How to measure time

Precise timekeeping is crucial for many of our daily activities. High-speed communication (on the internet or in a mobile phone network), satellite navigation, and many other tasks require time synchronisation over long distances to work properly. But how is time measured? And can quantum physics help reach better accuracies?

The basic idea behind measuring time is simple and similar to any other measurement — you simply compare the time duration with a reference. The reference has to be an event that regularly repeats itself so that a single repetition is the basic time unit and the number of repetitions gives the overall time. An example of such  process can be the Sun rising and setting every day. Its regular movement in the sky defines one of the most fundamental units of time: a day. It is a very simple and natural way to measure time but it has one disadvantage — it is long. If we want to measure shorter times, we need a better reference — a process that repeats itself faster than once a day.

For this, we can use a pendulum and let it swing. Its movement will be periodic and counting the number of swings, we can measure time. Since the period of the oscillations depends on the length of the pendulum, we can even tune it and choose how fast our reference should be. If the length of the pendulum is about 25 centimetres, its period will be 1 second. (Clocks normally use pendulums that are about 99.4 centimetres long resulting in a period of two seconds, or a half-period of one second.) Using a system of gears, the periods can be counted and transformed into movements of hands that then show time on a clock.

There is one problem with using pendulum, though. The exact period of the swinging depends on the local gravitational field which varies on different places on Earth, depending on their latitude and altitude. A pendulum that oscillates with 1 second frequency on the Equator will have a period of 997 milliseconds on the North Pole. That might not seem like such a big difference but in a single day, the North Pole clock will be faster by more than four minutes! Clearly, if we want a more precise time measurement, we need something that oscillates even faster.

Quartz crystal for a wristwatch or a clock.
Quartz crystal for a wristwatch or a clock. (Public domain, source.)

The most commonly used oscillator in today’s clocks and watches is a quartz crystal. It can be made very small and due to its mechanical properties, it can vibrate at much larger frequencies. Typically, the crystal vibrates more than 32 thousand times in a single second and is therefore much more precise than pendulum clocks. The accuracy is improved from about 15 seconds per day to half a second per day — an improvement by a factor of 30. (The improvement is not larger because quartz clocks — especially wristwatches — suffer from many technical imperfections that are not so strong in pendulum clocks.)

We can use even faster processes to further improve the accuracy of timekeeping. But it is difficult to make mechanical oscillators — pendulums, vibrating crystals, or anything else — that can oscillate at such high frequencies. We therefore need some natural oscillator with a very high frequency. For that, we can use atoms because their internal energy can only have certain discrete values and an energy difference between two levels corresponds to a certain frequency of electromagnetic field that can be emitted or absorbed by this energy transition.

On-chip atomic clock.
On-chip atomic clock. (Public domain, source.)

Atomic clocks have two advantages: they are natural oscillators (not human-made) so that atoms of a given species will always oscillate at the same frequency, and they oscillate very fast — billion times a second. There is a price to pay for this precision because, naturally, it is extremely difficult to count individual periods of a system oscillating so fast. It can still be done, though, and such clocks are now the most precise time standards we have — their error is about one second in 100 million years.

Some atomic transitions have even higher frequencies than a few gigahertz which are used in atomic clocks now. Transitions in the optical domain (in contrast to microwave transitions for gigahertz frequencies) oscillate million billion times in a single second. Those oscillations are, of course, even more challenging to count than the oscillations in current atomic clocks. Clocks based on the optical transitions — called optical clocks — are nevertheless being developed and promise incredible accuracy. With optical clocks, it is possible to measure the age of the universe (about 14 billion years) with error smaller than one second!

What are such highly precise measurements good for? Without well synchronised time across the Earth, internet communication (and any other form of high-speed communication, including mobile phone networks or TV and radio signals) would be much slower. Navigation systems (such as GPS) would not work with a few-metre precision. GPS receivers measure time delay in signals from satellites and determine the position from the delay and positions of the satellites. More precise time means better accuracy of the navigation system.

There are also many scientific applications. With precise time measurements, we can, for instance, test one of the predictions of Einstein’s general relativity which states that the flow of time is affected by a gravitational field. In a strong gravitational field, time passes slower than when the gravity is weaker. The effect is very weak in the conditions on Earth but it still has to be taken into account for satellite systems. Current atomic clocks are, in fact, so precise that this difference in passage of time can be measured in two places that are about ten centimetres above one another.

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