Source:
https://brentshadbolt.substack.com/p/the-truth-about-gps-relativity-not
"Mar 18, 2024
"Welcome to A Universe Without Relativity. This is a forum to share
research and ideas that (1) expose the flaws in relativity and (2)
utilise empirical data to build a new model of the universe that is
closer to reality, a universe without relativity. We don’t propose to
have all the answers. But even those of us outside of the Physics
Academy can see that the current standard model is seriously broken and
needs to be replaced.
Ever since Edwin Hubble expressed his doubts about an expanding universe
a century ago, a long line of scientists have similarly voiced their
concerns, and new data from JWST continues to confirm their dissension.
Is the redshift of light from distant stars a measure of their
recessional velocity? Or could it be the result of a loss of energy in
transit? Or has the light stayed the same as it traversed billions of
light years towards Earth and started with a longer wavelength under
very different conditions? Should we believe the mathematical construct
we call spacetime? Is curved spacetime our best understanding of
gravity? Should exposing the problems of expanding spacetime cost you
your reputation or even your career?
We kick off this monthly stack by debunking the most popular everyday ‘proof’ of relativity, which comes from the Global Positioning System (GPS). If, at this moment, we could turn off all corrections due to
relativity, would we wake up tomorrow to find that our pinned home
location on Apple Maps had drifted into the house next door?
GPS is used to pinpoint locations on the Earth’s surface and relies on
radio signals sent from satellites in space. The signals carry coded information about the satellite’s location and the signal's time. A GPS receiver on Earth collects this information from three or four
satellites simultaneously and calculates the distance to each satellite.
The receiver then calculates where these distances intersect to
determine its location in three-dimensional space. The coordinates of longitude, latitude and altitude are given in reference to a
three-dimensional mathematical model of the Earth's ellipsoid shape (a
slightly squashed sphere) called the ‘Conventional Inertial Frame’ or ‘World Geodetic System 1984’ (WGS 84)1 (figure 12).
Figure 12. Official diagram of the WGS 84 Reference Frame, a 3D
mathematical model of the Earth’s ellipsoid centred at the Earth’s
Centre of Mass. (The ellipsoid's oblateness is exaggerated in this
image.) The Z axis (rotational axis) is orientated at the Conventional Terrestrial Pole (CTP) and the X axis at the Zero Meridian as defined by
the Bureau International de l’Heure (BIH). ω = nominal mean angular
velocity of the Earth. Credit: Defense Mapping Agency (Public Domain).
The positioning system's success relies on radio signals' ability to
transmit extremely precise information. To this end, GPS satellites
carry caesium atomic clocks that are correct to less than 5 parts in
1014, or about 4 billionths of a second per day.2 As the satellites are orbiting 20,184 km above the Earth, they are in a much weaker
gravitational field than clocks on the Earth, and general relativity
predicts that the satellite clocks will tick more quickly by 45
microseconds per day.3
Since the satellite clocks are moving relative to receivers on Earth,
special relativity predicts the satellite clocks will tick more slowly
by some amount compared to ground-based clocks. Satellite orbital speeds
are cited as 3,874 m/s; thus, satellite atomic clocks are reported to experience a time dilation of about 7 microseconds per day.3
When the slowing effect of special relativity on a GPS satellite clock
rate is subtracted from the speeding-up effect of general relativity,
the result is about 38 microseconds of increase per day (45-7). GPS
engineers adjust the clock rates before they are placed into orbit to
correct this time increase in satellite atomic clocks. The clocks are
given a rate offset of 4.465 parts in 1010 from their nominal frequency
of 10.23 MHz so that, on average, they appear to run at the same rate as
a clock on the ground. The actual frequency of the satellite clocks
before launch is thus 10.22999999543 MHz.3 In other words, the clocks
are pre-tuned to count a different number of caesium oscillations per
second compared to the standard on Earth so that in space, they measure
the same duration of time for one second as on Earth.
