From Mass-Frequency Invariance to Velocity Cartography

Mass--frequency invariance is a confirmed feature of physics: every massive particle has a Compton frequency $f_C = Mc^2/h$, and the relation holds under all tested conditions. Treating that invariance as identity, $M \equiv f_C$, forces two reductions in classical $h$-based Planck units: $h = c^2$ and $G = l_p^3/t_p$. A single conversion factor, $f_{C,kg}/\mathrm{kg}$, does both. Define $Q := l_p^3/t_p$; then $Q/l_p^2 = c$, identifying $c$ as the one-dimensional shadow of a three-dimensional constraint. If $Q$ is the primary object and $c$ its projection, then space's dimensional structure is $L^3/T$. The Minkowski line element, divided by $dt^2$, becomes a velocity cartography: $ds^2/dt^2 = |\mathbf{v}|^2 - c^2$, bounded by the invariant $c$. The Lorentz factor's $1/\gamma^2$ is the unspent fraction of that bound. This paper's secondary claim is that mass as frequency is a convincing enough interpretation to begin using that identity in parallel with conventional physics to determine where interpretations diverge and whether such divergence is measurable in the observational regime.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-27
DOI
https://doi.org/10.5281/zenodo.20958696
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

From Mass-Frequency Invariance to Velocity Cartography

Ronald Shillings
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

From Mass-Frequency Invariance to Velocity Cartography

Ronald Shillings
preprint en

Abstract

Mass--frequency invariance is a confirmed feature of physics: every massive particle has a Compton frequency $f_C = Mc^2/h$, and the relation holds under all tested conditions. Treating that invariance as identity, $M \equiv f_C$, forces two reductions in classical $h$-based Planck units: $h = c^2$ and $G = l_p^3/t_p$. A single conversion factor, $f_{C,kg}/\mathrm{kg}$, does both. Define $Q := l_p^3/t_p$; then $Q/l_p^2 = c$, identifying $c$ as the one-dimensional shadow of a three-dimensional constraint. If $Q$ is the primary object and $c$ its projection, then space's dimensional structure is $L^3/T$. The Minkowski line element, divided by $dt^2$, becomes a velocity cartography: $ds^2/dt^2 = |\mathbf{v}|^2 - c^2$, bounded by the invariant $c$. The Lorentz factor's $1/\gamma^2$ is the unspent fraction of that bound. This paper's secondary claim is that mass as frequency is a convincing enough interpretation to begin using that identity in parallel with conventional physics to determine where interpretations diverge and whether such divergence is measurable in the observational regime.

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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