Technical Introduction

The developments of TSRT up to May 2026 have been summarized in a recent Zenodo publication, accompanied by a series of AI-generated podcasts. While these podcasts are intentionally expansive in style, they are intended primarily as an accessible introduction and invitation for interested readers to explore the underlying articles and the broader conceptual framework of this emerging paradigm. Overview and Podcasts.
Trembling Spacetime Relativity Theory (TSRT) is a unified, covariant relativistic framework that models spacetime itself as a hypo-metamaterial—an underlying, dynamically structured geometric medium whose fine-scale organization generates the effective forces, particles, and quantum-like phenomena observed throughout the universe.

Metamaterials—derived from the Greek meta (“beyond” or “above”)—are traditionally defined as media whose macroscopic properties arise not from their chemical composition but from engineered sub-wavelength structure, enabling wave behaviours unattainable in homogeneous materials. Extending this conceptual foundation to the deepest physical level, TSRT treats spacetime as a dynamically microstructured meta-medium: its intrinsic curvature oscillations (“trembling”) play the role that geometric microstructure plays in conventional metamaterials.

Within this fully covariant relativistic formulation—constructed such that all predictions remain invariant under spacetime coordinate transformations—the fundamental interactions, particle characteristics, and wave-like behaviours of nature emerge as effective responses of this geometric microstructure rather than as independent axioms. The theory thereby yields a unified description of all forces, provides a deterministic account of quantum-like phenomena (including interference, superposition-like pattern formation, entanglement-type correlations, and atomic spectra), and explains cosmic expansion, matter genesis, and the large-scale evolution of the universe as natural consequences of the underlying trembling geometry.

Although TSRT is fundamentally a theory of physics, not an engineered material, it aligns naturally with the metamaterials research paradigm: it investigates how waves, particles, and fields propagate through, resonate with, and derive their observable properties from a hierarchically structured medium. This perspective enables TSRT to bridge foundational physics with practical modelling across scales—linking cosmology, nuclear and atomic structure, and quantum-like effects with engineering applications inspired by metamaterial principles.

Within this broader context, TSRT forms the fundamental and paradigm-shifting pillar of Prof. Declercq’s research portfolio in the domain of metamaterials. While his established work in acoustic and ultrasonic metamaterials focuses on engineered structures—phononic crystals, sub-wavelength resonators, guided-wave metasurfaces, and architected media for imaging and sensing—the TSRT program extends these concepts to the foundations of physics itself. In this way, TSRT complements and deepens the metamaterials research he conducts at laboratory and engineering scales: both investigate how structured media shape wave propagation and energy localization, but TSRT does so at the level of spacetime geometry, where the “medium” is not fabricated matter but the trembling curvature of spacetime. Together, these lines of research form a coherent continuum—from practical metamaterial engineering to the geometric principles governing the universe—unified by a single guiding theme: understanding how structure, at any scale, determines physical behaviour.

Within the i-META consortium, this perspective places TSRT as the deep foundational axis complementing the engineered development of multifunctional metamaterials pursued across the project. i-META aims to design artificial meta-media capable of unprecedented control and structuration of acoustic, elastic, mechanical, and multiphysical waves—addressing societal challenges spanning aeronautics, biomedical imaging and therapy, energy, communications, civil engineering, and environmental technologies. Against this interdisciplinary backdrop, Prof. Declercq’s research portfolio forms a coherent continuum: at one end, his established work in acoustic, ultrasonic, nonlinear, and architected metamaterials directly contributes to the project’s technological objectives; at the other end, TSRT introduces a hypo-metamaterial model of spacetime itself, extending the metamaterials paradigm to its conceptual limit by examining how structured media determine wave behaviour across all scales, from laboratory ultrasonics to cosmology. By uniting engineered metamaterials and fundamental geometric meta-media within a single scientific vision, TSRT enriches i-META’s mission, strengthens its interdisciplinary core, and expands its conceptual territory—from designing materials that manipulate waves, to understanding the structured medium in which all waves, particles, and forces ultimately propagate.

Core Contributions to Date

Since its initial publication on CERN’s Zenodo platform, Trembling Spacetime Relativity Theory (TSRT) has evolved from a conceptual proposal into a broad, multi-sector scientific framework that addresses some of the deepest questions in physics. Across a rapidly expanding series of open-access articles, TSRT has demonstrated that a single geometric principle—the causal trembling of spacetime—can reproduce, unify, and extend physical phenomena traditionally explained by entirely separate theories of quantum mechanics, particle physics, nuclear structure, gravitation, and cosmology.

At the foundational level, TSRT shows that Lorentzian geometry, gauge interactions, Planck-scale limits, and even the familiar forms of the Schrödinger and Dirac equations emerge not as axioms but as consequences of causality applied to a dynamically fluctuating metric. This provides a fully covariant relativistic framework in which quantum-like behaviour arises deterministically from geometry, bridging a century-long conceptual divide between general relativity and quantum theory.

