QTT vs. Neutrino Observations — A Strong, Testable Match – QTT

Here upgrades the neutrino “scorecard” with a crisper Quantum Traction prediction, fuller equations, and concrete tests. Core result: the parameter-free QTT mass-gap ratio $\rho^2 \equiv \dfrac{\Delta m^2_{31}}{\Delta m^2_{21}} = 4\pi^2\cos^2\!\left(\tfrac{\pi}{8}\right) \approx \mathbf{33.697}$ aligns with current global fits (~33–35). Below we place this in a broader, falsifiable matrix.

Key QTT Equations (what the theory actually says)

Two-clock half-angle (A1):

$\displaystyle I_{\rm clk}=\cos\!\Big(\frac{\pi}{8}\Big) = \frac{\sqrt{2+\sqrt{2}}}{2}\,.$

This universal kinematic constant (no tuning) sets relative phase projections in the lab clock. Geometric mass pattern (A1 + A6 + A7, minimal sector):

$\displaystyle m_1 \approx 0,\qquad m_2=\frac{m_0}{\rho},\qquad m_3=m_0,\quad \rho:=2\pi\cos\!\Big(\frac{\pi}{8}\Big)\approx 5.804906\ldots$

Predicts one very light state and a fixed hierarchy. No continuous couplings are introduced. Smoking-gun mass-gap ratio (exact, parameter-free):

$\displaystyle \boxed{\ \frac{\Delta m^2_{31}}{\Delta m^2_{21}}=\rho^2<br /> =4\pi^2\cos^2\!\Big(\frac{\pi}{8}\Big)\approx 33.697\ }\,.$

Absolute scale anchor (capacity scale; optional check):

$\displaystyle m_0=\frac{(2\pi)^5 v^2}{E_\ast},\qquad E_\ast=\frac{\hbar c}{\tilde{\ell}}=\sqrt{\frac{\hbar c^5}{G}}\,,$

where $v=246.22\ \mathrm{GeV}$ . (This fixes the overall scale without adding free parameters; the gap ratio in (3) is independent of the overall scale.) Observable effective masses (for direct searches):
Beta-endpoint mass:

$\displaystyle m_\beta=\sqrt{\sum_i |U_{ei}|^2 m_i^2}\,;$

Neutrinoless double-beta effective mass (if applicable):

$\displaystyle m_{\beta\beta}=\left|\sum_i U_{ei}^2 m_i e^{i\alpha_i}\right|\,.$

In the minimal QTT pattern with normal ordering and $m_1\!\approx\!0$ , both fall naturally in the sub-0.1 eV range.

Why these matter: (2)–(3) are hard falsifiers (no knobs). (4) supplies the absolute scale if you want it (still knob-free). (5) maps theory to KATRIN/Project-8 and 0νββ searches.

QTT vs. Neutrino Observations — Updated Matrix (10 items)

\frac{\Delta m^2_{31}}{\Delta m^2_{21}}=\rho^2=4\pi^2\cos^2(\pi/8)\approx \mathbf{33.697}

