It is generally believed that the GPS need be calibrated with the relative time observed with the Hafele-keating experiment. But, it is not true.
1. The altitude of the GPS satellite is less than 25000km. In less than 0.1 seconds, the clock in the satellite can be calibrated one time with the clock on the surface of the Earth. Therefore, the clocks between on the surface of the Earth and in the satellite were calibrated many times in a day. But, the time effect in the Hafele-keating experiment only can be obtained in a long time, such as a day.
2. The Hafele-keating experiment could not be credible for two reasons: First, the Newtonian gravity has a bigger effect on an atomic clock. The variation of the height on the level less than 10cm by the Newtonian gravity can be observed with an atomic clock. However, this variation cannot be observed in the Hafele-keating experiment. The force F=GMm/r^2 between the Earth (M) and the atom (m) can affect the motion of the atom in this clock. (It is noted that, it does not affect the frequency of the atom.) This effect has been used as a usual method to measure the Newtonian gravitational constant G. But, in the Hafele-keating experiment this effect was not considered. Thus, the Hafele-keating experiment is invalid theoretically. Second, an atomic clock is very precise. A little change, such as motion, temperature, magnetic field, can make very big change of the readings of an atomic clock. Figuratively, as a person walk near to an atomic clock, the readings of it are changed. Thus, the Hafele-keating is not credible under the condition that Einstein’s time effect is right.
3. The gravitational effect of time cannot be measured with a random clock. For example, in different fountain standard atomic clock, the atoms run different length L. A phase shift of the motion of the atoms caused by the force F=GMm/r^2 between the Earth (M) and the atoms (m) is determined with the length L. Thus, with different L, the gravitational effect on the clock is different.
Kindly read my paper as attached and see if it helps.
http://pubs.sciepub.com/ijp/1/5/5/index.html
Dear Danci,
Thank you for your message. But, in any case, the Newtonian gravity of the Eearth on the atomic clock has not been considered in the H-K experiment. In fact, the variation of the height in less than 1cm can affect the readings of the atomic clock. It is much larger than the Einstein's time effect. However, this effect was not observed in the H-K experiment.
As soon as you consider the atom gravitational interferomer, you shall know the problem in the H-K experiment.
Dr. Yin, your discussions of a close body effect on an atomic time clock are compelling me to ask if this is a measurable effect, how does the observer (the measurer) overcome quantum uncertainty effects?
Dr. Rogers, 1) This is a measurable effect. For example, it was general known that the variation of the height of 1cm can affect on the readings of an atomic clock. 2) I do not know how does the observer (the measurer) overcome quantum uncertainty effects, too. The atomic clock is based on the radiac frequency of an atom. It seems that the radiac frequency is not realated with the uncertainty effects.
Thank you Dr. Yin. I look at the question of the close body observer in 4-space. If energy density tells us anything, it tells us that even at Plank lengths, space must curve. How can we make observations on this? In one thought experiment, I propose to use atomic / molecular interferometric pulsation measurements of two identical crystals, but place one of the crystals in close proximity to an ultra dense mass. I suggest placement of the two crystals at opposite poles on earth and as close as permissible at the same elevations (to negate any relativistic gravitational effects from orbital deltas. Also a Lagrangian point in space could work as well). Let the the crystals oscillate and record and count the oscillations over a year. I suspect a quantum vibrational delta will be observed between the two crystals. And with all other effects negated, the cause will be revealed to be the curved 4-space near the high energy density object. Thoughts?
The simple answer is yes. Orbits of satellites are always definable in curved space. The Einstein Field equations are well understood for these solutions. What is not understood is why the frequency of an atomic clock crystal is observed not to change in the presence of relativistic energy density to a significant degree. Two atomic clocks in different orbits operate differently in different orbits, BUT as you point out, the frequency of the crystal lattice for the two different clocks remains unchanged. If the frequency of the crystal lattice vibration remains independent of energy density (we assume it to be constant but in fact the vibrations are known to have a small upper and lower limit) which is otherwise known as 4-space (x, y, z, and time T) even at Plank lengths (Quantum order lengths), two different things are happening: either the Quantum world interactions such as crystal lattice vibrations in a small EM field are unaffected by relativistic energy density (i.e. curvature of space time - 4-space) which I believe is unlikely, or that we have yet to define and execute proper observational experiments which I believe is more likely. Thoughts?
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