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• Kristjan Salev

HOW DO CLOCKS MEASURE TIME

Updated: Apr 24, 2022

Atomic clocks are the most accurate time indicators we have today. In order not to mislead the reader, it must be said that this clock in the picture is not itself an atomic clock, but it has a built-in receiver that allows it to communicate with a real atomic clock. We can call such clocks atomic wall clocks. There are about 400 atomic clocks around the world, that are kept in special places such as laboratories or observatories. Some atomic clocks are also mounted on satellites and orbit the earth. As they are very complex and expensive devices, we will probably not be able to hang them on the wall at home in the near future. But there are clocks equipped with radio receivers that can synchronize their readings with a real atomic clock, located somewhere in the laboratory. They can be both digital and analog clocks. Before we see how atomic clocks can measure time with such unprecedented accuracy, let's take a brief look at how ordinary clocks measure time.

Before the clock was invented, a period of time was defined by the rotation of the Earth. The time it took for the Earth to make one revolution around its axis, was divided into smaller parts such as hours and seconds. In every 24 hours, Earth makes one full rotation, thus the Earth rotates at a certain angular frequency,

From each clock, we can find an object that oscillates at a certain frequency. This oscillating object is called frequency reference. In mechanical watches, this element is the balance wheel, while in pendulum clocks it is a swinging weight - the pendulum. It usually takes 1 second for the pendulum to make one swing and 2 seconds to complete one cycle (its called a seconds pendulum). This means that the oscillation period is 2 seconds. Although the oscillation period does not necessarily have to be 2 seconds, the seconds pendulum simply has an oscillation period of this duration.

The oscillation period of the seconds pendulum in the picture is 2 seconds, so in 1 second it goes through half of its full cycle. Frequency is the number of complete cycles performed in a unit of time so that the oscillation frequency of this pendulum is 0.5 hertz (0,5 cycles per second). Each time, when the pendulum has reached the leftmost or rightmost position, the gears inside the clock turn and one second is counted. Thus, if we know that the object oscillates at a certain fixed frequency, we can define a second (or a minute, or an hour, or any other unit of time) based on that frequency.

However, all such mechanical watches and pendulum clocks are never very accurate. There are many factors, that affect the accuracy of such mechanical devices. Moving parts wear out, and are affected by friction, temperature, gravity, shock, etc. Even the rotational speed of the Earth around its axis is not constant but slows down gradually, which means that the second is not exactly as long today as it was yesterday when we define the second by the length of the day.

In 1927, a much more accurate device for measuring time was introduced - the quartz clock. At the heart of each such clock is a quartz crystal. Quartz or silicon dioxide is a piezoelectric material, which means when a quartz crystal is subjected to some mechanical force, it generates a current. But there is also the opposite effect - when voltage is placed across the crystal, it deforms. By taking advantage of this property of quartz crystals, it is possible to make this crystal oscillate at a certain frequency.

This tiny quartz crystal tuning fork inside the clock is tuned to vibrate at a specific frequency. The microcontroller counts the oscillations, and if exactly 32 768 full oscillations have occurred, one second is counted. The oscillation frequency of such quartz crystals is much more accurate than the frequency of the pendulum or the balance wheel, which makes them far more accurate timekeepers. Even cheaper quartz watches can accumulate an error of a only few minutes per year, which is completely acceptable to the average user.

Now we come to the atomic clock. Atomic clocks are the most accurate timekeepers we have created, which makes them international time measurement standards. Atomic clocks around the globe provide us with the highly accurate time that is essential in today's globalized world. There is a huge amount of activity going on in the world at any given moment in time, such as transactions in the financial markets, traffic on the internet, thousands of planes flying in the sky, orbiting GPS satellites, etc. If we used clocks that were not accurate enough to coordinate and synchronize all this action, the result would be one big mess.

As you might have guessed, we also find something inside this clock that oscillates at a certain frequency. On this clock, these oscillating things are atoms themselves.

Most atomic clocks use cesium atoms, or more specifically the cesium atom isotope cesium 133. Isotopes are simply different forms of the same chemical element with the same number of protons in the nucleus, but the number of neutrons varies. Simply put, an atom can be thought of as a small Solar system, with the nucleus of the atom in the middle like the Sun and small electrons like planets orbiting the Sun. Each chemical element differs in the size of its Sun and the number of planets orbiting the Sun.

Now, if an electron receives energy from somewhere, it can move to a higher orbit and if it loses energy, it moves to a lower orbit again.

However, when an electron moves from a higher orbit to a lower one, it emits electromagnetic radiation of exactly the same energy as the energy required to move the electron from a lower orbit to a higher orbit. The more accurate the frequency of microwave radiation in the atomic clock is tuned to allow as many electrons to transition to a higher orbit, the more microwave radiation at the same exact frequency we can detect when the electrons go to a lower orbit again. The feedback loop adjusts the frequency of the resonator to match the frequency of microwaves emitted by atoms. We know when the frequency is matched because then virtually all the electrons make the transition. The frequency of microwave radiation emitted when an electron passes into lower orbit in a cesium atomic clock is exactly 9 192 631 770 hertz.

Based on that frequency duration of one second is defined - it is the time it takes to microwave oscillate exactly 9 192 631 770 times when an electron makes this kind of transition (cesium 133 atom moves from one state to another). It is a fixed frequency that is almost the same all the time and everywhere, thus it is a perfect frequency reference for a clock. That's why some of the best atomic clocks are so accurate, that it takes about 20 million years when they gain or lose one second.

There is a fairly wide range of different atomic wall clocks available in the market, both digital and analog. There are even atomic wristwatches. All these clocks use quartz crystals as oscillators but they have a built-in receiver that enables them to receive signals from a real atomic clock and correct their readings if necessary. There are two transmitters in Europe, located in the UK and Germany, which will cover the whole of Europe. In the continental USA, there is a transmitter in Colorado, which will cover the whole mainland USA. In Asia, there are transmitters in China, Japan, and Taiwan.