Eur. Phys. J. B 24, 231-239 (2001)
https://doi.org/10.1007/s100510170010

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

Department of Electrical Engineering, National Tsinghua University, Hsinchu, Taiwan

Corresponding author: ^a ccsu@ee.nthu.edu.tw

Received: 11 December 2000
Revised: 20 August 2001
Published online: 15 November 2001

Abstract

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 Schrödinger'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.