Theory of Fluids Enters the 21st Century

In the latter half of the 20th century, a conceptual revolution unfolded in the realm of physics, challenging the very foundations of our understanding of matter. The revelation that our world springs from a microscopic world of molecules, which in turn originates from an even more fundamental subatomic realm, led to the overhaul of our theories regarding matter.

However, this transformative shift remained confined to the domain of solids, as the governing equations of fluids persisted in their 19th-century form—the Navier-Stokes equations. These equations, successful in predicting fluid dynamics, fail to incorporate the existence of microscopic constituents that constitute matter. Recently, physicists have unveiled a new theory that transcends these limitations, marking a significant milestone in the evolution of fluid dynamics.

This theory, the result of a two-decade-long endeavor to reconstruct the theory of fluids from the ground up, introduces a novel approach to defining fluids based on fundamental properties known as symmetries. It also demonstrates that the Navier-Stokes equations are a consequence of these symmetries, accounting for their peculiar forms.

By grasping the origins of the Navier-Stokes equations, researchers have devised a method to surpass them, redefining the essence of fluids and forecasting emergent behaviors originating from microscopic particle movements. Ironically, the breakthrough came from physicists contemplating the universe's grandest scales, notably those investigating black holes and the cosmos.

Centuries of scientific inquiry have laid the groundwork for our understanding of fluids. Leonhard Euler, in the 1750s, adapted Newton's second law of motion to predict liquid motion, while Claude-Louis Navier and George Gabriel Stokes refined Euler's equations to encompass both perfect and imperfect fluids. Today, these equations are indispensable tools for engineers and scientists, guiding the design of aircraft wings and yacht propellers, forecasting hurricane landfall, simulating climate change impacts, and modeling lava, ash clouds, and stellar interiors.

Despite their success, the Navier-Stokes equations are approximations, as they presume fluids as continuous substances devoid of microscopic granularity. In contrast, modern fluids comprise molecules and atoms. To address this discrepancy, physicists have developed a new theory grounded in fundamental symmetries, offering a fresh perspective on fluids and unveiling unanticipated behaviors stemming from microscopic particle dynamics.