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  • 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.

How does your smartphone know exactly where you are?

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B1 TED-Ed satellite atomic frequency clock quantum

【TED-Ed】How does your smartphone know your location? - Wilton L. Virgo

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    稲葉白兎 posted on 2015/02/01
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