# How does your smartphone know your location?

How does your smartphone know exactly where you are? The answer lies 12,000 miles over your head in an orbiting satellite that keeps time to the beat of an atomic clock powered by quantum mechanics. Phew. Let’s break that down. First of all, why is it so important to know what time it is on a satellite when location is what we’re concerned about? The first thing your phone needs to determine is how far it is from a satellite. Each satellite constantly broadcasts radio signals that travel from space to your phone at the speed of light. Your phone records the signal arrival time and uses it to calculate the distance to the satellite using the simple formula, distance = c x time, where c is the speed of light and time is how long the signal traveled.

But there’s a problem. Light is incredibly fast. If we were only able to calculate time to the nearest second, every location on Earth, and far beyond, would seem to be the same distance from the satellite. So in order to calculate that distance to within a few dozen feet, we need the best clock ever invented. Enter atomic clocks, some of which are so precise that they would not gain or lose a second even if they ran for the next 300 million years. Atomic clocks work because of quantum physics.

All clocks must have a constant frequency. In other words, a clock must carry out some repetitive action to mark off equivalent increments of time. Just as a grandfather clock relies on the constant swinging back and forth of a pendulum under gravity, the tick tock of an atomic clock is maintained by the transition between two energy levels of an atom. This is where quantum physics comes into play. Quantum mechanics says that atoms carry energy, but they can’t take on just any arbitrary amount. Instead, atomic energy is constrained to a precise set of levels. We call these quanta. As a simple analogy, think about driving a car onto a freeway.

As you increase your speed, you would normally continuously go from, say, 20 miles/hour up to 70 miles/hour. Now, if you had a quantum atomic car, you wouldn’t accelerate in a linear fashion. Instead, you would instantaneously jump, or transition, from one speed to the next. For an atom, when a transition occurs from one energy level to another, quantum mechanics says that the energy difference is equal to a characteristic frequency, multiplied by a constant, where the change in energy is equal to a number, called Planck’s constant, times the frequency. That characteristic frequency is what we need to make our clock.

GPS satellites rely on cesium and rubidium atoms as frequency standards. In the case of cesium 133, the characteristic clock frequency is 9,192,631,770 Hz. That’s 9 billion cycles per second. That’s a really fast clock. No matter how skilled a clockmaker may be, every pendulum, wind-up mechanism and quartz crystal resonates at a slightly different frequency. However, every cesium 133 atom in the universe oscillates at the same exact frequency. So thanks to the atomic clock, we get a time reading accurate to within 1 billionth of a second, and a very precise measurement of the distance from that satellite.

Let’s ignore the fact that you’re almost definitely on Earth. We now know that you’re at a fixed distance from the satellite. In other words, you’re somewhere on the surface of a sphere centered around the satellite. Measure your distance from a second satellite and you get another overlapping sphere. Keep doing that, and with just four measurements, and a little correction using Einstein’s theory of relativity, you can pinpoint your location to exactly one point in space. So that’s all it takes: a multibillion-dollar network of satellites, oscillating cesium atoms, quantum mechanics, relativity, a smartphone, and you. No problem.

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