# Validating internal electron and proton energy configurations via a theoretical derivation of the mass ratio mp/me

## DOI:

https://doi.org/10.18203/issn.2454-2156.IntJSciRep20171472## Keywords:

Proton-electron mass ratio, Proton mass energy expression, Electron mass energy expression, Gravitational constant, G. Planck scale, Hierarchy problem## Abstract

**Background:** There are no particle models giving theoretical rest mass energy values for the electron or proton, and their internal energy configurations are unknown. Consequently there is no theoretical basis for the proton/electron rest mass ratio m_{p/}m_{e}. Previous articles established both electrons and protons consist of quantum loops of the same 6.8MeV base quantum energy, albeit in different relativistic states.

**Methods:** Prior work is extended by considering internal particle energy cross coupling factors to derive detailed theoretical expressions for the internal energy distributions of electrons and protons. These expressions consist of the base quantum energy modified by terms containing only relativistic factors of the fine structure constant, α ~ 1/137. For m_{p}/m_{e} the base quantum energy cancels and the derived mass ratio is given by the particle’s internal quantum loop relativistic states. The derived mass ratio is compared to the empirical value. Newton’s gravitational constant, G, is calculated from the electron internal energy configuration.

**Results:** Derived particle energy configurations give proton mass and proton/electron mass ratio values fully consistent with empirical data. The common base quantum loop energy is obtained to 6ppm. Combining particle mass energy expressions gives m_{p}/m_{e} to ten digits and consistent with the 2014 CODATA value via an expression containing only the fine structure constant. A theoretical value for Newton’s gravitational constant is obtained to an uncertainty of 6ppb. The Hierarchy problem is resolved, and the Planck scale of matter is adjusted.

**Conclusions:** The particle energy configurations are validated by providing particle mass energy values and a proton/electron mass ratio consistent with empirical data. Newton’s G is shown not a natural constant, and misunderstanding its nature gave rise to the Hierarchy problem and an erroneous value for the Planck scale of matter, both now resolved.

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## References

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