The elementary quantum E_min beyond electromagnetic radiation: verification in matter and atomic structure

A previous work [1] established that n_acts = E/E_min, where E_min = 6.62607015×10⁻³⁴ J is the elementary quantum of energy transfer, produces a slope-1 line on a log-log plot across the full electromagnetic spectrum (30 orders of magnitude, 1 Hz to 2.5 PeV). The present work extends this verification to matter and atomic structure using data from CODATA, PDG, AME2020, NIST and LBNL XDB, across seven domains: rest energies of electron, proton and neutron; subatomic scales; hydrogen energy levels; atomic transitions; fine structure; helium and lithium; electron shells of sodium (Z=11), iron (Z=26) and uranium (Z=92, radioactive). Beyond the geometric coherence across approximately 50 orders of magnitude, this work establishes a criterion of empirical selectivity: for each domain, n_acts = E/E_min coincides with a physical quantity measured independently and published in the literature, from the speed of light to the Rydberg constant, from Ångström's H-alpha line (1853) to the fine-structure splitting of hydrogen. No other value of the divisor reproduces these coincidences. No additional parameters are introduced.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-30
DOI
https://doi.org/10.5281/zenodo.21064871
Primary Topic
Quantum and Classical Electrodynamics
Type
preprint
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preprint

The elementary quantum E_min beyond electromagnetic radiation: verification in matter and atomic structure

Bruno Pantoli
Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
preprint

The elementary quantum E_min beyond electromagnetic radiation: verification in matter and atomic structure

Bruno Pantoli
preprint en

Abstract

A previous work [1] established that n_acts = E/E_min, where E_min = 6.62607015×10⁻³⁴ J is the elementary quantum of energy transfer, produces a slope-1 line on a log-log plot across the full electromagnetic spectrum (30 orders of magnitude, 1 Hz to 2.5 PeV). The present work extends this verification to matter and atomic structure using data from CODATA, PDG, AME2020, NIST and LBNL XDB, across seven domains: rest energies of electron, proton and neutron; subatomic scales; hydrogen energy levels; atomic transitions; fine structure; helium and lithium; electron shells of sodium (Z=11), iron (Z=26) and uranium (Z=92, radioactive). Beyond the geometric coherence across approximately 50 orders of magnitude, this work establishes a criterion of empirical selectivity: for each domain, n_acts = E/E_min coincides with a physical quantity measured independently and published in the literature, from the speed of light to the Rydberg constant, from Ångström's H-alpha line (1853) to the fine-structure splitting of hydrogen. No other value of the divisor reproduces these coincidences. No additional parameters are introduced.

Zenodo (CERN European Organization for Nuclear Research)
Giuliani (Italy) (IT)
Affordable and clean energy
Quantum and Classical Electrodynamics
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