Measurement-Induced Temporal Geometry

TL;DR

Measurement-Induced Temporal Geometry (MTG) offers a unified framework where time, causality, and spacetime emerge from quantum measurement processes acting on a fiber-valued internal time field, connecting quantum theory and gravity.

Contribution

It introduces a novel theoretical framework where spacetime and gravity emerge from quantum measurement and fiber bundle structures, integrating Standard Model fields and cosmological phenomena.

Findings

Derives dynamical equations for internal time and entanglement connection.

Shows how gravitational dynamics emerge from measurement-induced entropy.

Predicts observable effects like CMB anisotropies and black hole echoes.

Abstract

We propose a unified theoretical framework, Measurement-Induced Temporal Geometry (MTG), in which time, causality, and spacetime geometry emerge from quantum measurement acting on a fiber-valued internal time field. Each spacetime point supports a local degree of freedom $\tau$, modeled as a smooth section of a fiber bundle $\pi: E \to M$, with projection events $\mu[\tau]$ generating classical temporal flow. Quantum coherence and entanglement are encoded in the curvature $F = \nabla^2$ of a connection on the time-fiber, while the effective spacetime metric $g_{\mu\nu}^{\mathrm{eff}}$ arises as an integral over measurement histories. We derive the dynamical equations governing $\tau$, its supersymmetric completions, and the entanglement connection $A_\mu$, showing how quantization proceeds via both canonical and path-integral methods. Standard Model fields couple covariantly to the fiber geometry, and gravitational dynamics emerge from variational principles over projection-induced entropy. Cosmological inflation, dark energy, and large-scale structure are reinterpreted as consequences of modular coherence, topological obstruction, and fluctuations in the projection density $\rho(x)$. Within the AdS/CFT correspondence, MTG reinterprets modular Hamiltonians as boundary projections of bulk time flow and identifies entanglement wedges with surfaces minimizing measurement-induced projection current. A UV-complete embedding arises through string theory, where $\tau$ descends from compactified moduli and projection corresponds to brane interaction and spontaneous supersymmetry breaking. The framework yields a set of falsifiable predictions, including CMB anisotropies, black hole ringdown echoes, and modular deviations in lab-scale quantum systems, offering a consistent and testable account of spacetime as an emergent property of quantum measurement.