Hi Russ, > I still don't see how I would use it other than in devices that I don't build > but that take advantage of it--although I can't think of any of those either.
If I am not mistaken, accurate GPS, and perhaps even the GPS in common usage, needs to make appropriate corrections for the rate shift between clocks in orbit and clocks on earth, when the signals are sent from one to the other. The clocks are now that fine. If it did not do so, it would report locations that were wrong in a way that depended on the accident of where the satellites happened to be relative to each other and to the receiver. To the extent that E = mc^2 is a shorthand for the more general energy-momentum relation m^2 c^4 = E^2 + p^2 c^2 this is just the Fourier transform of the expression for the distance metric in Lorentizian geometry age^2 c^2 = t^2 c^2 - x^2 and from this Lorentzian geometry one is forced into clock shifts in a gravitational potential if gravity is to be no more than having to accelerate to stay where one is. So it's not super-direct, but to the extent that all of these relations are essentially expressions of the same geometric property, one couldn't have GPS without having got Lorentzian geometry right vis a vis nature. Eric
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