Koide-formula.

Title: The cosmology as origin of the Koide's mass formula.

Subtitle: Cosmic Kinomichi.

Author: © Thierry PERIAT.

French Matriculation: ISBN 978-2-36923-008-3, EAN 9782369230083.

Language: GB/USA.

Version: 1.

Pages: 11.

Published: 11 July 2022.

Document: Periat isbn 978 2 36923 008 3 koidePeriat isbn 978 2 36923 008 3 koide (263.7 Ko).

The context.

The Wikipedia article on that item starts with that sentence (citation, 14 December 2019): “The Koide formula is an unexplained empirical equation discovered by Yoshio Koide in 1981. In its original form, it relates the masses of the three charged leptons; later authors have extended the relation to neutrinos, quarks, and other families of particles”.

For many physicists, this formula is only understood as “numerology” without serious foundation. Therefore, some of them have proposed (citation again): “… mechanisms to explain origins of the charged lepton spectrum as well as the Koide formula, e.g., by constructing an effective field theory in which a new gauge symmetry causes the pole masses to exactly satisfy the relation”.

My contribution.

The driving idea of the demonstration relies on two hypotheses:

1. The speed of light should be preserved in vacuum, whatever the variation of the geometry is.

Due to the Morley and Michelson experiments, we already know that this firt prerequisite is true for a perfect Maxwell’s vacuum.

My exploration envisages what would happen in a FRW metric if that speed would be preserved, even when the vacuum is deformed; in extenso: when the spatial geometry and the definition of the cross-product are modified. I follow the comparaison with the water flowing in the water.

To control the first part of my demonstration, please read the document on the page: “Maxwell’s vacuum”.

The condition allowing the preservation exhibits a sub-condition that can be realized whatever the geometry is (decoupling case).

2. I pretend that the modifications of the definition of the cross product must also preserve a Lie algebra structure.

Therefore, I look for the condition allowing to equip W3(A) = {C ⊗ E(3, R), A} with a Lie algebra structure.

Then, I look for the situations allowing the simultaneous validity of both conditions.

An indirect and unexpected result of this confrontation is the discovery of trios of matrices (together, they form an admissible deforming cube). Each of them can be associated with a vector in W3(A), the Koide's ratio of which may eventually be 2/3 as demanded by the Koide's mass formula. 

© Thierry PERIAT, 11 July 2022.

Otherwise, go back to the page : « Cosmology ».

Date de dernière mise à jour : 10/08/2022