Rigorous Comparison of Gravimetry Employing Atom Interferometers and the Measurement of Gravitational Time Dilation

We present a gravitationally rigorous and clear answer, in the negative, to the question whether gravimetry with atom interferometers is equivalent to the the measurement of the relative gravitational time dilation of two clocks separated in space. Though matter and light waves, quantum states and oscillator clocks are quantum synonymous through the Planck-Einstein-de Broglie relations and the equivalence principle, there are crucial differences in the context of tests of gravitation theories.