An optical perspective on the theory of relativity -Ⅲ: Gravitational redshift

By using the concept of a space-time ruler, the clock difference between the clocks on two aircraft flying around the world, one east and one west, along the equator and a clock fixed on the equator is calculated (Hafele–Keating experiment). The calculated results are consistent with the classical formula associated with Einstein's theory of relativity. A generalized Hamiltonian, which can characterize the energy properties of matter, is given by using the space-time ruler. It is proved that the Hamiltonian in classical mechanics is an approximation of the generalized Hamiltonian under the conditions of low speed and a weak gravitational field. By using the generalized Hamiltonian, a new formula for gravitational redshift is obtained. Under the condition of a weak gravitational field, the new formula for gravitational redshift enables two classical formulas on gravitational redshift to be derived, both of which have been experimentally proven.