Earth’s physics attempt in mathematics open the secrets of time
Now, the three mathematicians finally presented such a result. Their work not only reflects the main progress in the Hilbert program, but also addresses questions about the irreversible nature at the time.
“This is a beautiful job,” said Gregory Vlacovic, a physicist at the Wizmann Institute for Science. “Tour Tour.”
Under Mesucope
Looking at the gas that is very molecule. There are many ways that the physicist may design.
On the microscopic surface, the gas consists of separate molecules that work like billiard balls and move in space according to the laws of Isaac Newton, 350. This model of gas behavior is called the Mattel Sol particles.
Now amplify a little. On this new “Mesoscopic” scale, your field of vision will include many particles for separate tracking. Instead, you can design the gas using the equation developed by James Menkol and Ludwig Boltzmann in the late nineteenth century. The Bolktmann equation, by name, describes the potential behavior of gas molecules and informs you of the number of particles that can be found 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 can flow around the space shuttle.
Zoom again, and you can no longer say that this gas consists of separate molecules. As an ongoing material. For the mixture of this sample behavior, how thick gas a lot and the speed of its move anywhere in space, you need another set of equations, called Navier-Stokes.
Physicists consider these three different models of consistent gas behavior. They simply have different lenses to understand the same things. But mathematicians hoped to participate in the Sixth Hilbert problem, they wanted to prove this carefully. They must make it clear that the Newton’s separate particle model creates the statistical description of Boltzmann, and that the Boltzmann equation in turn creates Navier-Stokes equations.
Mathematics has succeeded in the second stage and has proven that a microscopic model of gas from Mesoscopy can be extracted in different places. But they failed to solve the first step and make the logic chain incomplete.
Now this has changed. In a series of articles, mathematics at Yu Deng, Hani, and Xiao have proven a more difficult gas -to -gas steps in one of these settings and completed the series for the first time. “The results and techniques that made it possible” change the form, “said Yan Jofu of Brown University.
Announcement of independence
Bolkmanan can already make it clear that Newton’s auto laws lead to a medium minister equation, as long as the important assumption is correct: the particles move in the gas independently or in another. That is, it must be very rare for a specific pair of molecules to collide several times.
But Bolkmanan was certainly unable to indicate that this is true. “What he could not do is to prove that it has been proven,” said Sergio Simonella of the University of Sabinza in Rome. “There was no structure, there was no tool at that time.”
After all, there are many infinite methods that a group of molecules may collide. “I have received this huge explosion of the potential instructions that they can go there,” Lourmor said.
In 1975, an Oscar Lanford mathematician succeeded in proving this, but for only very short periods. (The exact amount of time depends on the primary state of the gas, but according to Simonella less than the eye on the eye.) Then the guide was broken. Before most particles have the opportunity to deal with them even once, Lanford can no longer ensure that reminders remain rare.
