Calculating the fine structure constant 𝛼 and the tau mass — Part 7

In the last part, a first guess of the electron mass was deduced from the strand tangle model of the electron. It was correct within a…

In the preceding part 6 of this series, a first guesstimate of the electron mass was deduced from the strand tangle model of the electron. It differed from measurements by a factor of a hundred. Obviously, the estimate must be refined. However, the search for a better estimate of the electron mass has not been successful yet. Nevertheless, something much better happened: the tangle model yields an estimate for the tau mass that is correct within a factor of 2. The tau is the heaviest particle in the sequence of the three charged leptons: electron, muon, and tau.

In the strand tangle model, the tangle topology limits the options for elementary particles. Leptons are made of three strands and thus have six tethers that connect them to the boundary of space. When the simplest possible tangles are classified, the strand tangle model only allows three generations of leptons: three charged leptons and three neutral leptons. The tau is charged and is the heaviest of all of them.

In the strand tangle model, mass is related to tangle chirality and tangle complexity. The tau mass is due to the propeller motion of the chiral tau tangle advancing through the vacuum strands. A lepton moves through a vacuum in a way that is similar to a maple seed falling through the air:

Leptons in the same way — but, in addition, they are tethered. Their propeller motion requires a continuous Dirac trick to occur:

The image shows how the six tethers of a lepton have to move to make the core of the tangle, shown here as a cube, rotate. A tethered particle is automatically a spin 1/2 fermion. Having spin 1/2, the tethered core rotates twice before the tangle returns to its original state. This is Dirac’s trick. The full animation, beautifully produced by Jason Hise, is found here:

What is the probability for this motion to occur? The six tethers have to move together in an orderly way. In each intermediate configuration, the six tethers must have the correct distribution in space and avoid the 6!-1 possible alternatives. Now, let us approximate the circle by a triangle, and thus, two circles (two rotations) by two triangles. Each of the resulting six configurations has to be followed in sequence. The probability of Dirac’s trick thus is at most
 (1/6!)⁶ ≈ 7 x 10 -¹⁸
This is the upper limit for lepton masses, in units of the maximum elementary particle mass, taken from the above image sequence or video. The limit is for leptons because it assumes 6 tethers. More precisely, the limit applies to all fermions with 6 tethers, thus to all leptons.

A muon and an electron also have 6 tethers; they are less massive than the tau, because their cores are simpler. When they move, the vacuum rotates them less. Their mass is thus not only limited by the Dirac trick but is also limited by the small chirality of their cores. Therefore, they are less massive than the tau. This is observed.

In the strand tangle mode, neutrinos also have six tethers. The chirality of neutrinos is much lower than that of the charged leptons. (They are only geometrically chiral, not topologically chiral.) The strand tangle model thus also implies that the neutrino masses are even smaller than the electron mass. All this is observed.

Here is the icing on the cake. The measured mass of the tau is 
 3 x 10 -¹⁹
This is 4% of the upper limit for lepton mass. The tau mass is thus near the upper limit.

Above all, the lepton mass bound solves the hierarchy problem, or at least a large part of it. The mass bound explains why elementary particle masses (leptons in this case) are so much smaller than the Planck mass. Many conjectures have been proposed as explanations. (For an overview, see this link to Google Scholar ). None of the numerous papers on the hierarchy problem agrees with the observations of particle physics. Many, for example, predict additional particles, additional dimensions, or different types of vacua. In contrast, the strand tangle model solves the hierarchy problem without any new physics.

In simple words, despite solving the hierarchy problem, the strand tangle model retains its prediction that the standard model with massive neutrinos is the full description of particle physics: no new energy scales, no new elementary particles, no new Lagrangian, no new interactions, and no new gauge groups are predicted to exist in nature. The strand tangle model solves the hierarchy problem while agreeing with all observations and all data.

Can one extend the estimate to other particle masses? Yes. I will write more about this soon.

In short, when a lepton advances, it rotates like a maple seed in air. The rotation has a small probability because, on average, each rotation requires a Dirac trick. To get a mass limit, the probability of Dirac’s trick must be estimated. An upper limit arises. The upper mass limit is extremely small. This explains why elementary particle masses are so much smaller than the Planck mass. Before the strand model, this so-called hierarchy problem had no solution that was compatible with the standard model with massive neutrinos and with observations. In contrast, the strand tangle model provides such a solution.

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Reference: The previous blog entry on the topic of particle mass calculations was here: https://medium.com/@motionmountain/calculating-the-fine-structure-constant-and-the-electron-mass-part-6-83debcdcbba4 It told about pinwheels instead of maple seeds.

Update: Many hypotheses and narratives about the hierarchy problem are invalidated by strands. A common one is here: https://massgap.wordpress.com/2017/03/26/reasons-to-panic-about-the-hierarchy-problem/

Update 2: The hierarchy problem is listed as one on the major problems of physics here: https://x.com/ToEmagazine_/status/1623351809770242050 . The blog entry shows that the hierarchy problem is just a side result of the problem of determining particle masses.

Update 3: Yes, I am writing a publication manuscript about this estimate. No, it is not yet on my ResearchGate page.

Update 4: The numbers have been corrected.