Quantum computers, superfluid vortices, and the unsolved turbulence mystery—how the next physics development might come from an unlikely source
International Year of Quantum Science and Technology
As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand reality. From computing and communication to materials science, quantum technologies continue to push the boundaries of what we once thought possible. Even my own research on dark energy and time travel has been shaped by these leaps. Yet, despite all this progress, one of the biggest unsolved mysteries in physics and mathematics remains—the Navier-Stokes equation.
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Quantum mechanics and fluid dynamics, though seemingly distinct, share deep conceptual and mathematical connections. While quantum mechanics governs microscopic particles through probability and wave functions, the Navier-Stokes equations describe fluid motion. Both fields exhibit inherent unpredictability—turbulence in fluids mirrors quantum complexity. Recent research suggests quantum principles could develop fluid dynamics, with quantum algorithms enhancing simulations, spin-based representations reformulating fluid equations, and quantum-inspired methods improving computational efficiency. These developments highlight the potential of quantum physics in unraveling turbulence and other complex fluid behaviors.
The Navier-Stokes Equation
First formulated in the 19th century by Claude-Louis Navier and George Gabriel Stokes, the Navier-Stokes equations describe the motion of fluid substances. These equations take into account pressure, viscosity, and external forces, allowing scientists and engineers to model phenomena ranging from ocean currents to blood flow in the human body. They are fundamental to aerodynamics, weather prediction, and countless other applications in science and engineering.
However, despite their apparent simplicity, the full mathematical nature of these equations remains unresolved. The Millennium Prize Problem, set by the Clay Mathematics Institute (CMI), offers a $1 million reward to anyone who can prove whether solutions to the three-dimensional Navier-Stokes equations always exist and remain smooth under all conditions. The core question is whether turbulence—one of the most common yet poorly understood features of fluid dynamics—can emerge in a way that leads to singularities (i.e., infinite values in velocity or pressure) in finite time.
This problem is more than just an abstract mathematical curiosity. Understanding the behavior of the Navier-Stokes equations has direct implications for practical applications. If solutions are always well-behaved, it means we can predict fluid motion with confidence. If they are not, it suggests that fluid flow may inherently break down into unpredictable patterns under certain conditions. This has vast implications for engineering, climate science, and even medical research.
The Quantum Connection: How Turbulence and Quantum Mechanics Overlap
The Schrödinger equation, which governs the behavior of quantum particles, is in some ways analogous to the equations governing fluid flow. In quantum physics, wave functions describe how particles evolve in space and time, much like fluid velocity fields describe how a fluid moves. A striking example of the connection between quantum mechanics and fluid dynamics is found in superfluidity. Superfluid helium, for instance, exhibits behaviors that defy classical intuition—flowing without viscosity and displaying quantum vortices. These quantum vortices behave in ways that resemble classical turbulence but follow discrete, well-defined rules. This phenomenon, known as quantum turbulence, provides a bridge between the chaotic nature of classical turbulence and the orderly laws of quantum mechanics.
Quantum Turbulence: A New Perspective on an Old Problem
One of the most significant challenges in fluid dynamics is understanding turbulence, a phenomenon characterized by chaotic and unpredictable motion. While statistical models provide approximations, a complete theoretical framework remains elusive. Interestingly, turbulence is not limited to classical fluids—it also manifests in quantum systems, though in a fundamentally different way.
Quantum turbulence occurs in superfluid systems, where vortices are quantized, meaning they follow discrete energy levels rather than the chaotic, continuous behavior seen in classical fluids. This makes quantum turbulence a valuable model for studying turbulence in a controlled manner. Researchers are investigating whether insights from quantum turbulence can help address the unresolved complexities of classical turbulence within the Navier-Stokes framework.
Moreover, quantum computing and quantum simulations are reforming the study of fluid dynamics. Quantum algorithms, which can solve differential equations exponentially faster than classical methods, offer the capability to simulate turbulent flows with unprecedented accuracy. By using quantum processors, scientists aim to reveal hidden structures and underlying principles in turbulence that traditional numerical models struggle to capture. These developments could lead to discovery in fields ranging from aerodynamics to climate science.
The International Year of Quantum Science and Technology: A Catalyst for Discovery
As the International Year of Quantum Science and Technology (IYQ) unfolds in 2025, it highlights the power of unexpected connections in scientific progress. Just as quantum mechanics once seemed like an abstract theory before revolutionizing technology, solving the Navier-Stokes problem could transform our understanding of fluid motion.
One of IYQ’s goals is to inspire young scientists to tackle the toughest challenges in physics. A century ago, quantum mechanics defied intuition but became the backbone of modern technology. The Navier-Stokes equation presents a similar enigma in fluid dynamics—one that could lead to profound breakthroughs.
This interplay between quantum science and fluid dynamics underscores the unity of physics, where different fields converge in surprising ways. The Navier-Stokes equation remains an unsolved mathematical puzzle, much like quantum mechanics once was. Yet, just as quantum theory evolved into a driving force for modern innovations, our understanding of turbulence and fluid motion may undergo a similar transformation.
As we celebrate 100 years of quantum mechanics, we also acknowledge the unanswered questions that fuel discovery. Quantum simulations, mathematical advances, or new experimental techniques may unlock the Navier-Stokes mystery—perhaps even from the quantum realm itself. The boundaries between classical and quantum physics are blurring, and the next great discovery may redefine the very laws of motion.
- Nishant Sahdev, Theoretical Physicist, The University of North Carolina, Chapel Hill, NC, United States.
Postal Address: Manning Hall, 216 Lenoir Dr. Suite 100, Chapel Hill, NC 27599, US.
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