GPS and SRT

[MacM]

I would be interested in some feedback on this issue:

 

GPS uses the eath's rotating axis (Pole) as a local preferred rest referance frame.

 

The earth's equator has a velocity of 463.8 m/s.

 

GPS satellites have a velocity of 3,874.5 m/s. The "Relative Velocity" between the orbiting clock and a clock at the equator is (3,874.5m/s - 463.8m/s) = 3,410.7m/s.

 

Using SRT in GPS one gets: 3,410.7/c = 1.1369E-5, squared = 1.2925E-10. Divided by 2 = 6.4627E-11.

 

Time loss would be 6.4627E-11 * 24 * 3,600 = 5.58378E-6 or - 5.58 micro-seconds per day maximum deviation by being at the equator. Other latitudes would be less.

 

HOWEVER: Using the absolute velocity of orbit of 3,874.5 m/s and NOT "Relative Velocity" per SRT one gets 1.2915E-5c, squared = 1.66797E-10. Divided by 2 = 8.33986E-11.

 

8.33986E-11 * 24 * 3,600 = 7.205E-6 or 7.2 micro-seconds per day due to orbit velocity.

 

In this case earth's equitorial velocity produces a dilation only in the pico-seconds/day and is disregarded.

 

Over a dozen considerations are made in the GPS system but prelaunch adjusments of GPS orbiting clocks consist of only two primary ones.

 

About +45 micro-seconds gain due to GR (Gravity) and for a -7.2 micro-second loss due to velocity, for a net adjustment of -38 micro-seconds.

 

Since it is known that GPS clocks are preadjusted for 7.2 microseconds loss per day (which matches absolute velocity of orbit and not SRT's Relative Velocity, GPS does not use SRT. It uses the Lorentz Relativity concept of absolute velocities and not SRT Relative velocity. The other adjusments are generally made by software based on signal data.

 

Further since the velocites and calculations are based on absolute velocities relative to a common preferred rest frame the two components are not reversable as they are in SRT where each can claim to be at rest. In this format the orbiting clock always has higher velocity and always is the clock which shows dilation.

 

Why is it so many physicists (Relativists) are so quick to claim GPS "Proves" SRT? It actually only proves the Lorentz Gamma function and discredits the SRT view where there is reciprocity between observers. SRT prohibits the use of local absolute rest frames and claims either observer can be at rest. It doesn't work that way in GPS. It appears GPS favors Lorentz over Einstein.

[swansont]

To do the proper SR calculation, though, you have to compare to an observer at rest. Even though we want to think of ourselves as being in an inertial frame, we are not.

 

Our reference clocks are referenced to be on the geoid - the idealized average sea-level. The earth is an oblate spheroid - there is an equitorial bulge and flattening at the poles - and one must also account for gravitational redshifts. If you solve for the equipotential surface of the geoid, you find that the kinetic term (time dilation) cancels the deformation term (gravitational redshift) so that a clock on the geoid always runs at the same rate, regardless of rotation speed. The rotational velocity is not "disregarded."

 

GPS satellites are in inclined orbits at about 55 degrees, not equatorial orbits, so your relative velocity calculation is flawed anyway, as velocity is a vector.

[MacM]

To do the proper SR calculation, though, you have to compare to an observer at rest. Even though we want to think of ourselves as being in an inertial frame, we are not.

 

Our reference clocks are referenced to be on the geoid - the idealized average sea-level. The earth is an oblate spheroid - there is an equitorial bulge and flattening at the poles - and one must also account for gravitational redshifts. If you solve for the equipotential surface of the geoid, you find that the kinetic term (time dilation) cancels the deformation term (gravitational redshift) so that a clock on the geoid always runs at the same rate, regardless of rotation speed. The rotational velocity is not "disregarded."

 

I appreciate your response. However, I cannot accept it as being signifigant in regard to defense of SRT. We all know the earth is an oblate spheroid. We all know gravity redshift is accounted for. I saw a figure that GPS uses 15 adjustments to achieve its current accuracy. However there are only two primary ones that regulate the overwhelming range of performance. That is GR due to orbit distance and Velocity affect of orbit.

 

GPS satellites are in inclined orbits at about 55 degrees, not equatorial orbits, so your relative velocity calculation is flawed anyway, as velocity is a vector.

 

I believe I indicated that the surface clock was at the equator and hence the maximum and that at other latitudes the affect would be even less. Surely you can see that the inclination of the earth's axis to the orbit plane has minimal affect on the issue. Of course it must be taken into account but that does not address the issue, nor alter the results.

 

The surface clock V2 (assumed at the equator) has an absolute velocity, with the pole being "0", of 463.8 m/s.

 

For this clock I calculate 1.195058E-16 * 24 * 3,600 = 10.325E-12 or -10.325 Pico-seconds per day

 

Based on SRT measurements one gets -5.58 micro-seconds per day because the earth's surface clock gamma affect is negligable and will be disregarded .

 

Perhaps you would care to address the issue which is the fact that GPS uses the earth's axis as a local preferred rest frame, a view prohibited in SRT.

 

Using relative veloicty between clocks one gets -5.58 micro-seconds.

 

As I have shown computing velocity gamma affect for absolute velocity of surface clocks and orbiting clocks relative to the rest frame produces a different result (the correct result and the one used by GPS is -7.2 micro-seconds).

[swansont]

I appreciate your response. However, I cannot accept it as being signifigant in regard to defense of SRT.

 

Oh, well.

[The Rebel]

ooo, someones envoking controversy in the relativity field.

 

I also think the factors implemented into GPS are outside the now infamous SR formula that so many are currently quoting. Maybe when quantum mechanics becomes as run of the mill as newtonian physics is, the assumptions and flaws will become more clearer. Then we can have all the answers without quoting equations and apparent (ambiguous) relationships with real life.

[MacM]

ooo' date=' someones envoking controversy in the relativity field.

 

I also think the factors implemented into GPS are outside the now infamous SR formula that so many are currently quoting. Maybe when quantum mechanics becomes as run of the mill as newtonian physics is, the assumptions and flaws will become more clearer. Then we can have all the answers without quoting equations and apparent (ambiguous) relationships with real life.[/quote']

 

Sounds like a fair proposition.