Unified theory proposes a mathematical framework for gravity, electromagnetism, and quantum interactions, suggesting novel applications.
This work presents a unified theory of physics based on the α-Triad — a three‑dimensional invariant that unifies three fundamental layers of reality: quantum action, electromagnetic charge, and gravitational mass. The Triad is given by a triple of dimensionless constants (α1,α2,α3)(α1,α2,α3) satisfying the normalisation condition: α12+α22+α32=1α12+α22+α32=1 Each component corresponds to one of the three interactions: α1α1 — quantum action (fine‑structure constant α≈1/137α≈1/137), α2α2 — electromagnetism, α3α3 — gravitation. We show that all known interactions are projections of the α‑tensor onto different scales of reality. Gravitation emerges as the curvature of spacetime through the macroscopic projection of the α‑tensor. Electromagnetism is generated by the rotation of the α‑charge in the planes of the Triad. Quantum action is determined by the discrete structure of the Triad itself, where the minimum action step ℏℏ follows from the normalisation condition. The work contains a complete mathematical derivation, connections with fundamental constants, predictions for experimental verification, and practical implications for quantum gravity, cosmology, the multiverse, and information technologies. A model of the Universe’s rotation is proposed as a consequence of the balance of the α‑Triad. Keywords:α‑Triad, unified field theory, quantum gravity, electromagnetism, three‑dimensional invariant, fine‑structure constant, normalisation, projective geometry, multiverse. Main Statements: The Triad as a fundamental invariant.Reality is described by a triple of dimensionless constants linked by a normalisation condition. This eliminates the need for parameter tuning and gives predictive power. Unification of interactions.Gravitation, electromagnetism, and quantum action are projections of the same α‑tensor onto different scales. The rotation of the α‑charge generates electromagnetism (αEM≈1/137αEM≈1/137), while spacetime curvature gives rise to gravitation. Quantisation of action.Planck’s constant ℏℏ emerges as the minimum step of the discrete structure of the α‑Triad, linking quantum mechanics to the geometry of state space. Predictions and tests.The model predicts exact numerical relationships between fundamental constants, which can be tested in experiments on quantum gravity, spectroscopy, and cosmology. Cosmological implications.The rotation of the Universe and the large‑scale structure are consequences of the balance of the α‑Triad, consistent with observational data (CMB anisotropy, galaxy distribution). Mathematical Framework: The α‑tensor as an element of R3R3 with unit norm. Projection operators onto physical layers: quantum, electromagnetic, gravitational. Coupling equations that derive the fine‑structure constant from the normalisation condition. Simulation of the Triad balance by generating random normalised states. Predictions: The exact value α−1≈137.036α−1≈137.036 is derived from the geometry of the Triad. A discrete mass spectrum of elementary particles as projections of the α‑Triad. Large‑scale structures in the Universe corresponding to the nodes of the Triad. Possibility of controlling the Triad balance to create technologies based on new physical principles. Practical Applications: Post‑quantum cryptography based on α‑invariants. Quantum‑resistant synchronisation systems. New materials with tailored properties (tetragraphene, phi‑quasicrystal). Navigation systems based on topological memory. Relation to Previous Work: This work builds upon the QEI (Quantum Energy Information) formalism previously developed by the authors, and the experimental data of Barontini (2026) confirming the discreteness of time with a quantum Tref=17.5Tref=17.5 ms, corresponding to a frequency fref=400/7fref=400/7 Hz. The α‑Triad generalises this formalism to all fundamental interactions. Conclusion: The α‑Triad represents a conceptual breakthrough, allowing the unification of all known physical interactions within a single mathematical structure. This work opens pathways to novel technologies, prediction of undiscovered particles, and a deeper understanding of the nature of spacetime. The Resonance Group continues to gather evidence and refine the model, aiming at experimental verification and the eventual practical implementation of these principles.
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Mark Markov (2026) studied this question.
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