Clocks on GPS satellites: A GPS fudge?-挑战相对论-西陆网

Clocks on GPS satellites: A GPS fudge?

[楼主] 作者:wangqi64 发表时间:2011/01/07 07:11

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Clocks on GPS satellites

from alternativephysics

Another strong piece of evidence supporting GR, and which affects our everyday lives, is the Global Positioning System (GPS). We are told that GPS satellites experience a net time dilation of 38,700ns (nanoseconds) a day: +45,900ns due to GR and -7,200ns due to SR. We discussed the SR aspects of this in an earlier chapter. Now let’s look at GR.

The satellites orbit at an approximate altitude of 20,200km. Using equation (3) in the chapter on General Relativity we can calculate the expected differences in time dilation at the Earth’s surface and at the satellite:

$\left.(1\left/\sqrt{1-\frac{2 G\text{ }M}{R c^2}}\right.-1\left/\sqrt{1-\frac{2 G\text{ }M}{(R+A) c^2}}\right.\right)*86400\text{ ----}(1)$

Where M is the mass of Earth, R is the radius, A is the altitude of the GPS, and 86400 is the number of seconds in a day. Substituting values of M=5.974x10²⁴, R=6.357x10⁶, and A=2.02x10⁷ we get:

Net dilation = 45850 ns.

And this closely matches the measured amount. Brilliant!

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[楼主] [3楼] 作者:wangqi64 发表时间: 2011/01/07 08:21

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A GPS fudge?

What does this mean? Why is it that when calculating the GR dilation on Earth we take into account centripetal force, basing calculations only on ‘net gravity’, while on GPS satellites we ignore centripetal force? Put another way, why doesn’t the Equivalence Principle apply to GPS?

In an earlier chapter on SR we noted that there are some problems relating to the SR dilation on GPS, namely (a) that any dilation due to movement should be equally experienced by both satellite and observer since velocity is purely relative, and (b) that the dilation should be adjusted in the GPS receivers, not the satellite, due to different latitudes moving at different speeds.

Now we have a third and much larger problem, namely that the proper calculation of GR dilation is off by a whopping thirty percent over the stated value. And yet the GPS works perfectly fine.

Is it possible that ... GPS satellites experience NO dilation at all ?

Keep in mind that prior to the invention of satellites there was no easy way to test the SR and GR postulates properly. Up to this point the evidence was shaky, the errors large, and hence much of GR and SR was just assumed to be correct. What would happen then, when GPS was being developed, if the engineers discovered that in fact no dilation occurred?

Information like that would be pretty embarrassing, especially to the mainstream scientific community who had been preaching relativity for the past 70 years. What to do? Admit they’re wrong? Not likely! The simplest solution would be to calculate the expected amount of dilation and then claim to have built that into the satellites.

Problem solved! The theory of relativity is not only preserved, it’s also exalted to a stage where the average Joe with a GPS receiver can vouch for relativity on a daily basis. After all, who would even suspect that atomic clocks aboard satellites might actually be running at the same rate as clocks everywhere else?

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Clocks on GPS satellites

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