Thank you for this question!
The Universe System, Volume III, of the UM has some chapters that are still in the process of being written. Because of this there is a huge bulk of information we have that is not ready to be published. We hope that you can be patient for that Volume, and I promise you that all your questions about Relativity will be covered in Ch. 25, The Relativity Pseudotheory.
Now to answer your question, what is our “stance on GPS systems being possible only because of the theory of relativity?”
First, lets clarify something about Global Positioning Systems. The GPS is a complex network of satellites that orbit the Earth and use light frequencies to triangulate locations of GPS trackers. GPS blueprints are extremely regulated by the government and Satellite engineers under oath cannot talk about the programs they are working on. Essentially, GPS is not public knowledge and no one can verify how they actually work. If regular folk like you and I, or even “non-security clearance” scientists can’t check or test the work of the engineers, how can we know that GPS indisputably uses General Relativity? Or Special Relativity? We can’t check what numbers they used, what equations are in place, how accurate it all is, or how much they adjust the clocks, or even if changes are made based on theory or engineering experience(in my experience, engineers never work with pure theory, ever).
Because of this GPS can’t be used as a truly scientific point of evidence. That is sort of a technical point to be made.
There are many other points to be made on GPS and Relativity, but it is a very complicated system and would require us to get extremely technical.
The key to GPS is timing. They depend on extremely precise atomic clocks to keep as exact a time as possible, down to a billionth of a second. To say for certain that these clocks go through “time dilation” because of Relativity is being presumptive. That is to say, “we know everything about the atom and we are not influencing the atoms in the slightest degree as we accelerate to thousands of miles per hour and leave Earth’s gravity” so to speak.
Louis Essen, the creator of the atomic clock, continually expressed his concern that physicists were putting way to much confidence of Relativity on atomic clocks, and that we still know very little about these clocks. The question is, is Relativity literally slowing time down? or are the clocks imperfect and being influenced in tiny amounts by the change of environment?
That all being said, the ultimate stance of the UM on the GPS ‘evidence’ of Relativity is that GPS is technology, and technology doesn’t translate into science. Technology is the what, where, and when used to benefit mankind. Science is the how and why of Nature. A good example of the difference is all the amazing technological uses we have for quartz, yet modern science still doesn’t know how quartz is formed.
The difference between technology and science can be read about in the Intro Chapters, especially sub-chapter 3.7 of the UM!
I apologize for being so wordy. In summary, no, scientists cannot use GPS as evidence for Relativity. There is still a lot to learn about GPS and atomic clocks. In the first 4 chapters of the Universe System we show how new experiments are totally refuting basic assumptions of Einstein’s Theory.
Thank you very much for your question, I hope I answered it.