Every time a wave (light, sound, electrons… even quantum waves) squeezes through a tight focus, it picks up a tiny, exact twist in its rhythm: a quarter-turn of phase. In the language of physics this is the “Maslov jump,” and in our framework (Quantum Traction) it is not a patch—it’s a built-in Artian geometric rule.

Posted byQuantum Traction Theory Leave a comment on Every time a wave (light, sound, electrons… even quantum waves) squeezes through a tight focus, it picks up a tiny, exact twist in its rhythm: a quarter-turn of phase. In the language of physics this is the “Maslov jump,” and in our framework (Quantum Traction) it is not a patch—it’s a built-in Artian geometric rule.

The one-liner

Maslov Jump (QTT):
\boxed{\mathcal A \;\to\; \mathcal A \,\exp\!\big(i\pi\,\tfrac{\Delta\sigma}{4}\big) \;=\; \mathcal A\,e^{\pm i\pi/2}}
\Delta\sigma=\pm 2 \Leftrightarrow \Delta\mu=\pm 1,\qquad \mathcal A_j \propto \dfrac{e^{\,iS_j/\hbar}}{\sqrt{|\det S_j''|}}\,e^{-\,i\mu_j\pi/2}.

What that means in plain English

  • Every focus adds a quarter-turn. When a wave passes a tight focus or “caustic,” its internal rhythm flips by exactly ±90° (that’s the “±π/2”).
  • It’s not a fudge factor. Textbooks usually “insert” this quarter-turn to keep the math smooth. In QTT, it falls out naturally from a simple geometric idea: two orthogonal time-like clocks rotated by a quarter-turn.
  • Same number, many places. The very same quarter-turn shows up in optics (Airy/Pearcey fringes), quantum interference, and even connects to our neutrino results.

Why this matters?

  • No new knobs. There’s nothing to tune; the quarter-turn is fixed by geometry.
  • Already seen in labs. Optics and matter-wave experiments have been measuring this ±90° step for decades. QTT explains why it must be that way. Lost ontological explained.
  • One idea, many payoffs. The same geometry helps unify wave optics, quantum phases, and (in the book) neutrino patterns—without adding extra particles or forces.

What’s next

We’ll publish the step-by-step derivation and new tests in the next release of the book. If you’re curious about how this quarter-turn connects to galaxy dynamics and neutrino mass ratios, that’s where we’ll show the full story.

Details coming in the next edition → quantumtraction.org/the-book

Shareable snippet

Every caustic, a quarter-turn: \boxed{\mathcal A \to \mathcal A\,e^{\pm i\pi/2}}.
Same number across light, sound, electrons—and now, a geometric reason why. QuantumTraction.org #QuantumTraction

Published by Quantum Traction Theory

Ali Attar

Leave a comment