Re: to sam


"Sam Wormley" <swormley1@xxxxxxxxx> wrote in message
news:JJcvi.57627$Fc.25728@xxxxxxxxxxxx
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.

Real-World Relativity: The GPS Navigation System
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

People often ask me "What good is Relativity?" It is a commonplace
to think of Relativity as an abstract and highly arcane
mathematical theory that has no consequences for everyday life.
This is in fact far from the truth.

Consider for a moment that when you are riding in a commercial
airliner, the pilot and crew are navigating to your destination
with the aid of the Global Positioning System (GPS). Further, many
luxury cars now come with built-in navigation systems that include
GPS receivers with digital maps, and you can purchase hand-held GPS
navigation units that will give you your position on the Earth
(latitude, longitude, and altitude) to an accuracy of 5 to 10
meters that weigh only a few ounces and cost around $100.

GPS was developed by the United States Department of Defense to
provide a satellite-based navigation system for the U.S. military.
It was later put under joint DoD and Department of Transportation
control to provide for both military and civilian navigation uses.

The current GPS configuration consists of a network of 24
satellites in high orbits around the Earth. Each satellite in the
GPS constellation orbits at an altitude of about 20,000 km from the
ground, and has an orbital speed of about 14,000 km/hour (the
orbital period is roughly 12 hours - contrary to popular belief,
GPS satellites are not in geosynchronous or geostationary orbits).
The satellite orbits are distributed so that at least 4 satellites
are always visible from any point on the Earth at any given instant
(with up to 12 visible at one time). Each satellite carries with it
an atomic clock that "ticks" with an accuracy of 1 nanosecond (1
billionth of a second). A GPS receiver in an airplane determines
its current position and heading by comparing the time signals it
receives from a number of the GPS satellites (usually 6 to 12) and
triangulating on the known positions of each satellite. The
precision is phenomenal: even a simple hand-held GPS receiver can
determine your absolute position on the surface of the Earth to
within 5 to 10 meters in only a few seconds (with differential
techiques that compare two nearby receivers, precisions of order
centimeters or millimeters in relative position are often obtained
in under an hour or so). A GPS receiver in a car can give accurate
readings of position, speed, and heading in real-time!

To achieve this level of precision, the clock ticks from the GPS
satellites must be known to an accuracy of 20-30 nanoseconds.
However, because the satellites are constantly moving relative to
observers on the Earth, effects predicted by the Special and
General theories of Relativity must be taken into account to
achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion
relative to them, Special Relativity predicts that we should see
their clocks ticking more slowly (see the Special Relativity
lecture). Special Relativity predicts that the on-board atomic
clocks on the satellites should fall behind clocks on the ground by
about 7 microseconds per day because of the slower ticking rate due
to the time dilation effect of their relative motion.

Further, the satellites are in orbits high above the Earth, where
the curvature of spacetime due to the Earth's mass is less than it
is at the Earth's surface. A prediction of General Relativity is
that clocks closer to a massive object will seem to tick more
slowly than those located further away (see the Black Holes
lecture). As such, when viewed from the surface of the Earth, the
clocks on the satellites appear to be ticking faster than identical
clocks on the ground. A calculation using General Relativity
predicts that the clocks in each GPS satellite should get ahead of
ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the
clocks on-board each satellite should tick faster than identical
clocks on the ground by about 38 microseconds per day (45-7=38)!
This sounds small, but the high-precision required of the GPS
system requires nanosecond accuracy, and 38 microseconds is 38,000
nanoseconds. If these effects were not properly taken into account,
a navigational fix based on the GPS constellation would be false
after only 2 minutes, and errors in global positions would continue
to accumulate at a rate of about 10 kilometers each day! The whole
system would be utterly worthless for navigation in a very short
time. This kind of accumulated error is akin to measuring my
location while standing on my front porch in Columbus, Ohio one
day, and then making the same measurement a week later and having
my GPS receiver tell me that my porch and I are currently about
5000 meters in the air somewhere over Detroit.

