“For static fields, such as …… the gravitational field connected to a massive object, the field extends to infinity, and does not propagate.”
Would it not follow from this that gravity is a static field, and that what is being measured is changes within a gravitational field, rather than any intrinsic motion of the field itself?
There is a problem we are going to confront and you haven't yet got to the point where we have introduced the problem.
So for a change I will sort of give you the problem we are about to hit and you decide what you want to discuss.
In the above you suddenly introduce the concept of a field which your idea and laws haven't even dealt with yet.
I will put that aside as I think you started it as a joke and now got buried in your own joke.
Fields were initially described in classical terms and the man that did the greatest contribution is James Clerk Maxwell. The part you need to read is the history of the equations he derived.
https://en.wikipedia.org/wiki/History_of_Maxwell's_equationsAgain I will be brief and just jump thru it just to sequence things for you. The key point about the equations is they connect electricity, magnetism, and the speed of light.
The problem with the equations and what we call "Maxwell's equations" really are not exclusively Maxwell's at all and its covered in that history. What you need to do is add in the concept of lines of force and vector mathematics to Maxwell's work.
The evolution is well covered in
https://en.wikipedia.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_FieldIt is actually discussed in that link that we are going to hit another complication. All that early work is classical and suddenly we are going to need to consider motion and especially speeds getting near the speed of light itself.
Albert Einstein used Maxwell's equations as the starting point for his Special Theory of Relativity, presented in The Electrodynamics of Moving Bodies, a paper produced during his 1905 Annus Mirabilis.
What we are describing is the connections of how and why GR (via it's connection to SR) isn't a law but is indeed a theory and Einstein makes it clear he is seeking to do that by this statement .. sigh I am doing your homework again
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"the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good"
Remember the requirements of a new theory to replace an old theory or laws it must explain all that the old covers and he makes that claim.
Finally we can address your question above and the problem rolls around motion. So do you think you are going to be able to use static field ideas on universal bodies that may well be moving at speeds a good fraction the speed of light? What they sort of hide in the statement above is they expect large objects not to be moving very fast and they sort of wave there hands and say we can thus treat them as static ... that is classically ... it's a justification not a statement of truth. You run into this problem with black holes, a spinning black hole vs a static black hole are very different beasts.
So the statement may be valid in a context of use, where classical physics and static fields would provide a correct answer and you can justify ignoring Special Relativity.
So for a more precise personal view I would need to see the full context. If you are asking is that some sort of "absolute truth" then no Special Relativity is the correct answer in all situations Einstein told you that ... don't you believe him
Bonus hint: In the second link was a hint for your journey, let me isolate it "Maxwell's equations can also be derived by extending General Relativity into five physical dimensions."
