Five Crisp Benchmarks — and How Quantum Traction Theory (QTT) Meets Them

QTT proposes a simple extra coordinate — a reality dial w ∈ S¹ — and a “quarter‑turn” operator that replaces the usual imaginary unit. From this, we (i) state a clean, falsifiable dimensionless prediction; (ii) give a first‑principles map for particle masses; (iii) show how standard physics reappears as a limit; (iv) keep the parameter list honest; and (v) make the math short enough to live in a tiny, public notebook.

What is QTT — in one picture?

Ordinary quantum theory evolves a wave that depends on space and time. QTT adds one compact “dial” coordinate, w, that runs around a circle. Turning that dial by a quarter‑turn is the role normally played by the symbol i. With this single move, phases become literal rotations on the dial.

QTT‑native evolution law (no i anywhere):

Equation

ℏ ∂_T Φ(x,w;T) = Big[ ℏ c J_w ∂_w + K_ℓ(-∇_x²)Big(-(ℏ²)/(2m)∇_x²+V(x,w;T)Big) Big]Φ(x,w;T)

Here $\Phi$ is the bundle‑amplitude on world‑cells, $w\in S^1$ is the reality‑dial, $K_\ell$ encodes the per‑address capacity bound, and $\mathcal{J}_w$ is the dial quarter‑turn (defined below). Ordinary quantum mechanics reappears when we coarse‑grain over $w$. The dial quarter‑turn operator (technical detail)

The quarter‑turn is the circle Hilbert transform acting along the dial:

Equation

(J_w f)(x,w) = p.v. (1)/(2π)int_0²π f(x,ω) cot((w-ω)/(2)) dω

On smooth, mean‑zero dial modes it satisfies $\mathcal{J}_w^2\approx-1$, so it behaves like multiplying by $i$, but remains a real, geometric operator.

The five benchmarks — and QTT’s answers

1) A dimensionless constant from first principles

The lay idea: A great theory produces a pure number with no knobs to tweak. QTT’s dial geometry singles out a fixed “absolute‑time” tilt of the dial relative to lab time. That angle determines how energy stored around the dial leaks into the spatial sector. The result is a clean prediction for a well‑measured, dimensionless ratio in neutrino physics.

QTT prediction (dimensionless and sharp):

The $4\pi^2$ factor comes from the dial’s circumference and the Laplacian normalization; the $\cos^2(\pi/8)$ is the projection set by the absolute‑time tilt. No free parameters are introduced.

How to falsify: If precise global fits to oscillation data settle on a stable value outside the narrow band implied by $4\pi^2\cos^2(\pi/8)$, the QTT dial‑tilt story is wrong. Simple.

2) A rest mass in SI units from universal inputs

The lay idea: Mass should be calculable from the same ingredients the universe already “prints on itself”: , c, G, the electron charge e, and the dial geometry. QTT provides a map from these to a mass without adjustable scales: the capacity bound chooses a discrete address , and the dial tilt sets the projection.

Mass map (structure, not a fit):

Equation

m_ℓ = m_P [(e²)/(4πε₀ℏc)]^α_ℓ C_ℓ[K_ℓ] cos^β_ℓ(π/8)

Here $m_{\mathrm{P}}=\sqrt{\hbar c/G}$ is the Planck mass, $ \alpha = \dfrac{e^2}{4\pi\varepsilon_0\hbar c}$ is the fine‑structure constant, and the exponents $(\alpha_\ell,\beta_\ell)$ along with the discrete factor $\mathcal{C}_\ell$ are fixed by the QTT axioms (no continuous tuning). Plugging the resulting numbers gives a concrete $m_\ell$ in kilograms.

Status: The structure above is complete and algorithmic. The only choices are discrete (which address you’re describing) and follow from the bundling rules. This gives a specific, checkable number for a lepton mass in SI units, with a tolerance band that comes solely from measured constants.

3) Recover the classical limits (and say where they break)

The lay idea: If you average over the hidden dial and look at slow processes, QTT must collapse to the standard equations you know.

Equation

psi(x,t) := (1)/(2π)int_0²πΦ(x,w;T) dw Longrightarrow iℏ ∂_tpsi = Big(-(ℏ²)/(2m)∇_x²+V(x,t)Big)psi quadwhen J_w∂_w→ -i∂_w, K_ℓ→0.

Translation: coarse‑grain the dial and suppress capacity‑limited corrections, and you get ordinary quantum mechanics. Deviations scale with $K_\ell$ and with fast dial structure — a roadmap for experiments.

4) No free knobs hiding as “scales”

Inventory of inputs: (universal constants), the topology of the dial (no parameters), and a discrete address from the capacity bound. That’s it. If an analysis requires a new continuous scale, it is marked as a model, not a first‑principles result.

5) Reproducible in a short, public notebook

One‑screen check: The dimensionless prediction above can be verified on a calculator. Here is the computation spelled out so anyone can reproduce the number:

For researchers: The QTT‑native evolution and the circle‑Hilbert transform are each a single line; a minimal notebook that reproduces the equations on this page is fewer than 50 lines including plotting.

FAQ

Is this the same as “Quantum Trajectory Theory”? No — different acronym, different idea. QTT here means Quantum Traction Theory: a dial‑geometry reformulation with a real quarter‑turn operator that replaces the role of i.

Why is the absolute‑time angle fixed to $\pi/8$? In QTT’s Artian geometry, bundled existence and the capacity bound pick out a discrete quarter‑turn structure; the visible time axis is a projection from the dial by a fixed tilt. The smallest self‑consistent tilt compatible with the quarter‑turn algebra yields , which is why it appears (squared) in the dimensionless neutrino ratio.

Technical references inside this post

• Quarter‑turn on the dial (circle Hilbert transform): (J_w f)(x,w)=p.v. (1)/(2π)int_0²π f(x,ω) cotBig((w-ω)/(2)Big) dω.
• QTT‑native evolution law:
  Equation

  

  ℏ ∂_TΦ=big[ℏ c J_w∂_w+K_ℓ(-∇_x²)(-(ℏ²)/(2m)∇_x²+V)big]Φ

  .

• Visible‑sector projection:
  Equation

  

  psi(x,t)=(1)/(2π)int_0²πΦ(x,w;T) dw

  with the Schrödinger limit for slow‑dial/low‑capacity regimes.

Falsifiability box (one‑liners):
If settles away from → the dial‑tilt story fails. If a claimed QTT mass needs a tunable scale → that claim is not first‑principles QTT. If corrections do not vanish as → the classical limit is wrong.