**Einstein's
Relativity and Everyday Life**

Global Positioning System (GPS)

Clifford M. Will

**http://www.physicscentral.com/writers/writers-00-2.html
**

**What good is fundamental physics to the person
on the street? **

This is the perennial question posed to
physicists by their non-science friends, by students in the humanities and
social sciences, and by politicians looking to justify spending tax dollars on
basic science. One of the problems is that it is hard to predict definitely
what the payback of basic physics will be, though few dispute that physics is
somehow "good."

Physicists have become adept at finding good
examples of the long-term benefit of basic physics: the quantum theory of
solids leading to semiconductors and computer chips, nuclear magnetic resonance
leading to MRI imaging, particle accelerators leading to beams for cancer
treatment. But what about Einstein's theories of special and general
relativity? One could hardly imagine a branch of fundamental physics less
likely to have practical consequences. But strangely enough, relativity plays a
key role in a multi-billion dollar growth industry centered around the Global
Positioning System (GPS).

When Einstein finalized his theory of gravity
and curved spacetime in November 1915, ending a quest which he began with his
1905 special relativity, he had little concern for practical or observable
consequences. He was unimpressed when measurements of the bending of starlight in
1919 confirmed his theory. Even today, general relativity plays its main role
in the astronomical domain, with its black holes, gravity waves and cosmic big
bangs, or in the domain of the ultra-small, where theorists look to unify
general relativity with the other interactions, using exotic concepts such as
strings and branes.

But GPS is an exception. Built at a cost of
over $10 billion mainly for military navigation, GPS has rapidly transformed
itself into a thriving commercial industry. The system is based on an array of
24 satellites orbiting the earth, each carrying a precise atomic clock. Using a
hand-held GPS receiver which detects radio emissions from any of the satellites
which happen to be overhead, users of even moderately priced devices can determine
latitude, longitude and altitude to an accuracy which can currently reach 15
meters, and local time to 50 billionths of a second. Apart from the obvious
military uses, GPS is finding applications in airplane navigation, oil
exploration, wilderness recreation, bridge construction, sailing, and
interstate trucking, to name just a few. Even Hollywood has met GPS, recently
pitting James Bond in "Tomorrow Never Dies" against an evil genius
who was inserting deliberate errors into the GPS system and sending British
ships into harm's way.

But in a relativistic world, things are not
simple. The satellite clocks are moving at 14,000 km/hr in orbits that circle
the Earth twice per day, much faster than clocks on the surface of the Earth,
and Einstein's theory of special relativity says that rapidly moving clocks
tick more slowly, by about seven microseconds (millionths of a second) per day.

Also, the orbiting clocks are 20,000 km above
the Earth, and experience gravity that is four times weaker than that on the
ground. Einstein's general relativity theory says that gravity curves space and
time, resulting in a tendency for the orbiting clocks to tick slightly faster,
by about 45 microseconds per day. The net result is that time on a GPS
satellite clock advances faster than a clock on the ground by about 38
microseconds per day.

To determine its location, the GPS receiver
uses the time at which each signal from a satellite was emitted, as determined
by the on-board atomic clock and encoded into the signal, together the with
speed of light, to calculate the distance between itself and the satellites it
communicated with. The orbit of each satellite is known accurately. Given
enough satellites, it is a simple problem in Euclidean geometry to compute the
receiver's precise location, both in space and time. To achieve a navigation
accuracy of 15 meters, time throughout the GPS system must be known to an
accuracy of 50 nanoseconds, which simply corresponds to the time required for
light to travel 15 meters.

But at 38 microseconds per day, the
relativistic offset in the rates of the satellite clocks is so large that, if
left uncompensated, it would cause navigational errors that accumulate faster
than 10 km per day! GPS accounts for relativity by electronically adjusting the
rates of the satellite clocks, and by building mathematical corrections into
the computer chips which solve for the user's location. Without the proper
application of relativity, GPS would fail in its navigational functions within
about 2 minutes.

So the next time your plane approaches an
airport in bad weather, and you just happen to be wondering "what good is
basic physics?", think about Einstein and the GPS tracker in the cockpit,
helping the pilots guide you to a safe landing.

**Clifford M. Will** is Professor and Chair of Physics at Washington
University in St. Louis, and is the author of **Was Einstein Right?** In
1986 he chaired a study for the Air Force to find out if they were handling
relativity properly in GPS. They were.