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• How does your smartphone know exactly where you are?

• in an orbiting satellite that keeps time to the beat of an atomic clock

• 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.

• 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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