A Detector-Based Inference Framework for Quantum Theory and Spacetime Geometry

TL;DR

This paper introduces a detector-based framework linking quantum theory and spacetime geometry through an inferential approach, reconstructing spacetime metrics and Einstein's equations from detector measurements.

Contribution

It presents a novel unified inference framework where quantum states and spacetime geometry emerge from detector interactions, connecting quantum information geometry with general relativity.

Findings

Distinguishability induces an information geometry described by the quantum geometric tensor.

A Lorentzian spacetime metric is reconstructed from detector data, with geometry influenced by amplitude and phase deformations.

The Einstein equation emerges as a stationary point of a combined detector-deformation and geometric functional.

Abstract

We develop a detector-based framework in which quantum theory and spacetime geometry arise within a common inferential structure. Detector states and a detector kernel assign amplitudes to measurement events, allowing quantum theory to be interpreted as weighting hypothetical configurations consistent with observed detector clicks. Using a Gaussian detector model with phase structure, we show that distinguishability induces an information geometry on detector-state space, described by the quantum geometric tensor. A Lorentzian spacetime metric is reconstructed from coupled position and time detector sectors, with both amplitude and phase deformations contributing to geometry. Scalar curvature acquires an operational interpretation as a local deficit of distinguishable outcomes. We construct an effective consistency functional combining detector-deformation cost with a geometric term selected by locality and diffeomorphism invariance. Its stationary configurations yield the Einstein equation, with a stress-energy tensor arising from detector deformations. Vacuum configurations need not be flat, while local deformations provide an operational notion of matter and recover standard field-theoretic behavior in the scalar sector.