[Edit: A few hours after posting, having now read the "Background" section of the second article mentioned below, I realize that I may be having crow for breakfast tomorrow morning. It's too early to know for sure, but I think I seriously misinterpreted TVF's first article on the subject. It is not my policy to sweep my errors under the rug; so I shall leave my somewhat premature comments untouched for all of you to jeer at. End of edit.]
I am ready to make a second, and hopefully final, installment in my criticism of VR, i.e., Van Flandern Relativity. This concerns TVF’s article, “
What the Global Positioning System Tells Us about Relativity
”. Ooops! I completely overlooked the more detailed "
twins paradox
" article. Well, I'm going to post this anyway on the assumption that the second article, which I haven't even begun to read, is just a more detailed version of the "twins paradox" portion of the first article.
I do not disagree with Tom’s explanation of the way GPS works; I’m sure he knows more about that than I do. I would, however, add that synchronizing any clock with the GPS clocks involves a light delay correction. A comparison of arrival times for the signals from several satellites tells you where you are. Knowing where you are, you may then determine how long it takes for the clock signal to reach you from each satellite. You must add that much time to the clock signal from the satellite to get your own correct Earth time.
At relativistic speed, however, there is another time correction factor to consider. Clocks synchronized to Earth time in Earth-stationary coordinates are not synchronized with one another in traveler coordinates. The difference between any two Earth clocks in traveler’s coordinates is proportional to their x-coordinate distance from the traveler (i.e., parallel to the direction of relative velocity). This must be corrected by the traveler’s GPS receiver to determine the Earth time at the receiver’s location; I doubt if any standard GPS receiver is programmed to do so. To avoid ambiguity, we should specify that the traveler’s clocks are synchronized with a clock at the North Pole as he passes it, allowing the appropriate light-delay time.
I am confused about the pre-flight correction to the traveler’s so-called GPS clock speed. Is it corrected to run at the same speed as any given Earth-coordinates clock? Or is it corrected to show the same time as each successive Earth-coordinates clock as the traveler passes it? The difference is certainly not trivial.
At the moment when the traveler synchronized his clocks with the North-Pole clock, the Earth-stationary coordinate system is contracted along the x-axis. If the traveler then changes direction, while keeping the relative speed constant, he changes the direction in which the Earth-stationary coordinate system is contracted. That changes the direction in which the SR time correction factor for the x-coordinate must be applied. That simply can’t be done without resorting to some form of general relativity.
Apparently, in VR, one may rotate the traveler’s coordinates and still pretend to have an inertial coordinate system. Sorry, Tom, but this is not up to your usual high standards. I’d delete it if I were you. Do that, and then you may delete this critique to avoid further embarrassment.
I might have more criticism after studying the second article.
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