Why Points Cannot Exist: V=N/D as the First Proof of the Non-Existence of Point Particles (v2)

The concept of the point particle is the source of the most persistent pathology in theoretical physics: ultraviolet divergence. String theory replaces points with strings. Loop quantum gravity replaces points with loops. Noncommutative geometry dissolves points mathematically. Yet none of these frameworks answers the fundamental question: why cannot points exist? We provide the first physical proof of point non-existence via the compression law V = N / D (V: existence coherence, N: field density J/m3, D: dispersive extent m3). A point particle requires D = 0. Under V = N / D, D to 0 implies V to infinity, exceeding V_max — the maximum sustainable coherence of any physical system. Resolution is immediate N-release: E = mc2. Points are therefore thermodynamically and field-theoretically forbidden. All particles are finite-D field condensations — nodes in the Ki-Net Field where N/D achieves stable ratio below V_max. Falsifiable predictions: finite electron radius, Planck length as universal D_min, IceCube neutrino market correlations. v2: dimensional analysis added, V_max formally defined, falsification conditions specified, objection to V_max addressed. Related: Genki Particle Dance DOI 10.5281/zenodo.20955834; Ki-Net Field Evidence DOI 10.5281/zenodo.20952863.

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Publication Details

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Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-27
DOI
https://doi.org/10.5281/zenodo.20956938
Primary Topic
Noncommutative and Quantum Gravity Theories
Type
preprint
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preprint

Why Points Cannot Exist: V=N/D as the First Proof of the Non-Existence of Point Particles (v2)

Yoshimitsu Katayama
Zenodo (CERN European Organization for Nuclear Research)
Noncommutative and Quantum Gravity Theories
preprint

Why Points Cannot Exist: V=N/D as the First Proof of the Non-Existence of Point Particles (v2)

Yoshimitsu Katayama
preprint en

Abstract

The concept of the point particle is the source of the most persistent pathology in theoretical physics: ultraviolet divergence. String theory replaces points with strings. Loop quantum gravity replaces points with loops. Noncommutative geometry dissolves points mathematically. Yet none of these frameworks answers the fundamental question: why cannot points exist? We provide the first physical proof of point non-existence via the compression law V = N / D (V: existence coherence, N: field density J/m3, D: dispersive extent m3). A point particle requires D = 0. Under V = N / D, D to 0 implies V to infinity, exceeding V_max — the maximum sustainable coherence of any physical system. Resolution is immediate N-release: E = mc2. Points are therefore thermodynamically and field-theoretically forbidden. All particles are finite-D field condensations — nodes in the Ki-Net Field where N/D achieves stable ratio below V_max. Falsifiable predictions: finite electron radius, Planck length as universal D_min, IceCube neutrino market correlations. v2: dimensional analysis added, V_max formally defined, falsification conditions specified, objection to V_max addressed. Related: Genki Particle Dance DOI 10.5281/zenodo.20955834; Ki-Net Field Evidence DOI 10.5281/zenodo.20952863.

Zenodo (CERN European Organization for Nuclear Research)
Technology Holding (United States) (US)
Responsible consumption and production
Noncommutative and Quantum Gravity Theories
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