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:As far as I'm aware, no. It's relativity that predicts that there will be a divergence in time, for reasons already discussed. However, I want to throw in: both of you aruging about whether GPS satellites use relativity are correct in certain ways. Andy, you're correct that there is no actual use of relativity on the circuits on board the satellite. For those arguing that relativity is used, you're correct too; based on predictions from both general and special relativity, the clocks on the satellites are fine tuned with an offset to minimize the nano-second order deviations from clocks on the ground. Then, for practical purposes, newtonian based approximations are acceptable accuracy-wise. [[User:Stryker|Stryker]] 14:08, 30 July 2007 (EDT)
:As far as I'm aware, no. It's relativity that predicts that there will be a divergence in time, for reasons already discussed. However, I want to throw in: both of you aruging about whether GPS satellites use relativity are correct in certain ways. Andy, you're correct that there is no actual use of relativity on the circuits on board the satellite. For those arguing that relativity is used, you're correct too; based on predictions from both general and special relativity, the clocks on the satellites are fine tuned with an offset to minimize the nano-second order deviations from clocks on the ground. Then, for practical purposes, newtonian based approximations are acceptable accuracy-wise. [[User:Stryker|Stryker]] 14:08, 30 July 2007 (EDT)
: Mr. Schlafly, I apologize for not responding more quickly. Newtonian mechanics cannot account for the observed divergence in clock rates. Classically, inertial reference frames are related by [[Galilean transformations]]:
:: x' = x + vt
:: t' = t
:: where x and x' are positions in the rest and moving frame, respectively
:: t and t' are times in the rest and moving frame, respectively
:: v is the velocity of the moving frame relative to the rest frame. Note that frame labels like "rest" and "moving" are arbitrary.
: According to those transformations, time in all inertial frames is the same (t' = t), and therefore no time dilation is predicted. However, the Lorentz transformations that relate inertial frames according to special relativity DO predict time dilation. So that would allow for corrections based on the relative speeds of the satellites. However, you could reconcile the time difference using classical mechanics IF you assert that the speed of light in the moving frame is different from the speed of light in the rest frame; that would essentially mean that the satellites are measuring a different light speed than the earth is. Such assertions would conflict with experimental evidence.
: Another, more significant time dilation effect is due to gravitational time dilation, predicted by general relativity, which is dependent on the curvature of spacetime. Newtonian gravity incorporates an "action at a distance" principle and does not incorporate spacetime curvature, and therefore predicts no gravitational time dilation.
: Also, your statement that no sources have been provided showing that corrections for relativistic effects were historically incorporated is incorrect, as I have twice quoted from a Physics Today article (see above) showing that devices allowing for such corrections to clock frequencies were used when the satellites were first launched. I'm still convinced we have a misunderstanding; the satellite clock frequencies have used and do need relativistic corrections, but once those corrections are implemented, Newtonian physics works fine for communication and position calculations (although some sources seem to indicate that may not be true for fast-moving objects, like jets and so forth). However, you have successfully convinced me that there is something of a political element in some areas of science :)--[[User:Bayes|Bayes]] 14:40, 30 July 2007 (EDT)