Early applications demonstrated that phenomena regarded as quintessentially quantum—such as the double-slit interference pattern—can be recovered without invoking wave-particle duality or superposition. In TSRT, particles follow deterministic geodesics that are subtly redirected by local curvature trembling, yielding the same fringe structures long attributed to quantum interference. A similar geometric reinterpretation has been applied to entanglement: correlations that violate Bell-type inequalities arise from proper-time-synchronized geodesic ensembles encoded in the background geometry, offering a locally causal, Lorentz-invariant explanation that reproduces quantum predictions at short range while yielding testable departures over long distances or in curved spacetime.

TSRT has also provided a deterministic derivation of Planck’s radiation law and the thermodynamics of light. By analysing the statistical structure of trembling null geodesics, the theory recovers the blackbody spectrum, the energy–frequency relation, and curvature-suppressed entropy limits, including a geometric form of the Bekenstein–Hawking area law. This accomplishment shows that the quantization of light and the thermodynamics of radiation can emerge without postulating photons as wave–particle hybrids or introducing quantized fields.

Perhaps the most striking achievement to date is the theory’s high-precision modeling of atomic structure. TSRT reproduces the full hydrogen and muonic-hydrogen spectra—including excited states, fine-splitting, and curvature-induced redshift corrections—with no adjustable parameters beyond a single calibration line. The predictions achieve sub-millielectronvolt accuracy relative to experiment, demonstrating that atomic energy levels, photon emission, and redshifted spectral transitions can be derived purely from the geometry of trembling spacetime.

Building on this, TSRT has reinterpreted fundamental particles themselves as stable geometric eigenmodes of the trembling metric. The known particle families arise solely from the four symmetry classes permitted by causal coherence—U(1), SU(2), SU(3), and curvature—providing a finite and complete classification that matches the Standard Model while excluding further stable generations, supersymmetric partners, or exotic forces unless they can be realized as causally coherent trembling configurations. Mass, spin, charge quantization, color confinement, and spin–statistics behaviour all emerge from the topological and variational properties of the geometric modes.

The cosmological sector of TSRT builds the universe itself from causal trembling dynamics. Proper time, dimensionality, cosmic expansion, entropy growth, baryon asymmetry, and the small observed cosmological constant all emerge from curvature limits imposed by causality. The theory reproduces the standard thermal history without inflation or quantum vacuum fluctuations and predicts distinctive signatures—such as Bessel-type modulations in the Hubble parameter—testable with upcoming astronomical surveys.

TSRT has been extended into nuclear physics, producing a deterministic description of nuclear structure, decay, fission, and fusion. By treating each nucleus as a localized trembling-curvature eigenmode, the theory reproduces nuclear half-lives across more than twenty orders of magnitude using a single global calibration fixed once on a reference isotope. It explains anomalies such as the long lifetime of carbon-14, deep sub-barrier fusion hindrance, and odd–even staggering in fission yields without empirical adjustments or quantum tunneling postulates. Magic numbers, Q-values, and reaction energetics arise directly from curvature–stiffness relations, and TSRT achieves accuracy that surpasses leading microscopic and empirical models by several orders of magnitude.

Together, these developments establish TSRT as one of the few modern theoretical frameworks capable of unifying wave phenomena, particle spectra, gravitational behaviour, cosmic evolution, and nuclear stability under a single covariant geometric principle. The work remains fully falsifiable, offering clear experimental and observational predictions across atomic precision spectroscopy, long-range entanglement tests, astrophysical redshift measurements, gravitational-wave propagation, and nuclear decay systematics.

Fundamental Physical Principles from Trembling Geo

The most recent extension of TSRT advances the theory from a collection of successful sectorial applications to a fully consolidated foundation for physics itself. In this work, the classical pillars of mechanics and field theory—inertia, gravitational response, equivalence, least action, and gauge coupling—are no longer treated as independent postulates or empirical axioms. Instead, they are shown to arise from a single geometric mechanism: the causal response of localized trembling modes to the long-wavelength structure of spacetime.

Within this framework, inertial mass emerges as a geometric susceptibility, quantifying the overlap between a localized trembling configuration and the ambient cosmological envelope of spacetime. Gravitational mass is shown to arise from the same scalar functional, evaluated under a curvature perturbation of that background, rendering the equivalence principle a geometric identity rather than an assumption. Importantly, this treatment applies equally to extended bodies and composite systems, explaining why all parts of a bound object fall together in free fall and why internal structure does not affect universality except through tidal corrections.

The principle of stationary action is likewise reinterpreted. In TSRT, it is not imposed as a variational axiom but appears as the macroscopic projection of curvature–stationary trembling trajectories constrained by monotone proper time. In the weak-field, slow-motion limit, this recovers the classical Lagrangian formulation of mechanics, while remaining fully covariant and deterministic at the microscopic level.

By unifying inertia, gravitation, and least action within a single geometric susceptibility formalism, this foundational extension completes the conceptual arc of TSRT: from interference and spectra to particles, nuclei, and cosmology, and finally to the underlying principles that structure all physical dynamics. With this synthesis, TSRT stands not merely as an alternative model for specific phenomena, but as a coherent geometric framework capable of organizing the fundamental laws of physics themselves.