Privately contracted physicist Ron Hatch (1938 – 2019) was one of the co-inventors of GPS and one of the world’s foremost experts on GPS. Over
his fifty-year career, he wrote many technical papers outlining
innovative techniques for GPS navigation satellites and held over 30
patents. He also served as the Chair and President of the Satellite
Division of the Institute of Navigation (ION). In 1994, Hatch received
the Johannes Kepler Award for significantly contributing to satellite navigation. In 2000, he was awarded the Thomas L. Thurlow Award and
elected an ION Fellow.
Hatch also published several papers showing that GPS has nothing to do
with relativity. In his 1992 book Escape From Einstein, he presented GPS
data that provided evidence against special relativity.
Calculations of special relativistic time dilation are not necessary for
GPS operation. In special relativity, time dilation can only be
calculated using the relative velocity strictly along the line of sight
between two frames of reference; no other reference frames are relevant. However, physicists have calculated the time dilation for satellite
atomic clocks using the satellite’s orbital velocity.3 The problem here
is that orbital velocity is not a velocity along the line of sight
between the satellite and a receiver on Earth. The orbital velocity is
in a direction that is perpendicular to the radius between the satellite
and a non-rotating point at the centre of the Earth.
To illustrate this problem, consider the example of a satellite orbiting
in sync with the Earth’s rotation. It remains at a fixed point above a specific location on Earth (weather and TV satellites utilise
geostationary orbits of this kind). From the perspective of an observer
on Earth, this satellite appears to remain fixed in the sky. In this
case, the satellite’s velocity along the line of sight with a receiver
on Earth is effectively zero. If we then calculate time dilation using
this satellite’s orbital velocity of, say, 4,000 m/s (in a direction perpendicular to its orbit radius), we get an incorrect result.
Not only are special relativistic time dilation calculations not
necessary in GPS, but they are also not performed. The two reference
frames needed to calculate the component of time dilation in special
relativity are each continuously changing. GPS satellites orbit the
Earth about twice a day, continuously sweeping across from one horizon
to the other. Furthermore, the reference frame of the receiver, your
phone, for example, even if it is ‘stationary’ relative to the surface
of the Earth, is moving relative to the GPS satellite’s orbit due to the rotation of the Earth about its axis. The rotational speed of a
particular point on the Earth’s surface will depend on its latitude,
ranging from approximately 460 m/s for points along the equator to 0 m/s
at the north or south poles. In other words, unless the receiver is at
one of the Earth’s poles, it will be moving in a direction tangential to
a satellite’s line of sight. In practice, these complexities are
accounted for by approximating all motion with reference to a third, independent frame, the WGS 84 Reference Frame.3
In addition to the time variations attributed to the effects of special relativity, there are other well-documented time delays inherent in the
GPS system. The signal transmitted from a satellite is subject to time
delays on its way to a ground-based receiver. These delays include
slowing the radio signal (Shapiro delay), Doppler effects, interference
with the signal, and satellite orbits' eccentricity.3 Given these
inherent delays, scientists admit that ‘it would be difficult’ to use
GPS clocks to actually measure the relativistic effects.3
The overall correction factors incorrectly attributed to general and
special relativity do not need to be calculated by individual receivers
on Earth for the system to work. This is because a GPS receiver’s
position is determined solely by comparing the time signals it receives
from several different satellites with each other, not with the clock in
the receiver itself. In other words, as long as the satellite clocks are
in sync relative to each other, the clock rate on Earth becomes
redundant. To keep satellite signals in sync with each other and the
ground, satellite data is continuously monitored by receiving stations
around the globe and forwarded to a master control station at the US
Naval Observatory.3 In this way, satellite clocks are periodically
synchronised with a ground-based reference clock.
