Why particles weigh what they weigh

Physics has never had a good answer to this question. The electron weighs what it weighs. The proton weighs 1,836 times more. The muon, an electron-like particle that lives for about two millionths of a second before decaying, weighs 207 times what the electron does. No one knows why these numbers are what they are. They are measured and written into the theory.

Knots have rules

Rest-State Inversion Theory offers a different picture. If the universe is a physical medium, the Eternal Consonance, held under a specific tension, then particles are not things that sit in the medium. They are knots in it, and knots have rules.

A knot in a rope can only be so tight before the rope gives way, and only so loose before it slips undone. Between those limits, only certain shapes hold. The electron is the simplest: a single loop that must turn through 720 degrees before it returns to its starting state, because a loop turned through only 360 degrees comes back inverted and unwinds. The proton is a braid of three loops, the quarks, sealed together where they mesh at the Shadow Junction.

The notes of the medium

A guitar string under tension can sound only certain notes, fixed by its tension and length. RSI proposes that the particles are the notes of the Eternal Consonance: the knot shapes its tension can sustain. Leptons such as the electron, muon and tau are single loops, the muon and tau being the electron's loop wound tighter. Baryons such as the proton and neutron are three-loop braids. Mesons are a loop bound to its mirror image and live only briefly. The W and Z bosons are momentary compressions that relax at once, and the Higgs boson is the medium itself, struck hard enough to ring.

The proton's weight follows from its braid. Three loops on six axes give 6π⁵ ≈ 1,836.12 electron masses, within 19 parts per million of the measured value.

A forty-year-old mystery

The three electron-like particles carry a further clue. In 1982 the physicist Yoshio Koide found that their masses satisfy a simple formula, equal to exactly 2/3. At the time the tau's mass was poorly known; the formula implied 1776.97 MeV, and a precise measurement in 1992 found 1776.9 MeV. Today's measurements confirm the formula to 9 parts per million. No one has explained why.

The formula has a geometric meaning: it places the three masses exactly 45 degrees from the diagonal of three-dimensional space. RSI reads the three generations as one loop wound about the three axes of space, the same geometry that sets the proton's three loops 120 degrees apart and gives the quarks their thirds of a charge. In RSI, Koide's relation is not a coincidence. It is space itself, written into the masses of the particles.

The next test

The formula can be written with the three generations spaced 120 degrees apart around a circle, and in 2006 Carl Brannen noticed that the circle's phase is 2/9 to within one part in a million. With just two geometric numbers, √2 for the 45 degrees and 2/9 for the phase, the electron's mass alone yields the muon's mass to within 10 parts per million and the tau's to within 0.007 percent.

So RSI's next task is unusually clear. The whole family of electron-like particles comes down to one mass and two geometric numbers. Derive those two numbers from the medium, and every charged lepton mass follows. If the theory succeeds, the case for RSI becomes very difficult to dismiss. That is a precise research program, and that is what a serious theory owes its readers.