Re: to sam

Tom Potter wrote:


Here is a question that I have asked Sam,
and all of the people who claim that
General Relativity is essential to the
GPS system, and so far they have just chanted
GTR mantra,. and avoided the question.



Einstein's Relativity and Everyday Life
Clifford M. Will
http://www.physicscentral.com/writers/2000/will.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.
.