You’ve likely heard of the Global Positioning System—or at least its acronym, GPS—since you probably have a receiver in your car, your cellphone, or both. But did you know that GPS wouldn’t tick if not for the laws of quantum physics? This is because on board each GPS satellite is an atomic clock, the most accurate time and frequency standard available.
From the Chinese water clock to a Swatch wristwatch, just about every clock counts time by registering something that occurs at a certain, regular frequency. The pendulum of a grandfather clock, for example, oscillates back and forth about once per second (or a frequency of one hertz), so that about 60 of these equals a minute. A modern wristwatch relies on a quartz crystal, which oscillates more than 10,000 times per second. A lot more cycles are needed to count a minute, but the principle is the same.
A quantum jump in any given atom can also be used as a measure of frequency. Not the rate at which quantum jumps occur, which can be random, but the frequency carried by the emitted photons when they do. Since this frequency is set by the difference in atomic energy levels, which is the same for every atom of the same type, a collection of similar atoms can be used to keep time.
QUANTUM LEAP
The fundamental unit that physicists use for time is based on a quantum jump. Since 1967, one second has been defined as 9,192,631,770 oscillations of the light from a certain transition in a cesium-133 atom in a cesium clock. This is just another way of saying that the photon emitted during this atomic transition has a frequency of 9,192,631,770 hertz, which corresponds to a wavelength of about 3 millimeters.
In theory, all you need to make an atomic clock is to know your particular atom’s transition frequency. Then, you can just sit back and work out how many oscillations equals one second. In practice, you also need to make sure your atoms are in a very stable environment so that there are no inadvertent shifts in their energy levels. If you can pull this off, you can build a clock that is off by a second only about once every 50 million years!
Since the energy of any single photon is negligibly low, real-world atomic clocks require some form of amplification. For this reason, the earliest atomic clocks relied on stimulated emission in the microwave range—the so-called masers we introduced in the previous section. Typically, atomic clocks will use a higher power oscillator (like a quartz crystal) that is “locked” to the atomic transition frequency by way of an electronic feedback mechanism.
The GPS itself relies on a network of satellites, each traveling in a circular orbit about 20,000 kilometers above Earth’s surface. Each contains an atomic clock at the same frequency, which means that the time kept on any one satellite is exactly the time kept on any other (to within about a billionth of a second). Furthermore, each satellite broadcasts its position and time continuously. The position is well determined at all times by good old-fashioned classical physics courtesy of Isaac Newton.
Meanwhile, back on Earth, your GPS receiver can detect the broadcast signals from at least four satellites at any given moment, no matter where you go. The receiver then determines its own position by calculating its distance to these four satellites. This can be done since the transmitted signals travel to the receiver at the speed of light (c) and therefore cover the distance (r) between the satellite and the receiver in a time Δt = r⁄c. The receiver measures the discrepancy between its own time and the satellite time, and then calculates the distance as r = c × Δt. This informs the receiver that it lies on a sphere of radius r centered on the satellite’s known position.
When the other three satellites are accounted for, the receiver establishes that it lies on four spheres of known radii and centers. Two of these spheres intersect in a circle, while the third sphere intersects this circle in two points. The fourth sphere determines the position unambiguously.
All this relies on your GPS receiver also measuring time very accurately. Does this mean that your mobile phone needs its own atomic clock? Fortunately, no. The GPS receiver derives its own time from the four satellites by calculating the three coordinate positions (x,y,z) and time. Solving for four unknown quantities with four equations is an easy task for even the simplest computer chip.
Incidentally, if you want to know your location to better than 1 meter, you are going to need more than just quantum physics. To achieve this level of accuracy, you are also going to need to use the theory of relativity. Since the satellites themselves are orbiting at such high speeds, their atomic clocks run faster than the clocks on the earth. If your receiver does not correct for this, it will lead to errors in positions of a few hundred meters—enough to make you miss more than one turn, most likely during rush hour.
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