In addition to corrections for time differences, ongoing corrections for position are also needed. As noted, GPS receivers calculate accurate
position coordinates with respect to the WGS 84 reference frame. The
accuracy of this quasi-inertial frame is continually monitored and
updated to account for factors such as the Earth’s crustal motion, plate tectonics, and other geophysical changes. The WGS 84 is aligned with
Earth’s centre of mass, which in turn is oriented to the ‘International Celestial Reference Frame’, a point centred at the centre of mass (barycentre) of the solar system.3 In this way, the ongoing accuracy of
GPS positioning depends on a fixed reference point with respect to the
solar system.
Relativity is not needed to explain the offset of satellite time (atomic
clock frequency). Alternative explanations of the same time increase
onboard GPS satellites have been provided based on a variable speed of
light and quantum mechanics.4 In a weaker gravitational field, atoms
increase their oscillation frequency, consequently making atomic clocks
run faster. This approach ties in with the observations of Einstein in
1911 and Dicke in 1957 affords a more intuitive, mechanistic
understanding of the gravitational redshift effect.
An experiment to test the effect of gravitational field strength on
clock rate, as well as the speed of light, was proposed in the late
1990s. The speed of light was to be measured onboard the International
Space Station using a new-and-improved atomic clock with a very stable super-cooled chamber.5 The aim was to compare the stable atomic clock’s microwave frequency with that of a regular atomic clock (to an accuracy
of 1 x 10-17) as a function of position and gravitational potential. It
was also intended to detect any direction-dependent changes in the
velocity of light.6 This particular mission, funded by NASA, was
unfortunately cancelled to make way for something else.
In summary, relativistic effects are completely unnecessary to account
for the effects of lower gravitational field strength on satellite
atomic clock rates. This is because the clock rates are: (1)
pre-adjusted on the ground before launch to account for the
gravitational field strength of their intended orbit, and (2)
periodically corrected using a ground-based reference clock.
Additionally, satellite positions are regularly calibrated with
reference to an Earth-centered frame, which itself is calibrated
relative to the solar system's center of mass.
What would happen to GPS if the scientific community suddenly discarded Einstein’s theory of relativity? Would GPS locations become inaccurate
within a day? In reality, a relativity-free world would have minimal
impact on GPS functionality. The system already incorporates built-in corrections calibrated using independent reference frames. Any
adjustments previously attributed to special or general relativity would
simply be reinterpreted with greater probity, without disrupting
operations. GPS receivers would continue to deliver precise positional
data: relativity not required.
References:
Ashby, N. (2002) Relativity and the Global Positioning System.
Physics Today, May 2002, vol 41.
https://www.academia.edu/62486812/Relativity_and_the_global_positioning_system
Ashby, N. (2003) Relativity in the Global Positioning System. Living Reviews. Relativity, 6, 2003, 1.
http://www.livingreviews.org/lrr-2003-1
Nelson, R. (2013) The Global Positioning System – A National
Resource. Posted on May 20, 2013, ATI Applied Technology Institute
Courses.
https://web.archive.org/web/20210518210959/https://www.aticourses.com/2013/05/20/the-global-positioning-system-a-national-resource/
Chang, D. (2018) A quantum mechanical interpretation of
gravitational redshift of electromagnetic wave. Optik Vol. 174, Dec
2018, pp.636–641.
Buchman, S. Turneaure, J. P. Lipa, J. A. Dong, M. Cumbennack, K. M.
and Wang, S. (1998) A Superconducting Microwave Oscillator Clock for Use
on the Space Station. IEEE international frequency control symposium.
https://web.stanford.edu/~sbuchman/publications-PDF/A%20Superconducting%20Microwave%20Oscillator%20Clock%20for%20Use%20on%20the%20Space%20Station.pdf
Buchman, S. Dong, M. Moeur, W. Wang, S. Lipa, J. A. and Tumeaure J.
P. (2000) A Space-Based Oscillator Clock. Adv. Space Res. Vol. 25, No.
6, pp.1251–1254
https://www.sciencedirect.com/science/article/abs/pii/S0273117799009965
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