How does your smartphone know your location? - Wilton L. Virgo

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GPS location apps on a smartphone can be very handy when mapping a travel route or finding nearby events. But how does your smartphone know where you are? Wilton L. Virgo explains how 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.

Lesson by Wilton L. Virgo, animation by Nick Hilditch.

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.