Anisotropic propagation speed of light on rotating Earth's surface - theoretical derivation, implications for definition of meter, and crucial experiment

摘要: Whether the speed of light at the surface of rotating Earth is isotropic or not is both an important theoretical problem and one that has significant implications for scientific practices. Especially the unit of length, a meter, is defined as the length of the path travelled by light in vacuum in 1/299792458 of a second, on the basis that the speed of light is constant, c = 299792458 m/s. By applying the GPS range equation whose correctness has been fully verified by GPS practices, we found that the speed of light on rotating Earth's surface is neither constant nor isotropic, but    rE c' c v d ˆ , where rE v is the local linear velocity of Earth's rotation, and d ˆ is the unit vector of the light propagation's direction. It follows that the anisotropy of the speed of light at the Earth's surface has a significant impact on the definition of the meter. For example, at the equator, in 1/299792458 of a second the length of the eastward light path is 3.1 m shorter than the westward one's. Based on this, and the difference between Earth rotation's Sagnac effects on the equator and the meridian, we propose a crucial experiment to examine the anisotropy of the speed of light: let a stable pulsed laser emitting pulses in two opposite directions, use the ultrafast imaging techniques for visualizing, measuring and comparing the spacing of the pulses in opposite directions. Then we can decisively conclude whether the speed of light is anisotropic or not.