Emergence of Gravity from QCD Mass Generation: A Unified Framework Based on Fermion–Boson Duality, Auxiliary Metrics, and ETC Phase Symmetry

Changes in Version 3 Version 3 extends Version 2 by adding a new symmetry-theoretic interpretation of the proposed QCD-based emergence of gravity. The central addition is a new subsection, “Symmetry-Theoretic Interpretation of Gravity: gamma–omega Asymmetry and Non-Euclidean Spacetime.” This subsection reformulates the framework in terms of fermion–boson conversion, symmetry breaking, and spacetime curvature. The revised version proposes that gravity may be interpreted as the interaction that mediates conversion between F-type and B-type components in the fermion–boson duality framework. In this interpretation, the strong and electromagnetic interactions govern particle dynamics without changing the particle type, the weak interaction changes flavor, and gravity is reinterpreted as the interaction associated with statistical F/B conversion. A conceptual parallel with supergravity is also discussed. While the present FBD conversion is distinct from supersymmetry, both share the structural idea that a boson–fermion-type conversion symmetry is closely related to gravity. Version 3 introduces an “FBD isospin” structure based on SU(2) for the F/B sector. The F-type and B-type components are organized as doublets, and the Pauli matrices are used as generators of the corresponding internal symmetry. This leads to a proposed unified symmetry structure consisting of SU(2) for the F/B sector and U(1) for the ETC phase sector, which is presented as structurally analogous to the electroweak SU(2) and U(1) framework. A major new conceptual point is the interpretation of the gamma–omega asymmetry as the physical origin of mass. The revised manuscript explains that the construction from two gamma components to an omega component is straightforward, whereas the inverse process from omega back to two gamma components is incomplete because information in the time and longitudinal directions is lost through the light-cone projection. The residue of this irreversibility is identified with the mass term already present in the FBD-QCD Lagrangian. Version 3 also adds the FBD-Curvature Equivalence Theorem, which states that flat spacetime, vanishing mass, perfect gamma–omega symmetry, full preservation of the Poincare group, and a spacetime-constant effective metric are mutually equivalent. Conversely, nonzero mass corresponds to gamma–omega asymmetry and to non-Euclidean spacetime. This theorem provides a mathematical bridge between the FBD mass-generation mechanism and the emergence of spacetime curvature. The revised manuscript further introduces a concrete effective metric constructed from the FBD transition weights. It shows how the time and longitudinal components of the metric become energy-dependent, and how a position-dependent mass distribution naturally leads to a position-dependent effective metric, which is interpreted as the mathematical substance of curvature. Version 3 additionally discusses a three-stage symmetry-breaking hierarchy of spacetime: a massless Minkowski stage, an anisotropic but non-curved intermediate stage, and a localized-mass stage in which genuine curvature appears. This clarifies how mass localization, rather than mass alone, is responsible for the full emergence of non-Euclidean spacetime. Finally, the gamma–omega asymmetry is related to the Inonu-Wigner contraction of Lie algebras. In this interpretation, the omega algebra is understood as a light-cone contraction of the Lorentz algebra, in which one boost generator disappears. This provides an additional algebraic interpretation of how symmetry reduction, mass generation, and curvature are connected. Overall, Version 3 strengthens the theoretical foundation of Version 2 by adding a symmetry-based explanation of why FBD mass generation should lead to gravity. The main content of Version 2—the QCD-centered FBD Lagrangian, the separation into gauge and gravitational-source sectors, the auxiliary-metric structure, and the connection to hadron masses—is retained, while Version 3 adds a deeper interpretation in terms of FBD SU(2) symmetry, ETC U(1) phase symmetry, gamma–omega asymmetry, Lie algebra contraction, and the emergence of non-Euclidean spacetime.