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. 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.^{(a)}
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,^{(b)} 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 nonrotating earth centered inertial (ECI) reference frame. Even Hatch's counterorbiting 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.^{(c)} 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 counterorbiting 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.^{(d)}
In the rotating earthcentered, earthfixed, (ECEF) reference frame of a stationary ground receiver, counterorbiting 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, counterrotating satellites are not applicable to GPS.
The standard GPS orbiting clocks stay in sync with each other, but uncompensated 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) 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.
(b) 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 https://link.springer.com/article/10.12942/lrr20031. Prof. Ashby really knows his relativity and his GPS.
(c) 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/ReUniversalTime
(d) The simplest argument for two identically counterrotating 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 counterorbiting 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 picoseconds per orbit). In any case, we are ignoring all gravitational effects for this discussion and counterrotating satellites are not applicable to GPS. Gravitomagnetic effects are the same for all GPS satellites.
J

Re: GPS and Relativity Misconceptions 1