TSRT investigations

This work is introduced through a book that does not contain equations:

Trembling Spacetime: A Conceptual Introduction to Geometry, Motion, and Matter Beyond Quantum Postulates. 2026 ISBN: 9798242522565 (hardcover); ISBN: 9798242520431 (softcover). The authoritative version is archived at Zenodo: 10.5281/zenodo.18144832

Pre-Prints

TSRT is a project under development and is published strategically. In 2025, the most important outcome was published in an accessible manner, through open-access publications on CERN's Zenodo (See Published Results below). Currently, building blocks are separately developed and described, to be submitted to Physics journals and shared, in advance, on HAL (CNRS) to allow readers to frame each paper into the holistic TSRT framework, rather than reading them only as stand-alone items. The list of those papers is provided here.

Published Results

“Derived Dynamics in Trembling Spacetime Relativity, A Unified Geometric Basis for the Principles of Inertia, Equivalence, Action, and Energy-Mass Relations”
This paper represents the conceptual culmination of the TSRT program, consolidating its earlier results into a unified geometric foundation for classical and quantum physics. Rather than addressing a specific domain (such as atomic spectra, cosmology, or nuclear decay), it revisits the most fundamental principles of physics themselves—inertia, gravitational mass, the equivalence principle, least action, and gauge interaction—and demonstrates that all of them emerge from a single causal trembling geometry.
The work shows that inertial resistance is not an intrinsic property of matter but a geometric response: a scalar overlap susceptibility between localized trembling modes and the long-wavelength structure of spacetime. The same susceptibility governs gravitational response, rendering inertial and gravitational mass identical as a geometric identity. Extended and composite systems are treated explicitly, explaining why bound bodies fall as a whole and why internal structure does not violate universality of free fall except through suppressed tidal effects.
The principle of stationary action is derived as the macroscopic limit of curvature, i.e., stationary trembling worldlines constrained by monotone proper time, recovering the classical Lagrangian formulation without postulating variational principles. The paper further clarifies how gauge interactions arise from internal trembling symmetries and their associated causal Noether currents, completing the bridge between geometry, dynamics, and interaction structure.
By integrating these results, the paper reframes long-standing axioms of physics as consequences of a single causal geometric premise. It establishes TSRT not only as a theory capable of reproducing known phenomena across scales, but as a foundational framework for organizing physical law itself.
Published on Zenodo (CERN), HAL (CNRS), and ResearchGate.

“A Unified Geometric Theory of Trembling Spacetime Relativity”
This foundational paper introduces the full TSRT framework and derives from first principles how classical spacetime, quantum statistics, and fundamental interactions emerge from deterministic trembling. It unifies general relativity and quantum mechanics without invoking separate fields or wavefunction collapse. Published on Zenodo (CERN), HAL (CNRS), INSPIRE (CERN), and ResearchGate.

“Beyond Superposition and Collapse: Double-Slit Interference from Trembling Spacetime Geodesics”
This paper reinterprets the famous double-slit experiment. It demonstrates that interference fringes can be derived from deterministic, curved geodesics in trembling spacetime—removing the need for wave-particle duality or superposition. The model matches experimental data across particle types (photons, electrons, neutrons) and makes precise geometric predictions. Published on Zenodo (CERN), HAL (CNRS), INSPIRE (CERN), and ResearchGate.

"Causal Entanglement from Deterministic Geodesic Correlation in Trembling Spacetime"
This paper presents a reinterpretation of quantum entanglement as a causal, geometric phenomenon arising from deterministic correlations in a trembling spacetime fabric. Rather than invoking wavefunction collapse or nonlocal influences, it shows that entanglement-like correlations—including violations of the CHSH inequality—can emerge naturally from proper-time-synchronized geodesic fluctuations governed by spacetime curvature. The result is a fully Lorentz-invariant and falsifiable model that reproduces quantum predictions at short ranges while predicting measurable deviations at larger distances or under gravitational modulation. It opens a new path for understanding entanglement not as a mysterious quantum effect, but as a visible imprint of causal geometry. Published on Zenodo (CERN), HAL (CNRS), INSPIRE (CERN) and ResearchGate.

