An Operational Planck–Compton Route to Quantum Gravity: From Macroscopic Rest Wavelengths to an Uncertainty–Certainty Principle
Abstract
We develop an operationally anchored route from the invariant rest-mass Compton wavelength to a modified quantum kinematics at the Planck boundary. The empirical core is a two-channel determination. First, a macroscopic source is assigned an aggregated reduced rest-Compton wavelength without using its kilogram mass or a tabulated \(\hbar\): the electron Compton scale is obtained from Compton scattering, nucleon scales from measured cyclotron-frequency ratios, and the source scale from constituent counting with composition and binding-energy corrections. Second, the source's geometrized mass \(r_g=GM/c^2\) is inferred from a gravitational experiment without separately inserting \(G\). The identity \(r_g=\ell_{\mathrm P}^2/\bar\lambda_M\) then gives \(\ell_{\mathrm P}=\sqrt{r_g\bar\lambda_M}\). Agreement across sources, compositions, and gravitational protocols is proposed as a direct test of the Planck--Compton organization of gravity. This test alone verifies an operational relation, not the microscopic ontology. We further hypothesize that gravity is the macroscopic record of Planck-mass collision events and that \(\eta=\ell_{\mathrm P}/\bar\lambda_C=\omega_Ct_{\mathrm P}\) is their Planck-time occupation weight. At \(\eta=1\), Haug's maximum-velocity law gives \(v_{\max}=0\); if this is an outcome-support bound, the Planck event has definite zero momentum and occupies one definite relational Planck cell. We therefore propose \([X,P]=i\hbar(I-\Pi_{\mathrm P})\) and \(\Delta…
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