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] [2楼] 作者:wangqi64 发表时间: 2011/01/07 08:19

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No equivalence for GPS

The fact that SR & GR cancel across the Earth’s surface is a mixed blessing. On one hand it’s good because we don’t need to worry about unsynchronized clocks at different latitudes. On the flip side it means that we can’t use them to verify relativity. But there is a reason for pointing this out and that has to do with the Equivalence Principle.

We know that gravity at the equator is made of two components: actual gravity from the Earth (a downward pull), and centripetal (upward) force which lessens the effect. We can easily calculate the strength of the centripetal component to be 0.034 m/s2.

In above equation (2) the quoted value of gravity at the equator, 9.78 m/s2, is the measured value. The true equatorial gravity must be 9.780+0.034=9.814 m/s2. However we don’t use this true value of gravity in our calculation of GR time-dilation, only the net (real gravity minus centripetal force) value. The reason for this has to do with the Equivalence Principle which states that gravity and acceleration are indistinguishable and should be treated alike. If we used the number 9.814 we would calculate a gravitational dilation at the equator that is higher than at the pole – the opposite of what we need to counteract SR at the equator.

Now cast your eye to our earlier calculation of GPS time dilation shown in equation (1). Here we determined the difference between dilation at the equator and dilation at the satellite. The first term, with R in denominator, represents time dilation at the equator. The second, with R+A, represents dilation at the satellite. Let’s split these apart:

Time dilation at equator is:
1 + 6.9774x10-10

Time dilation at satellite is:
1 + 1.6702x10-10

The first term represents the gravity at the equator. The second represents gravity at the satellite. Is something amiss here?

Hang on a tick... gravity at the satellite? There’s no ‘gravity’ on man-made satellites! The satellite is in orbit and experiences an outward force exactly equal to the inward real-gravitational pull. The net gravity, according to the Equivalence Principle, is therefore zero and the satellite shouldn’t experience gravitational time dilation.

So what should the net dilation between the equator and satellite be? Using the above equation (2) with the second term set to 1 (for zero dilation), we get:

\left(1\left/\sqrt{1-\frac{2 9.78 6378000}{c^2}}\right.-1\right)*86400

= 59960 ns

This value is 31% higher than the quoted value of 45900ns.

[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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