The proposed chapter enunciates the physical laws governing the way that the rates of atomic clocks vary in free space with their state of motion and position in a gravitational field. However, such ideal conditions are periodically disrupted by space-weather events that can lead to critical deviations from the norm and therefore require correction. Both theoretical aspects need to be properly taken into account in order to insure maximum reliability for the distance determinations that are the goal of this technology. It is pointed out that Einstein actually had proposed two quite distinct theories of time dilation in his original paper describing the special theory of relativity (STR). One is based solidly on the Lorentz transformation (LT) and the relativity principle (RP) and takes the view that the measurement process is fundamentally subjective. Specifically, it states that there is a symmetry principle whereby observers in relative motion can disagree as to which of two clocks is running slower as well as which of two objects has greater dimensions. However, the other theory of measurement is perfectly objective in character and is totally unambiguous in making the above comparisons. Six experiments are discussed which were eventually carried out to test these conclusions, ranging from measurements of the transverse Doppler effect in the laboratory and on rockets to the determination of the lifetimes of meta-stable particles and the rates of atomic clocks carried onboard airplanes. This part of the chapter closes by pointing out that Einstein made an undeclared assumption in his derivation of the LT which itself raises theoretical questions about its validity. An example is given which in fact shows that the LT leads to contradictory predictions for the same event (clock riddle). Making a different assumption leads to an alternative Lorentz transformation (ALT) which is nonetheless compatible with the two postulates of relativity and the same velocity transformation (VT) that is obtained using conventional STR. This version of the theory corresponds to a completely objective theory of measurement that recognizes that the rates of proper clocks do differ between inertial systems. This conclusion is perfectly consistent with the RP, which can be restated as follows: The laws of physics are the same in all inertial systems but the units in which they are expressed can and do differ in a systematic manner. This condition makes it impossible for a given observer to determine his state of motion on the basis of strictly in situ measurements, consistent with Galileo’s original statement of the RP, but it also emphasizes that proper clocks in different rest frames need to be adjusted in order to ensure they run at the same rate, as the success of the GPS technology has proven.
The second part of the chapter considers results demonstrating the influence of 2N and 2O molecules on spontaneous UHF radiation in the decimeter–wave range arising in the two-temperature plasma recombination in the D- and E-layers of the Earth's ionosphere during strong geomagnetic disturbances. This is caused by radiative transitions between medium-perturbed orbitally degenerate Rydberg atomic and molecular states that occur without changes in the principal quantum number 0.nΔ= Available experimental data were used to calculate the dependence of «neck of flow» states and orbitally degenerate state populations on the sun storm levels. Effective radiation bands were constructed for transitions between highly excited 2**NA and 2**OA quasimolecules. The emission spectrum was shown to be inhomogeneous and to contain three frequency bands in which a noticeable decrease in the radiation intensity occurred. It is induced by a shift of the emission spectra of quasimolecules containing unexcited 2N and 2O molecules. The frequency profiles of radiation intensity in the 0.8 – 1.8 GHz band were calculated as a function of the medium concentration, electron temperature and flux. It was shown that the radiation profiles change noticeably with increase in the geomagnetic storm level. They increase strongly close to the right-region edge corresponding to high transition frequencies. This explains the observed effect of the consistent loss of 1L and 2L frequency GPS signals in this range as the sun storm intensity increases. Therefore, the physical cause of reducing the propagation rate of the satellite signal may be due to the process of re-radiation of electromagnetic radio waves on the Rydberg particles located in the E- and D- layers which produces positioning errors on the order of 100 m. The general properties of the photoionization plasma formed under the action of light output from a solar flare are analyzed.