For nearly two centuries, the Navier-Stokes equations have provided the mathematical foundation for understanding fluids. Engineers and scientists use them to model aircraft aerodynamics, hurricanes, climate patterns, lava flows, and even stellar interiors. Yet the equations treat fluids as continuous substances, ignoring the microscopic particles and fluctuations that make up real matter, tells Quanta Magazine.
Physicists have now developed a deeper framework that connects fluid behavior to the microscopic world. The effort draws on effective field theory, an approach pioneered by Nobel laureate Kenneth Wilson. Rather than tracking every atom, effective field theories identify fundamental symmetries and determine which microscopic features remain important at larger scales.
Researchers discovered that fluids can be defined through their symmetries. Unlike solids, fluids allow parcels of material to exchange positions without requiring additional energy. Using these symmetries and effective field theory, physicists were able to derive the Euler equations for ideal fluids from basic principles.
Describing viscous fluids proved more difficult. Insights from black hole physics helped researchers make progress. Black holes dissipate energy in ways that resemble viscous fluids, suggesting that a suitable effective field theory should exist. MIT physicist Hong Liu and collaborators eventually developed a framework that incorporated microscopic fluctuations, thermodynamics, and the direction of time. Their work showed that the Navier-Stokes equations emerge naturally from underlying symmetries.
The framework also captures subtle effects that conventional fluid equations overlook. Researchers have used it to predict that heat can initially spread more slowly through certain liquids because of microscopic fluctuations and to develop fluidlike equations for exotic states such as fracton matter.
More fundamentally, the research offers a new definition of a fluid. Instead of being classified by its microscopic ingredients, a fluid can be understood as any form of matter possessing a particular collection of symmetries. This perspective explains why microscopically different substances can display remarkably similar behavior when they flow.
