WEBVTT

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How does your smartphone
know exactly where you are?

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The answer lies 12,000 miles 
over your head

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

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powered by quantum mechanics.

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Phew.

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Let's break that down.

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First of all, why is it so important 
to know what time it is on a satellite

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when location is what
we're concerned about?

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The first thing 
your phone needs to determine

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is how far it is from a satellite.

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Each satellite constantly 
broadcasts radio signals

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that travel from space to your phone
at the speed of light.

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Your phone records 
the signal arrival time

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and uses it to calculate 
the distance to the satellite

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using the simple formula,
distance = c x time,

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where c is the speed of light
and time is how long the signal traveled.

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But there's a problem.

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Light is incredibly fast.

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If we were only able to calculate 
time to the nearest second,

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every location on Earth, and far beyond,

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would seem to be the same 
distance from the satellite.

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So in order to calculate that distance
to within a few dozen feet,

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we need the best clock ever invented.

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Enter atomic clocks,
some of which are so precise

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that they would not gain or lose a second

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even if they ran 
for the next 300 million years.

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Atomic clocks work 
because of quantum physics.

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All clocks must have a constant frequency.

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In other words, a clock must carry out
some repetitive action

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to mark off equivalent increments of time.

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Just as a grandfather clock 
relies on the constant swinging

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back and forth of a pendulum 
under gravity,

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the tick tock of an atomic clock

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is maintained by the transition 
between two energy levels of an atom.

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This is where quantum physics 
comes into play.

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Quantum mechanics 
says that atoms carry energy,

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but they can't take on 
just any arbitrary amount.

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Instead, atomic energy 
is constrained to a precise set of levels.

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We call these quanta.

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As a simple analogy, 
think about driving a car onto a freeway.

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As you increase your speed,

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you would normally continuously go 
from, say, 20 miles/hour up to 70 miles/hour.

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Now, if you had a quantum atomic car,

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you wouldn't accelerate 
in a linear fashion.

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Instead, you would instantaneously jump,
or transition, from one speed to the next.

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For an atom, when a transition 
occurs from one energy level to another,

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quantum mechanics says

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that the energy difference 
is equal to a characteristic frequency,

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multiplied by a constant,

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where the change in energy is equal to 
a number, called Planck's constant,

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times the frequency.

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That characteristic frequency 
is what we need to make our clock.

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GPS satellites rely on cesium and rubidium
atoms as frequency standards.

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In the case of cesium 133,

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the characteristic clock frequency
is 9,192,631,770 Hz.

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That's 9 billion cycles per second.

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That's a really fast clock.

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No matter how skilled a clockmaker may be,

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every pendulum, wind-up mechanism

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and quartz crystal resonates 
at a slightly different frequency.

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However, every cesium 133 atom 
in the universe

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oscillates at the same exact frequency.

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So thanks to the atomic clock,

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we get a time reading accurate
to within 1 billionth of a second,

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and a very precise measurement
of the distance from that satellite.

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Let's ignore the fact that you're almost
definitely on Earth.

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We now know that you're at a fixed 
distance from the satellite.

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In other words, you're somewhere 
on the surface of a sphere

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centered around the satellite.

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Measure your distance 
from a second satellite

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and you get another overlapping sphere.

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Keep doing that,

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and with just four measurements,

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and a little correction 
using Einstein's theory of relativity,

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you can pinpoint your location to exactly
one point in space.

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So that's all it takes:

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a multibillion-dollar 
network of satellites,

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oscillating cesium atoms,

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quantum mechanics,

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relativity,

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a smartphone,

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and you.

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No problem.