Abstract 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… Click to show full abstract
Abstract 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.
               
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