-Future.html

[6] Hebra AJ. The Physics of Metrology: All about Instruments: From Trundle Wheels to Atomic Clocks. Springer Vienna; 2010. doi:10.1007/978-3-211-78381-8

[7] Audoin C, Guinot B. The Measurement of Time: Time, Frequency and the Atomic Clock. Cambridge University Press; 2001.

[8] Federal Aviation Administration. Satellite navigation - GPS - How it works. https://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/gps/howitworks

[9] Lea R. Atomic clocks on Earth could reveal secrets about dark matter across the universe. Space.com. Updated September 2, 2023. https://www.space.com/ultra-precise-atomic-clocks-investigate-dark-matter-earth