Michelson-Morley experiment within the quantum mechanics framework

It is revisited the Michelson-Morley experiment within the quantum mechanics framework. One can define the wave function of photon in the whole space at a given moment of time. The phase difference between the source and receiver is a distance between the source and receiver at the time of reception hence it does not depend on the velocity of the frame. Then one can explain the null result of the Michelson-Morley experiment within the quantum mechanics framework. The Maxwell-Lorentz equations describe electromagnetic field as a wave propagating with the velocity c. It is reasonable to think that electromagnetic wave propagates with the velocity c with respect to a privilege frame. If some frame moves with the velocity v with respect to a privilege frame then one can expect that electromagnetic wave propagates with the velocity ~c − ~v with respect to the moving frame. The MichelsonMorley experiment was suggested to determine the velocity of electromagnetic wave with respect to a moving frame with the earth being taken as a moving frame. However the Michelson-Morley experiment [1] yielded the null result. The special relativity [1] explains the null result of the Michelson-Morley experiment with the Lorentz transformation for coordinates of space and time. Electromagnetic field is a quantum object. Below we shall revisit the Michelson-Morley experiment within the quantum mechanics framework. Consider electromagnetic field within the Newtonian framework. Consider electromagnetic field as a wave with the vector potential ~ A in the Euclidean space and time of a privilege frame. We shall take the cosmic microwave background radiation (CMB) [2] as a privilege frame. The Maxwell-Lorentz equations for the electromagnetic wave are given by [3] △ ~ A− 1 c ∂ ~ A ∂t = 0 (1) where c is the velocity of light. One can represent the solution of eq. (1) as a plane monochromatic wave ~ A = ~ A0e −iφ (2) with the phase φ = ωt− kr (3) where ω is the frequency, k is the wave vector. In the quantum mechanics [4], one can consider electromagnetic field as a bunch of photons with the momentum and energy given by respectively