Wave Function Collapse as a Condition of Geometric Consistency in General Relativity as a Quantum Theory
Abstract
We present an ontological and dynamic derivation of wave function collapse within the context of General Relativity formulated as a Quantum Theory (GRQT), a formulation that maintains ontological realism and conceptual continuity with General Relativity. Starting exclusively from the discrete geometric structure of spacetime and its fundamental elastic properties, we demonstrate that collapse constitutes neither an additional postulate of quantum mechanics nor an external phenomenological effect, but emerges as a necessary consequence of the requirement for geometric consistency in the temporal update of the causal lattice. We show that quantum superpositions of massive systems imply geometric bifurcations of spacetime, associated with incompatible metrics in the transition between successive simultaneity slices. The energy identified in Objective Reduction theories as gravitational self-interaction energy is reinterpreted, in GRQT, as the elastic deformation energy of the lattice, governed by the fundamental geometric impedance $\alpha$. We derive a quantitative criterion for the viability of temporal evolution and a closed-form expression for the characteristic collapse time, without introducing free parameters. Wave function collapse thus arises as the physical process by which spacetime eliminates geometric ambiguities incompatible with the unique definition of the subsequent slice, preserving the topological continuity of the causal manifold. The boundary between quantum and classical regimes becomes quantitative and derived, resolving the measurement problem in strictly geometric terms. The formulation maintains ontological realism, conceptual continuity with General Relativity, and provides explicit experimental predictions in mesoscopic regimes.
Fields of Study & Subjects
Quantum Mechanics and Applications
Noncommutative and Quantum Gravity Theories
Relativity and Gravitational Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 14 January 2026
- Document type
- Preprint