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Ronald R. Hatch of NavCom
Technology has published a number of controversial relativity articles, mostly
in 'fringe' publications and forums. One example is titled Relativity and
GPS.(a). Here I will only discuss one of the several issues I
have with that article: the misinterpretation of a scholarly article by Prof.
Neil Ashby of the University of Colorado in Boulder, titled Relativity and
the Global Positioning System.(b)
Hatch wrote: "Ashby,
in the opening paragraph of his abstract, states:
Important relativistic effects arise from relative motions of GPS satellites
and users, ...
And Ashby also states, at the start of a section on time dilation:
First, clocks in relative motion suffer (relativistic) time dilation, ..."
Taking these quotes out of
context, Hatch then laboriously "shows", through an example of two
satellites in identical, but counter rotating orbits, how the satellites of the
GPS should suffer velocity time dilation relative to each other. Since it is
common knowledge that the GPS satellites do not suffer velocity time dilation
relative to each other,(c) Hatch then wrongly claims that Ashby -
and hence special relativity theory - must be in error.
This is obviously not the
case, because the GPS satellites are not moving relative to each other in the
chosen non-rotating earth centered inertial (ECI) reference frame. Even Hatch's
counter-orbiting satellites have the same relativistic clock rates in the ECI
frame, special relativity (SR) tells us. No need to call on Lorentz Ether
Theory (LET) to rescue SR.(d) Both clocks tick slower than an
identical clock, stationary in the ECI frame, though. This is compensated for
in GPS satellites.
I think the confusion comes
from the fact that in the inertial frame of each counter-orbiting satellite
their relative speeds do play a role. This is a much more difficult
relativistic problem to solve numerically, but SR unequivocally says that their
clock readings will be the same on every subsequent passing of one another.
They will stay in sync, despite their obvious relative speed.(e)
In the rotating
earth-centered, earth-fixed, (ECEF) reference frame of a stationary ground
receiver, counter-orbiting clocks do not stay in sync, of course. Earth's
rotation makes them pass overhead at different times and hence their clocks
appear to be out of sync with each other. What's more, they will both appear to
be out of sync with a ground receiver clock. Of course, counter-rotating
satellites are not applicable to GPS.
The standard GPS orbiting
clocks stay in sync with each other, but un-compensated orbiting clocks will
get increasingly out of sync with ground clocks. IMO, this is the context of
Prof. Ashby's statements, quoted and misinterpreted by Ron Hatch. This type of
misinterpretation is not uncommon amongst people with 'absolute frame'
mindsets.
Jorrie
(a) This is the only
workable link that I could find for Ronald Hatch's article: http://ivanik3.narod.ru/GPS/Hatch/relGPS.pdf
(b) I did not have full
access to Ashby article in GPS World, but found a later (2002) version
on Physics Today.org: http://www.ipgp.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf.
(c) Apart from minor
corrections for orbital parameters and the uneven gravity of earth, GPS
satellite clocks run in sync with each other. A broader, more advanced and
regularly updated GPS paper by Ashby is available at http://relativity.livingreviews.org/Articles/lrr-2003-1/.
Prof. Ashby really knows his relativity and his GPS.
(d) Contrary to some of
Hash's claims, LET and SR are not distinguishable by means of experiment. They
are just different philosophies for explaining special relativistic effects.
LET has a few problems when it comes to accelerated frames and GR, of course.
In his Modified LET (MLET) Ron Hatch attempted to add gravity to LET. AFAIK,
the GPB results refuted MLET experimentally. http://cr4.globalspec.com/comment/787587/Re-Universal-Time
(e) The simplest argument
for two identically counter-rotating satellites is that for every possible
inertial frame of reference, the spacetime paths of the two satellites are
equivalent. Consider them as first sitting statically at the same altitude in
the ECI frame. Their clocks will remain in sync. Now accelerate them
horizontally and identically for a short time, but in opposite directions and
then let them coast inertially. The satellites are still equivalent in terms of
spacetime paths and their clocks will remain in sync. Because they have traveled
a longer spatial route and hence 'traveled' less in time, the clocks will
however both lose time relative to a theoretical ECI frame clock. It is a
consequence of the invariance of the spacetime interval in Minkowski spacetime
and the Tartaglia paper mentioned below confirms this mathematically.
Due to the dragging of
inertial frames by earth's rotation (gravitomagnetism), there are some
gravitational effects that differ for the counter-orbiting clocks, which will
then very slowly desynchronize. See technical detail in http://polito.academia.edu/AngeloTartaglia/Papers/769566/Gravitomagnetic_effects,
around equation (43). These differences are orders of magnitude smaller than
what is needed for GPS work (calculated as a few pico-seconds per orbit). In
any case, we are ignoring all gravitational effects for this discussion and
counter-rotating satellites are not applicable to GPS. Gravitomagnetic effects
are the same for all GPS satellites.
-J
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