Quantum Systems Redefined by Gravity

Understanding how quantum systems interact with gravity is crucial for advancing technologies like atom interferometers, which measure gravitational effects with unprecedented accuracy. This research provides a systematic to derive quantum equations in weak gravitational fields, moving beyond ad hoc approaches to ensure all relativistic corrections are accounted for without guesswork. The study focuses on developing a post-Newtonian expansion framework for quantum mechanics, where gravity is described by the Eddington-Robertson parametrized post-Newtonian metric. This metric includes parameters that allow testing deviations from general relativity, making it ideal for experimental applications. By expanding the Klein-Gordon equation—a relativistic wave equation—in powers of the inverse speed of light, the researchers derived a Schrödinger-like equation for quantum particles. This , compared to traditional canonical quantization, shows agreement up to linear momentum terms, ensuring consistency in describing effects like gravitomagnetism. Key include the derivation of Hamiltonian terms that incorporate gravitational corrections, such as potential energy modifications and momentum-dependent interactions. For example, in a simple atomic system, the total mass-energy includes internal energy contributions, aligning with mass-energy equivalence. The framework was applied to a two-particle atom model, revealing how gravity couples to both kinetic and electromagnetic parts of the system. Limitations noted in the paper include the neglect of higher-order terms beyond the inverse speed of light squared, which could involve retardation effects not captured in the Hamiltonian formalism. Additionally, the approach assumes weak gravitational fields and stationary spacetimes, leaving strong-field or highly dynamic scenarios for future work. This systematic derivation not only validates intuitive concepts like the composite particle behavior but also sets the stage for precise quantum tests of gravity, potentially refining measurements in laboratories and space-based experiments.