How Laurent Nottale and Thierry Lehner solved the "Closure Problem" of fluid dynamics and revealed macroscopic quantum states in a simple air jet.
For a century, physics has been divided. On one side, we have Quantum Mechanics, describing the probabilistic behavior of the very small. On the other, Classical Fluid Dynamics, describing the chaotic flow of the very large. But a groundbreaking series of papers suggests these two worlds are connected by a single geometric concept: Fractality.
Solving the "Closure Problem"
Turbulence is often called the last unsolved problem of classical physics because of the "Closure Problem." When engineers try to average the Navier-Stokes equations to smooth out chaos, the math bites back: you end up with more unknowns than equations. You cannot solve the system without guessing or adding empirical "fudge factors."
Gemini representation: Please excuse the crudity of this model. I didn’t have time to build it to scale or paint it.
Nottale theory of Scale Relativity solves this. They propose that turbulent trajectories are fractal (non-differentiable). When you apply Newton’s laws to fractal paths, the equations spontaneously integrate into a macroscopic Schrödinger equation. This provides a direct way to calculate the probability of fluid motion, effectively "closing the loop" without guesswork.
The Macroscopic Planck Constant
How can a quantum equation describe a massive fluid jet? It comes down to dimensional equivalence.
In quantum mechanics, ℏ (Planck’s constant) dictates the "fuzziness" of an electron's position.
In this new theory, ℏ is replaced by a macroscopic diffusion constant, D. While the numbers are vastly different in size, they play the exact same mathematical role. D tells the fluid how "fuzzy" or fractal its trajectory is, allowing quantum-like behavior to emerge at the human scale.
Deriving the "Magic Numbers" of Physics
The true power of a theory lies in prediction. For decades, engineers have relied on empirical constants—numbers that we know exist but don't know why. Nottale and Lehner derived these from first principles:
The von Karman Constant (κ): A dimensionless number dictating flow speed near walls. Long measured as ≈ 0.40, the theory predicts it exactly.
The Velocity Correlation (ρ): A measure of how chaotic velocity in one direction affects another. The theory derives the universal value of ≈0.4 observed in shear flows.
The Jet Opening Angle: Why do turbulent jets always spread at an angle of ≈11.5∘? The theory calculates this geometric constant (≈ 0.2 radians) based on the energy levels of a quantum harmonic oscillator.
The "Smoking Gun": A Hole in the Jet
Theory is cheap; proof is gold. In their "PROJET" experiment, the authors didn’t just do the math—they built a box.
A standard free jet behaves like a quantum particle in a "soft" potential—it settles into the Ground State, forming a bell-curve profile with maximum concentration in the center.
But the authors predicted that if they confined the jet inside a physical cone that matched the jet's natural opening angle perfectly, they could create an "infinite potential well." This should force the jet into a First Excited State. The math predicted that this state must have a node in the center.
They turned on the fog machine, and the prediction held: A stable, hollow jet. Instead of a central peak, there was a hole—zero concentration—running down the centerline. It was a macroscopic quantum state, visible to the naked eye.
Nobel-Worthy Physics?
The Nobel Prize is rarely awarded for pure theory; it rewards discovery that changes our understanding of the world and has practical application.
This work suggests that fractal geometry is the missing link between the classical and quantum worlds. It offers a new way to engineer flow—potentially revolutionizing how we design rocket nozzles, pipelines, and climate models. If these results are replicated, confirming that we can manipulate matter into quantized states simply by tuning geometry, we are looking at a discovery that deserves the highest recognition in science.
Primary References:
No comments:
Post a Comment