Bridging Electrodynamics and Gravitation Equivalence principle and the conservation laws

Atomic clocks are devices based on quantum electrodynamics, under the influence of gravitation and motion. To this purpose a revisitation of a well-known derivation of Schiff, about variations of periods of atomic clocks, is performed. The Weak Equivalence Principle and Special Relativity are not found sufficient to derive, from Schiff’s proposal, gravitational time dilation, even to a first order approximation. Nevertheless, Schiff’s proposal of time dilation, by relying on conservation of energy also in gravitation, can be extended to match all orders of approximation with the results in static gravitation. Energy conservation and the Weak Equivalence Principle can be a bridge between the two interactions, such that variations of periods of oscillators on Earth depend on their kinetic energy and potential energy, referred to the ECI frame.