A trio of mathematics has signed a discovery that could rewrite the foundations of modern physics. After more than a century of attempts, they managed to Mathematically connect the invisible world of atoms with the behavior of fluidslike ocean currents, wind or smoking in the air.
It is the Possible solution of the sixth problem of Hilbertan enigma placed in 1900 and remained open for 125 years.
A single logical thread among Newton’s laws, Boltzmann’s kinetic theory and fluid equations
Everything starts from Paris, year 1900. In the great amphitheater of the Sorbonne, the German mathematician David Hilbert He presented a list of problems destined to guide the future of science. The sixth of these challenges was clear and radical: “Axiomatize physics”that is to build it on logical and solid bases, as is done with geometry.
The heart of the question? Demonstrate that Macroscopic laws of fluids – those that describe the motion of the wind, water, even clouds – They logically descend from the laws that govern the movement of atomslike the famous laws of Newton. But for over a century, nobody had managed to trace this path completely.
Today, however, three researchers – Yu Deng, Zaher Hani And Xiao but – they succeeded in the company. In a study published on the platform Arxivhave reconstructed the entire logical chain: From Newton’s mechanical physics, to Boltzmann’s kinetic theory, to the Navier-Stakes equationswhich regulate the behavior of the fluids.
A complex and rigorous mathematical test, which finally manages to demonstrate how the turbulence of the air or the waves of the ocean are born, ultimately, from the chaotic and invisible motion of the microscopic particles. The work develops in two fundamental passages.
First step: from the atoms to the equation of Boltzmann
The team analyzed a system consisting of millions of rigid particles who move and collide elastically in a periodic space (a sort of “mathematical bull”, useful for avoiding physical boundaries). Applying the so -called Boltzmann-grad limit – in which particles become smaller and smaller while their number grows – they have shown that The system evolves according to Boltzmann’s equationdeveloped in the 19th century.
This equation allows you to describe the behavior of a gas in a statistical way, without having to know the exact position of each atom. But nobody, before, had managed to demonstrate rigorously that he actually derives from Newton’s mechanical laws, especially on long times.
Second step: from statistics to fluidinamic
Once this bridge has been built, the researchers went to a second, crucial phase: to demonstrate that when the collision rate becomes very high, the system behaves like a continuous fluid.
It is at this stage that two fundamental results emerge:
Are the same equations that the engineers use to simulate the flight of a plane, the weather forecasts or climatic models. But now we know they don’t work just from experience: they work because they are an inevitable mathematical consequence of the most fundamental laws of physics.
A result that changes the way we understand physical reality
This study does not rewrite the equations of fluidinamics. But it changes deeply the reason why we can trust them. So far they were used because they adapted well to experimental data. Now, for the first time, we can say that those equations are “necessary”, because they logically derive from the fundamental principles of nature.
It is a huge step for theoretical physics, which has always tried to combine the microscopic world with the visible one. And it could Open the road to similar approaches in other fieldslike plasma physics, condensed matter or even quantum mechanics. What seemed like a purely mathematical question proves to be instead a milestone in understanding the world around us. From the behavior of the atoms to the breath of the wind: now there is a logical thread that holds everything together.