#	Open neutrino question	QTT claim / answer (expanded)	Observable signature / test	Status vs. observations
1	Why are neutrino masses so tiny?	Two-clock phase-slip (A1) imprints a universal, ultra-small inertial “drag” on near-luminal, weakly interacting carriers. No heavy see-saw needed. In capacity language (A6/A7), neutrinos are the minimal-disturbance ledger carriers, thus naturally feather-light.	Stable non-zero masses inferred from oscillations.	✅ Qualitatively matches: oscillations require tiny but non-zero masses.
2	What sets the mass-splitting pattern?	Exact, parameter-free geometric ratio: $\frac{\Delta m^2_{31}}{\Delta m^2_{21}}=\rho^2=4\pi^2\cos^2(\pi/8)\approx \mathbf{33.697}$ . The same half-angle (A1) that organizes amplitudes fixes the hierarchy—no fits.	Global fits of $\Delta m^2_{21}$ and $\Delta m^2_{3\ell}$ independent of model priors.	✅ Very good agreement: PDG compiles ~33–35 today; QTT gives 33.697.
3	Absolute mass scale?	With (4), QTT yields sub-eV absolute masses (sum below ~0.1–0.2 eV typical). The ratio in (2) is scale-free, so tests bifurcate: first confirm the ratio; then constrain the overall scale by β-endpoint and cosmology.	β-decay endpoint $m_\beta$ ; cosmological $\sum m_\nu$ .	✅ KATRIN: $m_\beta<0.45$ eV (90% C.L.). Cosmology prefers $\sum m_\nu\lesssim 0.1\text{–}0.2$ eV. Both consistent.
4	Mass ordering (NO vs IO)?	Minimal QTT geometry favors normal ordering (NO) as the least-slip configuration: $m_1\approx 0 < m_2 \ll m_3$ .	Matter-effect asymmetries in long-baseline (LBL) and atmospheric data.	✅ Current global fits modestly prefer NO—compatible.
5	Mixing angles—why these values?	A1 half-angle + address symmetries imply angle sum-rules with few effective parameters (e.g., constraints linking $\theta_{12},\theta_{23},\theta_{13}$ ). Details depend on how the address sectors couple to flavor. (Work in progress: mapping exact sum-rules to fitted values.)	Global fits of $\theta_{12}, \theta_{23}, \theta_{13}$ , octant of $\theta_{23}$ .	◑ Qualitatively compatible; needs the finished sum-rule map for a numeric test.
6	CP violation phase $\delta_{\rm CP}$ ?	Complex phase arises naturally from the clock-projection geometry; QTT expects an order-one $\delta_{\rm CP}$ without tuning. Predicts specific correlations with the angle sum-rules once the full map is fixed.	$\nu/\bar\nu$ appearance asymmetries in LBL (T2K, NOvA; soon DUNE/Hyper-K).	◑ Hints exist; decisive resolution awaits next-gen exposure.
7	Dirac or Majorana?	Minimal QTT predicts very suppressed 0νββ rates (if any): an effective Majorana-like phase emerges geometrically, but amplitudes are tiny with $m_1\approx 0$ and small $m_2,m_3$ .	0νββ half-life limits (GERDA/LEGEND, CUORE, nEXO, KamLAND-Zen).	◑ Current null results consistent; future sensitivities will probe deeper.
8	Sterile (eV-scale) neutrinos needed?	No. The parameter-free pattern (2) fills the observed structure without extra eV-scale states; little room is left once capacity/closure (A6/A7) is enforced.	Short-baseline anomalies vs global 3ν fits.	✅ Global 3ν is broadly consistent; SBL hints remain inconclusive.
9	Decoherence / exotic damping?	Planck-scale dephasing predicted to be far below current bounds; standard coherence over terrestrial and solar baselines.	Search for extra baseline-dependent damping beyond matter effects.	✅ No extra damping seen—consistent.
10	Time-of-flight (ToF) & causality	Neutrinos are strictly subluminal (propagate on the lab t-clock). No superluminal effects permitted by the two-clock map.	Beam ToF, supernova bursts (SN1987A-type) constraints.	✅ No credible superluminal signals—consistent.

How to Falsify QTT Quickly

Gap ratio: If global fits settle away from $4\pi^2\cos^2(\pi/8)\approx 33.697$ , the minimal QTT neutrino sector is falsified.
Lightest mass: If precision data require $m_1 \gg 0$ (not just tiny), the minimal pattern is ruled out.
Large 0νββ rate: A near-term discovery with $m_{\beta\beta}$ well above the sub-10 meV window would strongly disfavor the minimal construction.

Sources for the experimental numbers: PDG neutrino review (global fits, mass splittings, ordering, ToF & decoherence overviews); KATRIN β-decay endpoint limit (latest combined runs); contemporary global-fit papers collated by PDG. These consistently give $\Delta m^2_{21}\sim(7.3\text{–}7.5)\times10^{-5}\ \mathrm{eV^2}$ , $\Delta m^2_{3\ell}\sim(2.48\text{–}2.58)\times10^{-3}\ \mathrm{eV^2}$ , hence a ratio in the $33\text{–}35$ band—aligned with the QTT value 33.697.

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QTT vs. Neutrino Observations — A Strong, Testable Match

Key QTT Equations (what the theory actually says)

QTT vs. Neutrino Observations — Updated Matrix (10 items)

How to Falsify QTT Quickly

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Key QTT Equations (what the theory actually says)

QTT vs. Neutrino Observations — Updated Matrix (10 items)

How to Falsify QTT Quickly

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