One of the great examples of practical application of both special and general relativity is in the Global Positioning System (GPS). There’s a nice description of how relativity simply has to be accounted for if GPS is going to work well or for long; read it here. The short version is that relativistic considerations cause a difference in the rate at which the atomic clocks aboard the GPS satellites tick, such that measurements based on them would be off by about ten kilometers in a day, and the errors would accumulate. The whole system is engineered with the consideration of relativity built in, as evidenced by textbooks and even the GPS specification.

Some people, though, don’t like the very notion of a theory of relativity. While looking up other material on GPS systems, I ran across a rant that appeared in the Usenet sci.physics newsgroup early this year. A fellow by the name of Tom Potter posted his “The GPS – General Relativity Myth” message there on February 1st. After a general round of name-calling, Potter gets to his argument:

I, for one,
would like to see any General Relativity Cultists
and work their way, step by step,
to the artifact they claim is proof that
General relativity is essential to the GPS System,

and then show why this cannot be handled in a system
by simply setting constants and multipliers to values
that provide the desired results.

For example, note that constants are used to
set calendars to agree with Moses, Jesus, Mohammed, etc.
and multipliers/dividers are used to adjust the clocks
on the Earth to agree with days or years, etc.

The Mayans, Chinese, Babylonians, etc.
managed to sync their days and moons
up to the rotation of the Earth about the Sun,
and to my knowledge they never used General Relativity.

I found this an intriguing way to argue. After all, this concedes that the “General Relativity Cultists” actually do derive the adjustments needed to make the GPS system work based on the theory. All Potter is trying to assert, then, is that the theory was not necessary to the implementation of a working GPS system: all the needed adjustments could be derived ad hoc as we go along. I have two responses. Perhaps a working GPS could come about without knowledge of relativity, but it seems unlikely to happen in one go. Without a theory of relativity, the satellites would quite likely not have any capacity built in to adjust the basic clock rate. Why would they? In classical physics, an atomic clock under any conditions of acceleration or position relative to a large mass would keep the same time. It would only be after the first set of satellites went up that the engineers would discover that the calculations were off, and getting further off with time. So maybe the second set of satellites goes up, and these have an adjustment facility built in. (Oh, and somebody has to turn off or destroy the first set of satellites, the ones that were wildly erroneous.) Now comes a period of adjustment as the engineers try to solve a problem in a large number of variables. It probably could be done. It almost certainly would be no fun, and it would leave the issue of how to validate the system. Remember, GPS was originally a military project, where part of its work was to assure the proper placement of ordnance. Once you’ve dropped your bomb, it is a bit late to be worrying over whether the engineers managed to empirically adjust the actual situation your GPS is dealing with at the moment.

That leads to the second point. Machine learning is a fascinating field. I’ve spent a good chunk of my career with it in one form or another. But one generally doesn’t use machine learning techniques to address a problem with a closed-form solution. Why would you? And the theory of relativity provides some excellent analytical solutions to problems like those posed in implementing a GPS system. It at once provides you with an understanding of the mechanics of what is happening and the means to engineer general solutions, with all the confidence that goes with the decades of testing the theory has undergone. It doesn’t leave one wondering if one has suitably managed to train a learning system to generalize appropriately from a sample of training cases. It is easy to explain how your system works under any particular set of parameters. So, Tom Potter, let’s use machine learning for things where we have no efficient solutions worked out in closed form, and let’s apply our best knowledge when it is appropriate to do so. That latter clause includes applying relativity to GPS systems.

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