Equality of the Inertial and the Gravitational Masses for a Quantum Particle

Details Equality of the Inertial and the Gravitational Masses for a Quantum Particle Equality of the Inertial and the Gravitational Masses for a Quantum Particle

2003-01-24

arxiv.org/abs/gr-qc/0301102v5

Acta Phys.Polon. B35 (2004) 613-624

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revised version, supported by the Polish State Committee Research (KBN) grant no. 5 P03B 093 20, 11 pages

Scientific paper

We investigate the interaction of the gravitational field with a quantum particle. We derive the wave equation in the curved galilean spacetime from the very broad Quantum mechanical assumptions and from covariance under the Milne group. The inertial and gravitational masses are equal in that equation. So, we give the proof of the equality for the non-relativistic quantum particle, without applying the equivalence principle to the Schr\"odinger equation and witout imposing any relation to the classical equations of motion. This result constitutes a substantial strengthening of the previous result obtained by Herdegen and the author.

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