A quantum theory of gravity based on the local-ether wave equation

[[abstract]]Suppose that the gravitational potential as well as the local ether for wave propagation associated with the Earth or the Sun is stationary in a geocentric or a heliocentric inertial frame, respectively [1]. It is postulated that under a gravitational potential, the local-ether wave equation proposed in [2] is modified as [ frac1n_gnabla ^2-fracn_gc^2fracpartial ^2 partial t^2 Ψ (r,t)=fracω _0^2c^2Ψ +2 fracω _0hbar c^2qΦ Ψ , ] where the gravitational index n_g(r)=1+2Φ _g/c^2, the gravitational potential Φ _g(r)=GM/r, and the position vector r and the time derivative are referred to the local-ether frame. Suppose that the temporal variation of Ψ is close to the harmonic e^-iω _0t. Let Ψ (r,t)=ψ (r,t)e^-iω _0t. Then, it can be shown that the wave equation leads to the evolution equation similar to Schrödinger's equation as ihbar partial ψ /partial t=-(hbar ^2/2m_0)nabla ^2ψ +qΦ ψ -m_0Φ _gψ , where m_0=hbar ω _0/c^2. The m0 under nabla ^2 is known as inertial mass. As in deriving Ehrenfest's theorem, this evolution equation leads to acceleration a=-qnabla Φ /m_0+nabla Φ _g. Thereby, electrostatic force F=-qnabla Φ and gravitational force F=m_0nabla Φ g with the gravitational mass being equal to the inertial mass. Furthermore, the deflection of light by the Sun, the increment in interplanetary radar echo time [3], the gravitational redshift, and the gravitational phase shift can be derived from the wave equation as various wave-motion phenomena under different conditions.[[fileno]]2030130010017[[department]]電機工程學