The engineers who designed the GPS system included these
relativistic effects when they designed and deployed the system.
For example, to counteract the General Relativistic effect once on
orbit, they slowed down the ticking frequency of the atomic clocks
before they were launched so that once they were in their proper
orbit stations their clocks would appear to tick at the correct
rate as compared to the reference atomic clocks at the GPS ground
stations. Further, each GPS receiver has built into it a
microcomputer that (among other things) performs the necessary
relativistic calculations when determining the user's location.

Relativity is not just some abstract mathematical theory:
understanding it is absolutely essential for our global navigation
system to work properly!

the author of this article uses a few logical fallacies,
and makes false claims and a number of mistakes in the article.

1. Note that the author states that the
"atomic clock that "ticks" with an accuracy of 1 nanosecond".

This statement doesn't make sense.

2. "an airplane determines its current position and heading by comparing the
time signals it
receives from a number of the GPS satellites (usually 6 to 12) and
triangulating on the known positions of each satellite."

This is incorrect. The "triangulation" occurs on the airplane,
not on "the known positions of each satellite."

3. "because the satellites are constantly moving relative to
observers on the Earth, effects predicted by the Special and
General theories of Relativity must be taken into account"

False claim, effects must be "taken into account", NOT models.
The main "effects being the "Galileo Effect" discovered
over 300 years ago that oscillators are affected by acceleration,
and the Doppler Effect, discovered over 150 years ago.

4. "The combination of these two relativitic effects means that the
clocks on-board each satellite should tick faster than identical
clocks on the ground by about 38 microseconds per day (45-7=38)!
This sounds small, but the high-precision required of the GPS
system requires nanosecond accuracy, and 38 microseconds is 38,000
nanoseconds."

Note that the author makes the false claim here,
that Relativity, rather than Nature, affects the clocks,
and the implication the fact that the constant affect
of acceleration on the oscillators cannot be negated by simply
offsetting them with no consideration of what model models the
offset best.

And the fact of the matter is that although it is desirable
to offset the satellite oscillators so that when in orbit,
they will oscillate near the same frequency as the master oscillator
on the ground, the system would work fine by simply letting the
airborne oscillators run at their most stable, natural frequency,
and making the oscillator drift part of the transmitted message.
In fact, as the crystal oscillators used in GPS receivers
have better short term stability than "atomic clock" oscillators,
the best GPS receivers compensate for the short term
instabilities of the satellite oscillators.

As can be seen the author does not seem to know that
a "time unit" is a function of the frequency of one's
MASTER OSCILLATOR, and "time" is the
accumulated time units in one's MASTER CLOCK
from some auspicious event, such as gate open,
sun rise, January 1, the birth of some famous person, etc.

5. Note that the suthor makes tha false claim:
"The engineers who designed the GPS system included these
relativistic effects.."

I dare say that the engineers who designed the GPS system
were smart enough to design a closed loop system
that compensated with measured offsets, with an
equal and opposite offset, and they cared less about
speculating philosophically or religiously about
what caused the offset, or what model best modeled it.

A closed loop system uses negative feedback to force
a system into compliance regardless of what caused
it to go out of compliance, acceleration, velocity, distance,
temperature, pressure, radiation, electric field, magnetic field,
shock, chemical aging the weather, etc.

6. The author states:
"GPS receiver has built into it a microcomputer that
(among other things) performs the necessary relativistic calculations"

No doubt GPS receivers take the "Doppler Effect" into account,
but I know of no receiver that incorporates Relativity into
its' computer program, and if anyone knows of one,
I'd like to see the program and analyze it.

6. The author states the obvious lie:
"Relativity is not just some abstract mathematical theory:
understanding it is absolutely essential for our global navigation
system to work properly!"

Galileo discovered over 300 years
that acceleration affect the frequency of oscillators,
and England sent ships all over the world
with pendulums to count the number of swings from
sunrise to sunrise.

Newton used this data to compute many things about
the Earth and the Moon, including the shape of the Earth,
and the tides in many places.

Any number of models can be used to model
frequency vs. altitude of the atomic oscillators in the GPS
but the fact of the matter is that the GPS system
would (And does) work just fine ignoring ALL of the models.

--
Tom Potter

*** Time Magazine Person of the Year 2006 ***
*** May 2007 Anti-Bigot Award ***
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