THE QUANTUM NATURE OF THE GRAVITATIONAL SHIFT OF FREQUENCY

By reconciling gravity with the flat space-time requirements of specia l relativity, we derive the explicit dependence of mass on gravitation al potential energy. We also determine that the mass of a small test p article is a constant of motion during its fall under the action of gr avity; that is, the increase in its mass, due to the increase in its k inetic energy, is compensated for by a corresponding decrease in its m ass related to the change in potential energy. The relativistic nature of gravity is encompassed by a generalized energy-momentum relation o f a test particle, which leads to a modified Dirac equation. Within th is framework we consider an electron bound to the atomic nucleus by a Coulomb potential, which is under the action of a centrally symmetric gravitational field. The exact solution of the Dirac equation for this system leads to the conclusion that the energies of the atomic levels increase at high altitudes. This means that the gravitational redshif t (or blueshift) of frequency is an effect of gravity on the quantizat ion of atomic internal energies. Since the radiative lifetime tau of a sample of excited atoms is related to the resonance frequency nu of t hese atoms, it is possible to test the effect of gravitational interac tion on the atomic energy levels with optically pumped atomic clocks.