One Angle to Rule Them All: How QTT Ties Together Leptons and Neutrinos

In plain language, with a few gentle equations in boxes.

Reference: https://doi.org/10.5281/zenodo.17594186

The Idea (no jargon)

In ordinary physics, the masses of the electron, muon, and tau are just three separate numbers we measure and then live with. The pattern of those masses is a mystery: we know what they are, but not why.

The same goes for neutrinos: experiments tell us how “far apart” their squared masses are, but the ratio between the big splitting and the small splitting is treated as a free fit parameter.

Quantum Traction Theory (QTT) does something bolder: it claims that both of these sectors are controlled by a single universal angle, encoded in the number

QTT’s universal projection angle

\( I_{\rm clk} = \cos\!\left(\dfrac{\pi}{8}\right) \approx 0.923879 \)

That’s a tilt between an underlying Absolute Background Clock and the lab time we use in experiments. QTT’s claim is:

• The same tilt angle that appears in time/geometry also quietly shapes the pattern of lepton masses.
• The same angle again controls the ratio of neutrino mass splittings.

Below are the two key sectors where QTT turns “mysterious numbers” into simple functions of this angle.

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1. Charged Leptons (Electron, Muon, Tau)

Layman’s version

Think of each charged lepton (electron, muon, tau) as a “slot” that can hold a certain amount of mass-energy. In standard physics, these capacities are just three unrelated numbers: we measure the masses and that’s the end of the story.

In QTT, each lepton has a capacity index. The idea is:

• Define a universal “capacity unit” based on fundamental constants.
• Measure how many of those units each lepton uses.
• See if a simple pattern appears once you include the angle \( I_{\rm clk} = \cos(\pi/8) \).

QTT finds that if you choose one simple integer pattern for how strongly each lepton feels the projection angle: \((\beta_e,\beta_\mu,\beta_\tau) = (2, 0, 1)\), then you can calibrate the angle once from the electron and the muon and tau both fall into place automatically, with tiny errors (parts in a million or better).

Boxed equation: lepton capacity in QTT

QTT lepton capacity formula

\( \displaystyle \mathcal{C}_\ell \;=\; \frac{m_\ell}{m_{\rm P}\,\alpha^{\alpha_\ell}\,I_{\rm clk}^{\beta_\ell}} \)

Here:

• \(m_\ell\) is the lepton mass (e, μ, or τ).
• \(m_{\rm P}\) is the Planck mass, \(\alpha\) is the fine-structure constant.
• \(\alpha_\ell\) and \(\beta_\ell\) are simple integer exponents.
• \(I_{\rm clk} = \cos(\pi/8)\) is the universal QTT projection factor.

With the pattern \( (\beta_e,\beta_\mu,\beta_\tau) = (2,0,1) \), QTT finds \( \mathcal{C}_e \approx \mathcal{C}_\mu \approx \mathcal{C}_\tau \approx 1 \), once \(I_{\rm clk}\) is fixed from the electron.

What this means in simple terms

Instead of three arbitrary masses, QTT says:

1. The electron picks out the angle \(I_{\rm clk} = \cos(\pi/8)\).
2. Once that angle is fixed, the muon and tau are no longer “free”: their masses are essentially determined by the same structure.

In other words, QTT removes two free knobs from the lepton sector and explains their pattern with a single angle.

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2. Neutrino Mass–Squared Ratio

Layman’s version

Neutrinos come in three “flavours” and three mass states. Experiments don’t measure their individual masses very cleanly, but they do measure the differences between the squared masses: one small splitting and one large splitting.

The key question is: how much bigger is the large splitting than the small one? In standard physics, this ratio is just a number you fit from data.

In QTT, the same angle \(\pi/8\) that controlled the lepton pattern also fixes this ratio: you don’t get to choose it independently. The ratio becomes a pure number built from \(\pi\) and \(I_{\rm clk} = \cos(\pi/8)\).

Boxed equation: QTT neutrino prediction

QTT neutrino mass–squared ratio

\( \displaystyle \rho^2 \;\equiv\; \frac{\Delta m^2_{31}}{\Delta m^2_{21}} \;=\; 4\pi^2 \cos^2\!\left(\frac{\pi}{8}\right) \;\approx\; 33.70 \)

Here:

• \(\Delta m^2_{31}\) is the large mass–squared splitting.
• \(\Delta m^2_{21}\) is the small mass–squared splitting.
• The ratio \(\rho^2\) is no longer a free parameter: it’s fixed once you accept \(I_{\rm clk} = \cos(\pi/8)\).

What current data say

Current global neutrino fits give a ratio around 34.0 (depending on details of the analysis). QTT’s prediction of about 33.7 is within roughly a percent of that value, which is about the same size as today’s uncertainties.

That means:

• QTT doesn’t obviously fail; it passes a basic consistency check.
• The test will sharpen as neutrino experiments improve.

The important part is not that the match is perfect today, but that the same angle that organizes the charged leptons also controls the neutrino sector — without adding a new free constant.

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Why this matters

In the usual approach, each sector gets its own “settings”: three lepton masses here, a mass–squared ratio there, and so on. QTT’s philosophy is different:

• One geometric angle (\(\pi/8\)) and its cosine \(I_{\rm clk}\) are the common thread.
• Charged leptons use it through their capacity exponents.
• Neutrinos use it through a clean mass–squared ratio formula.

If future data continue to line up with these boxed equations, it will mean that what looked like “random constants” are actually shadows of a deeper geometric structure — the same structure that also appears in QTT’s time and rotation tests.