"Corpuscular Light in Trembling Spacetime: A Geometric Foundation for Planck's Radiation Law and the Limits of Temperature."
This article offers a new geometric foundation for understanding blackbody radiation—without relying on traditional quantum assumptions. By working within the framework of Trembling Spacetime Relativity Theory (TSRT), it shows that the discrete energy exchange predicted by Planck’s law arises not from postulated quantization, but from the causal and curvature constraints of spacetime itself. In this view, light is fundamentally corpuscular—a localized excitation traveling along null geodesics shaped by metric fluctuations. The work reveals how the blackbody spectrum, the ultraviolet cutoff, and even the emergence of Planck’s constant can be derived from purely geometric principles. It explains why wave-based models fail in this context and how quantized behavior naturally results from the requirement that proper time remain physically admissible. By grounding thermodynamic and radiative phenomena in spacetime geometry, this article helps reshape our understanding of the interface between classical and quantum physics—and points toward a deeper, unified picture of physical law. Published on Zenodo (CERN), HAL (CNRS), INSPIRE (CERN) and ResearchGate.

"A Geometric Theory of Atomic Structure Without Quantum Postulates."
This study demonstrates that the structure of atoms can be derived from geometric principles, without invoking quantum mechanical postulates. The work is grounded in the framework of Trembling Spacetime Relativity Theory (TSRT), a deterministic model in which particles follow stable geodesic paths through a dynamically fluctuating spacetime geometry.
The paper shows that hydrogen, deuterium, and even muonic hydrogen energy levels and transition frequencies can be accurately predicted using this approach — with agreement to within microelectronvolt precision of experimental data, and without wavefunctions, probabilistic interpretations, or quantized energy assumptions. Instead, the dynamics arise from curvature-driven confinement and geodesic resonance within the trembling spacetime manifold. The work not only challenges the necessity of quantum postulates in atomic theory but also offers a promising pathway toward a unified, causal, and geometrically transparent account of atomic phenomena. Published in Zenodo (CERN), HAL (CNRS), INSPIRE (CERN) and Researchgate.


"The Geometric Origin and Finite Classification of Fundamental Particles in Trembling Spacetime"
This paper completes a key milestone in the development of Trembling Spacetime Relativity Theory (TSRT) by deriving the entire spectrum of known fundamental particles—quarks, leptons, gauge bosons, and the Higgs—as localized, symmetry-bound trembling modes of spacetime curvature. Unlike conventional quantum field theories, which postulate independent fields and symmetry breaking to explain particle diversity, TSRT shows that mass, spin, and charge all emerge deterministically from causal coherence and geometric stability of trembling geodesic configurations. The work proves that exactly four geometric symmetry classes (U(1), SU(2), SU(3), and coarse curvature) suffice to account for all observed forces and matter types. It also demonstrates why no additional generations or superpartners are predicted and explains charge quantization and spin-½ holonomy as consequences of topological constraints. The paper details empirical consistency with known mass and interaction patterns while outlining testable predictions that distinguish TSRT from standard models. By unifying gravity and particle physics through a single geometric principle, it offers a falsifiable and conceptually transparent foundation for understanding the fabric of matter. Published on Zenodo (CERN), HAL (CNRS), INSPIRE (CERN), and ResearchGate.

"Emergence of 4D Spacetime and Cosmic Expansion from Causal Geometry"
This cosmology paper applies the TSRT framework to the universe as a whole, showing that spacetime expansion is not an added assumption but a direct geometric consequence of causal trembling. It derives the existence of four-dimensional spacetime, explains why expansion must occur, and demonstrates how redshift and the cosmological arrow of time follow deterministically from amplitude growth of metric fluctuations. Unlike inflationary models or dark-energy-driven acceleration, the expansion emerges naturally from causal coherence constraints, with the cosmological constant interpreted as a curvature-saturation effect rather than a fundamental input. The work connects local trembling dynamics to the global structure of the universe, establishing TSRT as a predictive cosmological framework that avoids singularities and unifies microphysical and cosmic scales under the same principle. Published on Zenodo (CERN), HAL (CNRS), INSPIRE (CERN), and ResearchGate.

"Deterministic Nuclear Structure, Decay, Fission & Fusion"
This work extends TSRT to the nuclear domain, treating each nucleus as a localized trembling-curvature eigenmode.
With one global normalization fixed on ⁶⁰Co, the theory reproduces experimental half-lives across more than 20 orders of magnitude with a mean logarithmic deviation below 10⁻⁶—surpassing the accuracy of leading microscopic and empirical models by up to four orders of magnitude.
TSRT provides first-principles explanations for: β decay, α decay, and spontaneous fission; emergence of magic numbers; odd–even staggering in fission yields; deep sub-barrier fusion hindrance; absolute Q-values and reaction energetics; electron-screening corrections; the exceptional stability of carbon-14.
All arise from deterministic curvature dynamics without shell corrections, preformation factors, or per-nucleus tuning.
Published on Zenodo (CERN), HAL (CNRS), and ResearchGate.

See also Tracie Troha, George W. Woodruff School of Mechanical Engineering, December 16, 2025.