Theory of Fluids Enters the 21st Century

Theory of Fluids is finally getting its long overdue rewrite. For over a century, the Navier-Stokes equations have ruled the study of how liquids and gases move, and they've done it brilliantly, helping engineers shape aircraft wings, meteorologists forecast hurricane landfalls, and climate scientists model drought risk. But these equations were built on a 19th-century assumption that fluids are perfectly smooth, continuous substances. They ignore the fact that a fluid is really a swarm of individual molecules and atoms. It's a shaky foundation. So we can't keep pretending the old math works when it doesn't.

Twenty years of work, and it's finally done. Physicists have rebuilt the theory of fluids from the ground up, using the profound mathematics of symmetries to derive fluid behavior from first principles,no, scratch that, from the very start, they've grounded everything in modern physics' deepest insights. It's not an academic exercise. But this isn't just for show. So the shift is fundamental: it changes how we understand one of the most common states of matter in the universe, and we can't overstate the weight of that.

The story of this revolution begins with a conceptual tsunami that swept through physics in the second half of the 20th century. As scientists discovered that our world emerges from molecules, which emerge from atoms, which emerge from subatomic particles, they rewrote their theories of matter. But fluids were left behind. The Navier-Stokes equations, first developed in the 1800s, remained in their vintage form.

A Century-Old Approximation

“Navier-Stokes is very much an approximation,” said Michael Landry, a physicist at the Massachusetts Institute of Technology. “It’s not an exact equation.” This puts our theory of fluids in an odd position. In the 1900s, physicists revamped many theories of matter to account for atoms. The new theories were approximations, because tracking every atom is impossible, but they were built on a foundation that acknowledged the microscopic world.

The breakthrough came from Kenneth Wilson, a physicist at Cornell University. It’s hard to overstate how strange that leap seemed. In the 1970s, Wilson developed a method for building high-level theories, called effective field theories, and he showed with rigorous calculations why the smaller scales of the universe bleed through to our level in mercifully few ways, which is why we can actually make sense of physics at all. That work won him a Nobel prize. But the real miracle? It’s that the math works.

It all started with magnets.

Symmetries Over Substance

Since the 1960s, physicists puzzled over a mystery. When a metal is cooled, its atoms align, causing it to magnetize. This collective alignment always happens at precisely the same speed, whether the metal is iron, nickel, or cobalt. Wilson’s approach showed why. The key was to look at a material’s symmetries.

The Power of Zooming Out

Think of a symmetry as a change that doesn’t matter. A square has some symmetry. Rotate it 90 degrees and no one notices; a circle has more, because you can spin it at any angle and it still looks exactly the same. Wilson used symmetries to calculate how the math describing a material changes as you zoom in and out, and his two-step process first identified the symmetries at the microscopic level, then zoomed out to the macroscopic one. As you zoom out, most mathematical terms shrink to nearly zero. Only broad trends survive. So it's a filter, really.

“This is the power of Wilson’s understanding,” Landry said. “You can just skip to the answer.” Wilson’s machinery seeped into many areas of physics, from quantum field theory to the study of solids. But fluids remained stuck. Their defining symmetries were not clear.

That changed in the 2000s, when a group of cosmologists was developing an effective field theory for the universe as a whole. They stumbled upon a key insight.

A Cosmic Connection

The universe’s expansion breaks a crucial symmetry in space-time. In general, space and time have no reference point against which you can measure speed. In a windowless spaceship, you can't tell if you're moving quickly or slowly. But in an expanding universe, there is a special reference point: the one where the expansion of space moves galaxies uniformly away from you, and that point makes your motion measurable, absolute, and real, which is a strange twist on the old rules. Fluids, the group noted, break the same symmetry. So there it is.

Resting liquid surrounds you, and you know you're at rest. That's a given. But start to swim, and you'll feel the drag, the resistance pressing against every stroke, a tangible force that confirms your movement through a medium that itself holds no preference for motion or stillness. The resting fluid lacks the underlying speed symmetry of space-time. So does the expanding universe. It's the same story.

“At the level of the symmetries, they are the same,” said Alberto Nicolis, a physicist now at Columbia University, who worked on the effective field theory of the cosmos.

The group needed one more ingredient. They found it by considering what changes they could make to a fluid without changing its energy, and that's when the realization hit: you could always swap two parcels of a fluid for free. This swapping symmetry was the key. You could shuffle three, four, or any number, and the group had identified an unlimited number of fluid symmetries, so they zoomed out and let the microscopic details wash away, landing right on the Euler equations. They're elegant.

It was a major step. But the theory only worked for perfect fluids. The next step was to include the imperfect ones.

Black Holes and Viscous Soup

The new effective field theory accelerated efforts in a community studying black holes. A late-1990s breakthrough had established that, under special conditions, you could view a spherical black hole as a flat quantum soup. Theorists connected the viscosity of this soup to the black hole’s ability to gobble up energy. “Things can fall into the black hole,” Nicolis said. “That’s a form of dissipation.”

