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Spin, gravity, and inertia.

¹Institute of Theoretical Physics, Technical University of Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.

Physical Review Letters

|February 15, 2001

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This study explores relativistic quantum mechanics and gravity. We found that spin-gravity interactions in Dirac fermions do not violate the equivalence principle.

Area of Science:

Relativistic quantum mechanics
Quantum field theory in curved spacetime

Background:

Investigating gravitational effects on quantum particles is crucial for unifying general relativity and quantum mechanics.
The Foldy-Wouthuysen transformation is a key tool for analyzing relativistic quantum systems in external fields.

Purpose of the Study:

To investigate gravitational effects within the framework of relativistic quantum mechanics.
To construct an exact Foldy-Wouthuysen transformation for a Dirac particle interacting with a static spacetime metric.
To analyze the nonrelativistic limit and identify spin-gravity interaction terms.

Main Methods:

Development of an exact Foldy-Wouthuysen transformation for a Dirac particle coupled to a static spacetime metric.
Analysis of the nonrelativistic limit of the derived quantum relativistic theory.

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Derivation and examination of the Hamiltonian, including specific spin-gravitational moment interactions.

Main Results:

An exact Foldy-Wouthuysen transformation was successfully constructed for the specified system.
The nonrelativistic limit revealed a new term in the Hamiltonian, representing a specific spin-gravitational moment interaction.
Comparison between gravitational coupling and inertial effects confirmed no violation of the equivalence principle.

Conclusions:

The study successfully derived the spin-gravity interaction term in the nonrelativistic limit.
The equivalence principle holds for Dirac fermions, as relativistic spin effects do not contradict it.
This work provides a foundation for understanding quantum particle behavior in gravitational fields.