The efforts made to establish physics in mathematics open the secrets of time

Now, three mathematicians finally presented such a result. Their work is not only a great progress in the Helbert program, but also represents questions about the irreversible time.

“It is a beautiful work,” he said Gregory ValkovicPhysical at the Weizmann Institute of Science. “Tour de Force.”

Under Mesucope

Consider the gas that spreads its molecules. There are many ways that the physicist may design.

At a microscopic level, the gas consists of individual molecules that work like billiard balls, and they move across space according to the 350 -year -old ISAAC Newton. This model of gas behavior is called the particles of the solid system particles.

Now slightly reduce. In this new range “Mesucopic”, your field of vision includes many molecules to follow them individually. Instead, you will design the gas using an equation for the development of physicists James, the writer of Maxwell and Ludwig Bolktmann in the late nineteenth century. It is called the Bolktmann equation, describes the potential behavior of gas molecules, and tells you about the number of particles that you can expect in different locations that move at different speeds. This model of gas allows physicists to study how air moves on small ranges – for example, how it might be Flow around space shuttle.

Reduce again, and you can no longer know that the gas consists of individual molecules. He behaves like one ongoing material. For the model of this sample behavior-how thick gas and the extent of its move at any time in space-you will need another set of equations, called Navier-Stokes equations.

Physicists view these three different models of gas behavior as compatible; They are simply different lenses to understand the same. But mathematicians who hope to contribute to the sixth Hilbert problem wanted to prove this precisely. They needed to show that the Newton model for individual molecules leads to Bolktman’s statistical description, and that the Bolktmann equation in turn leads to Navier-Stokes equations.

Mathematics achieved some success in the second step, which proves that it is possible to extract a microscopic model of gas from one endoscope in different places. But they were unable to solve the first step, leaving the incomplete logic series.

Now this has changed. In a series of papers, mathematicians Udingand Hani blossomAnd Xiao The microscopic step has proven to the most difficult theorizing Gas in one of these settings, Complete the series For the first time. The result and techniques that made it possible to “change the form” said, Yan Quh Brown University.

Yu Deng usually studies the behavior of surfing systems. But by applying his experience to the world of particles, it has now solved a big open problem in mathematical physics.

Photo: With the permission of Yu Ding

Independence Declaration

Bolkmanan can already make it clear that Newton’s movement laws lead to his average equation, as long as one decisive assumptions applies that particles in the gas are moving independently independently of each other. That is, it should be very rare for a certain husband of the molecules that collide with each other several times.

But Bolkmanan could not prove that this assumption was true. “What he could not do, of course, is theories installed about this.” Sergio Simonella Sabinza University in Rome. “There was no structure, there were no tools at that time.”

After all, there are many ways that a group of molecules may collide and remember. “You can only get this huge explosion of the potential trends they can go to” – which makes it a “nightmare” to prove that the scenarios that involve many rare relaxation operations like Bolsman.

In 1975, a mathematician named Oscar Lanford I managed to prove thisBut only for very short periods of time. (The exact amount of time depends on the primary state of the gas, but it is less than the blink of the eye, according to Simonella.) Then the evidence collapsed; Before most molecules are available to collision even once, Lanford can no longer ensure that relaxation remains a rare occurrence.