Interplanetary Clock Research Articles

The effect of f(T) gravity on an interplanetary clock and its time transfer link

As an extension of the “teleparallel" equivalent of general relativity, f(T) gravity is proposed to explain some puzzling cosmological behaviors, such as accelerating expansion of the Universe. Given the fact that modified gravity also has impacts on the Solar System, we might test it during future interplanetary missions with ultrastable clocks. In this work, we investigate the effects of f(T) gravity on the dynamics of the clock and its time transfer link. Under these influences, the Λ-term and the α-term of f(T) gravity play important roles. Here, Λ is the cosmological constant and α represents a model parameter in f(T) gravity that determines the divergence from teleparallel gravity at the first order approximation. We find that the signal of f(T) gravity in the time transfer is much more difficult to detect with the current state of development for clocks than those effects on dynamics of an interplanetary spacecraft with a bounded orbit with parameters 0.5 au ≤ a ≤ 5.5 au and 0 ≤ e ≤ 0.1.

A local-ether wave equation and speed-dependent mass and quantum energy

The east-west directional anisotropy in clock rate observed in the Hafele-Keating experiment with circumnavigation atomic clocks is commonly ascribed to the special relativity. In this investigation, based on the local-ether wave equation, an entirely different interpretation of this anisotropy is presented by showing that the clock-rate variation can originate from an intrinsic quantum property of the atom. For a harmonic-like wavefunction, the local-ether wave equation leads to a first-order time evolution equation similar to Schrodinger's equation. However, the time derivative incorporates a speed-dependent factor similar to that in the Lorentz mass-variation law. Consequently, the quantum energy, the transition frequency, and hence the atomic clock rate decrease with the atom speed by this speed-dependent mass-variation factor. According to the local-ether model, the speed is referred specifically to a geocentric or heliocentric inertial frame for an earthbound or interplanetary clock, respectively. It is shown that this restriction on reference frame is actually in accord with the various experimental results of the anisotropy and the clock-rate difference in the Hafele-Keating experiment, the synchronism and the clock-rate adjustment in GPS (global positioning system), and of the spatial isotropy in the Hughes-Drever experiment. Moreover, the switching of the unique reference frame is in accord with the frequency-shift formulas adopted in earthbound and interplanetary spacecraft microwave links. Meanwhile, the local-ether model predicts a constant deviation in frequency shift from the calculated result reported in an interplanetary spacecraft link. This discrepancy then provides a means to test the local-ether wave equation.