Relational Locality, Entanglement, and Projected Geometry

Jean-Paul Niko

We establish a structural correspondence between the quantum-mechanical description of the universe as a single, globally entangled system and the three-space ontology of Relational Three-Space Geometry (RTSG). Potentiality Space P is identified with the universal wavefunction Psi_total; the SemanticProjector Pi is identified with the decoherence operation; Actuality Space A is the resulting local fact; and the ContextualObstruction O is identified with the residual entanglement inaccessible to any given observer. This correspondence gives physical grounding to the RTSG ontology and reframes decoherence as a projection operation rather than an approximation scheme. The universe is one object (P), locality is a projection (Pi), and classical Actuality is a structural feature of what projection produces.

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more

G. Najarbashi, Seifi, B., Sevda Mirzaei

In this paper the geometry of two and three-qubit states under local unitary groups is discussed. We first review the one qubit geometry and its relation with Riemannian sphere under the action of group $SU(2)$. We show that the quaternionic stereographic projection intertwines between local unitary group $SU(2)\otimes SU(2)$ and quaternionic Möbius transformation. The invariant term appearing in this operation is related to concurrence measure. Yet, there exists the same intertwining stereographic projection for much more global group $Sp(2)$, generalizing the familiar Bloch sphere in 2-level systems. Subsequently, we introduce octonionic stereographic projection and octonionic conformal map (or octonionic Möbius maps) for three-qubit states and find evidence that they may have invariant terms under local unitary operations which shows that both maps are entanglement sensitive.

Sudipto Singha Roy, Silvia N. Santalla, Javier Rodríguez-Laguna +1 more

Borros Arneth

We develop a pre-geometric reconstruction framework in which quantum mechanics, entanglement structure, gauge symmetry, locality, Lorentzian spacetime geometry, gravitation, and physical constants emerge from recursively stabilized coherent Hilbert-relational organization. The framework begins from a primitive coherent substrate consisting of compositional accessibility relations and complex transport amplitudes. No background spacetime manifold, metric geometry, or particle ontology is assumed fundamentally. The central proposal is that coherent Hilbert structure is more fundamental than spacetime geometry. Observable spacetime emerges through projection stabilization: a physical stability-selection mechanism dynamically selecting recursively stable coherent sectors from deeper relational structure. Quantum mechanics emerges from norm-preserving coherent transport. Entanglement emerges from nonfactorizable relational closure. Gauge symmetry emerges as redundancy of coherent transport representation. Classicality emerges through decoherence and stability selection. Lorentzian geometry emerges statistically from projected accessibility organization. Gravitation emerges thermodynamically as equilibrium relaxation of projected geometry. The framework is presented not as a completed unified theory, but as a reconstruction program aimed at explaining why physical reality organizes itself through Hilbert structure, gauge redundancy, locality, spacetime geometry, and thermodynamic gravitational dynamics.

Masanori Ohya, Igor Vasil'evich Volovich