A Geometric Theory of Atomic Structure Without Quantum Postulates

Overview & Synopsis

Trembling Spacetime Relativity Theory (TSRT) provides a deterministic and fully geometric foundation for atomic structure, replacing the probabilistic framework of quantum mechanics with causally governed geodesic motion in a dynamically fluctuating spacetime. Previous work established TSRT as a unifying theory of all four fundamental forces, deriving interference without wave-particle duality, Planck’s radiation law without quantization postulates, and entanglement from geometric correlations. In this work, TSRT advances from theoretical coherence to high-precision empirical predictions, confronting experimental spectroscopic data across hydrogen, Deuterium, and Muonic Hydrogen. With only a single calibration line, the full spectrum of bound-state energy levels is derived from first principles without free parameters. TSRT reproduces excited states and fine-structure splittings to within a few millielectronvolts of experiment. The energy difference between the two fine-structure components of the second principal level is recovered with sub-percent accuracy, without invoking spin, operator algebra, or field-theoretic corrections. In Muonic Hydrogen, where curvature effects are amplified, refinements incorporating proton size, nuclear mass, and realistic density profiles yield agreement with experiment at the per-thousand level. These corrections arise naturally from the variational geometric structure of TSRT, requiring no renormalization or perturbative methods. Photon emission is described as a deterministic transition between complete geodesic ensembles, and the energy of the emitted photon is subsequently redshifted as it escapes the curved trembling geometry surrounding the atom. Further redshift may occur if the atom resides in a larger gravitational field, such as in a stellar environment. Atomic shell structure emerges as the equilibrium configuration of curvature-induced confinement, and an effective atomic coupling constant is derived from gravitational scaling, linking electromagnetism and gravity through geometry. Gravitational contributions, often neglected in atomic physics, are shown to be essential for spectral precision within TSRT. Even in weak fields, spacetime curvature determines energy levels with high accuracy, while in strong gravity environments, TSRT predicts additional geometric shifts beyond the standard redshift. These results demonstrate that trembling spacetime is not merely an alternative conceptual framework, but a viable and predictive physical foundation for atomic structure, unifying quantum and gravitational phenomena within a single geometric continuum.