What question did this study set out to answer?

This work aims to establish a geometrical framework for gravitational field equations using rotational propagation density and closure flow.

May 20, 2026Open Access

Toward QMU Gravitational Field Equations: Rotational Propagation Density, Closure Flow, and Phase Compression Geometry

Key Points

This work aims to establish a geometrical framework for gravitational field equations using rotational propagation density and closure flow.
Developed field framework based on Ledger One without coordinate geometry.
Introduced concepts of rotational propagation density and closure flow to describe gravitational behavior.
Analyzed closure flow conservation in spherical propagation geometry.
Demonstrated that acceleration can be expressed in terms of propagation density: g(r)=GM/r^2.
Established a conceptual foundation predicting closure boundaries and gravitational modes.
Uncovered a relationship between clock-rate variation and local changes in propagation advancement.

Abstract

Previous papers in the QMU Planck--Aether closure series established that the Planck system emerges from the bridge between electron closure and Aether closure, and that gravitational horizons correspond to rotational propagation boundaries satisfying: ₐc²=C\ The present paper develops the first geometrical field framework arising from the Quantum Measurement Units (QMU) ledger. Rather than beginning from metric curvature or coordinate geometry, the analysis begins from rotational propagation structure governed by Ledger One: ᵤ=Fq²C²=c²\ Within this interpretation, gravity emerges from gradients in rotational propagation density. The propagation-density field is introduced as: \g s\ and is related to QMU torsional structure by: \g curlC\ Using Ledger One, this becomes: \g c²AᵤC\ Closure flow is then introduced as the redistribution of propagation-density loading through Aether geometry. For spherical propagation geometry, closure-flow conservation gives: c (r) =4 r²g (r) =CM\ and therefore: \g (r) =CM4 r²\ This provides a QMU geometrical basis for the inverse-square structure of gravitational behavior. In SI projection, the resulting acceleration is: (r) =GMr²\ which may be rewritten in QMU closure-flow form as: (r) = (C Fq²) (Mmₐ) (C²r²) \ The paper further develops chronovibrational compression as the physical basis of clock-rate variation, redshift, and horizon freezing behavior. In this interpretation, clock-rate variation is a local change in propagation advancement within the present moment, not movement among separate time frames. A first-order propagation-density wave structure is proposed: \ₜ²g-v_²²g=C\ supporting scalar, longitudinal, torsional, transverse, and closure-harmonic gravitational modes. The framework predicts natural ultraviolet closure boundaries, scalar and longitudinal gravitational modes, rotational closure harmonics, RMFD magnetometer correlations, and propagation-density wave behavior. This paper establishes the conceptual foundation for future fully developed QMU gravitational field equations based on rotational propagation density, closure flow, and phase-compression geometry.

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