## The Case For Fractional Masses

According to the result from the Koide formula, we should be looking to use the masses of the electron, muon and tau as the 3 fundamental mass quanta in our unified model.

The trouble with this approach is how to explain the masses of the muon and the pion, which are very close to the 3:4 ratio. If we try to say that a pion is a muon plus a whole bunch of electrons, how do we end up with the pion being 33% heavier and not somewhere in between? In effect, we're no better off than we were trying make a proton from 1840 electrons.

For the necessary inspiration, we will turn to Murray Gell-Mann. Recall that when he proposed the quark model, he took the approach that charges can be +1/3 or -1/3, or multiples thereof. With a bit of hand-waving (quark confinement) to explain why we only see charges +1 or -1 in practice, he arrived at a model that does a good job of explaining particle charges and interactions via the strong force.

In our unified model universe, we don't have the option of introducing a strong force with a concept of colour, because then it wouldn't be a unified model at all. So the quark model has to go.

Instead we will apply Murrary Gell-Mann's logic to the particle masses. With a minor modification, we will simply divide all of our mass quanta by a factor of 3.

Accordingly, the 3 mass quanta will be:

Particle FractionMass Quantum
Electron / 30.170 MeV/c2
Muon / 335.2 MeV/c2
Tau / 3592 MeV/c2

At first glance, this might seem like a bit of a daft thing to do because although we now have a framework that can explain the muon and pion, we've lost the simple correspondence we had with the electron.

Nevertheless, we note that the 35.2 MeV/c2 mass quantum tallies with the suggestions from MalColm MacGregor and Paulo Palazzi.

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