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Hopf Fibration, Non-Homotopy and Mass

Author:

Goodwin, Garry

Category:

Research Papers

Sub-Category:

Mathematical Physics

Language:

English

Date Published:

February 09, 2025

Downloads:

77

Keywords:

Hopf fibration, topology, rest mass, Higgs field

Abstract:

Unable to determine a particles's specific mass the Standard Model leaves rest mass a free parameter. For a radical alternative that dispenses with the Higgs field and quark confinement we consider a 3-sphere intersecting three dimensional space. The intersection is a Hopf fibration with non Euclidean topology. Resistance to a force is entirely due to non-homotopy. In support of the thesis a number of equations detail a unified mathematical framework for hadron rest mass. The intersection's signature is seen across mass splitting formulae that treat lighter hyperons as functions of the proton, neutron, electron. Derived rest mass values for $Sigma^+$, $Sigma^0$, $Sigma^-$, $Xi^0$, $Xi^-$, $Omega^-$, $Lambda^0$ are within one standard deviation of observation, The $Sigma$, $Xi$ mathematical relationship provides a trivial solution to the neutron-proton mass difference problem. The last formula sheds light on the proton/electron mass ratio. Finessing function inputs and outputs also allows the neutron and proton masses to be dialled-in leaving the electron mass the remaining free parameter from the ten originally considered.

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