Physicists already had an effective field theory of black holes: Einstein’s theory of gravity. If a black hole acted like a viscous fluid, then an effective field theory for viscous fluids should exist. Multiple teams raced to find it. Hong Liu, a physicist at MIT, led one group. They noticed that the surface of a black hole had a swapping symmetry akin to the one used to define a fluid. But that was not enough to describe an imperfect fluid.

Liu’s group resorted to an old trick from quantum mechanics. They duplicated the substance in their theory, adding a second fluid with a clock that ticked backward while the first fluid’s clock ticked forward. Comparing the two fluids kept track of random variations. The real physical fluid was essentially an average of the two mathematical fluids.

Trial and error led them to a symmetry. It tied the fluid's thermodynamics to the two ways time worked. They switched the fluids, reversed their clocks, and fiddled with the temperature, and here's the remarkable part: if that same sequence happened again, the fluid snapped back to its original state, exactly as it was before. So the symmetry held.

“It’s a funny symmetry,” said Kristan Jensen, a physicist now at the University of Victoria in Canada. And it's vital. Before that, there are a ton of terms. And then [everything] collapses down and you just get known phenomena, nothing more and nothing less.”

They were done. In 2015, Liu’s group posted their new effective field theory, a 110-page magnum opus. “It blew my mind,” Landry said.

Beyond Navier-Stokes

It wasn’t immediately obvious how to harness the highly technical theory for specific applications. But Liu and Glorioso rewrote the equations in a more accessible way in 2018, and then the calculations started to trickle out, slowly at first, then faster as theorists realized they could push their work much further. That changed everything. The new work allowed theorists to work more efficiently and push their calculations further, and they could finally ferret out tiny terms in the Navier-Stokes equations that had previously been ignored, terms that capture some effects of random molecular motion. So it's a story of slow progress that suddenly picked up speed.

Landry insists it's more than an alternate version of fluid dynamics. It's a new way of thinking. And the stuff they're doing, the work itself, isn't just a tweak or a variation on what's come before, but something that fundamentally reorients how we approach the entire field. So don't call it a spin-off. It's not.

The implications are broad. This new Theory of Fluids finally brings the field into the modern era, connecting the macroscopic behavior of liquids and gases to the microscopic world that gives rise to them. It's a conceptual leap a century in the making, paving the way to forecast new behaviors caused by the movements of tiny particles.

“It is actually a new way of thinking about it.”

What It Means for the Future

The work is still highly theoretical, but it has already changed how physicists approach fluid dynamics. The symmetries that define a fluid are now clear, and the equations that govern them have been derived from fundamental principles. The theories are more than just an alternative version of the old ones. They are a complete foundation.

• The Navier-Stokes equations are now understood as a consequence of symmetries, not a standalone law.
• The new approach allows physicists to calculate corrections that account for molecular motion.
• The work bridges cosmology, black hole physics, and everyday fluid dynamics.

Decades of dreaming, that's what it took. Physicists have chased a unified theory for fluids, a quest that started with humble magnets and then took a wild detour through the bizarre geometry of black holes before finally landing on solid ground. So here it is. The theory of fluids has entered the 21st century, and it's here to stay.

Frequently Asked Questions

What is the main criticism of the Navier-Stokes equations according to the article?

The article states that the Navier-Stokes equations were built on a 19th-century assumption that fluids are perfectly smooth, continuous substances, and they ignore the fact that a fluid is really a swarm of individual molecules and atoms. It calls this a shaky foundation and says the old math doesn't work.

How did Kenneth Wilson's work contribute to the development of the new theory of fluids?

Wilson developed a method for building high-level theories, called effective field theories, in the 1970s, and showed with rigorous calculations why smaller scales of the universe bleed through to our level in few ways. His approach used symmetries to calculate how the math changes as you zoom in and out, filtering out most terms to leave only broad trends.

What symmetry did cosmologists discover that connects the universe's expansion to fluids?

The article explains that the universe's expansion breaks a crucial symmetry in space-time, creating a special reference point that makes motion measurable, and fluids break the same symmetry. A resting fluid lacks the underlying speed symmetry of space-time, just like the expanding universe, so at the level of symmetries, they are the same.

Who led the group that developed the effective field theory for viscous fluids, and what key symmetry did they find?

Hong Liu, a physicist at MIT, led a group that developed the theory. They used an old trick from quantum mechanics by duplicating the fluid with a backward-ticking clock, and through trial and error, they found a symmetry that tied the fluid's thermodynamics to the two ways time worked, which held when switching and reversing clocks.

What are the broader implications of the new theory of fluids mentioned in the article?

The new theory connects the macroscopic behavior of liquids and gases to the microscopic world, allowing physicists to calculate corrections that account for molecular motion. It unifies cosmology, black hole physics, and everyday fluid dynamics, and it reorients the entire field by deriving equations from fundamental principles, making Navier-Stokes a consequence of symmetries.