Christian Kastrup, James Baylis
The new self -propelled particle powder
Can a single mathematical picture describe the movement of a fluid and the individual particles that compose it? This question, first asked in 1900, now has a solution and helps us understand the complex behavior of the atmosphere and the oceans.
The mathematicians have finally managed to unify the main laws of physics governing particle movements to different scales.
The study at the beginning of the month in the arXiv It comes to resolve an issue posed by mathematician David Hilbert in 1900 as part of an ambitious program for all twentieth -century mathematicians.
As explained by, the new investigation demonstrates how it is possible consistently and significantly join physical laws to three different scales.
Firstly, there is the microscopic domain of individual particles that collide with each other according to the laws of the Isaac Newton.
Then, in the mesoscopic domain of larger objects, the collections of these particles follow the statistical laws created by Ludwig Boltzmann.
On the even larger macroscopic scale, where we reside, physicists resort to notoriously difficult mathematical tools, such as the equation of Navier-Stokeswhich captures all the complexities of the behavior of a fluid.
Over the years, physicists and mathematicians have established some connections between the three structures, but so far they have never been fully united.
This eventually turned into Sixth Hilbert Agenda Problem – which requires the derivation of laws that dictate the behavior of fluids from the most basic mathematical axioms.
Here’s 125 later…
The research team found a key ingredient of the approach that is the reformulation of calculations in terms of diagrams originated by the physical Richard Feynmanwhich used them to solve problems of the quantum theory of the fields.
Mathematicians have learned to use these diagrams to resolve difficult particles that repeatedly interact with each other, as in a fluid, but this can become overwhelming. Instead, the team found a way to reduce the number of diagrams which they had to calculate exactly, which allowed them to build a clear mathematical path from the laws of Newton to the Navier-Stokes equation.
As noted to New Scientist, the new proof reaffirms the way physicists have been thinking about fluids and gases for over a century, giving simultaneously a solid mathematical base.
“The importance of Hilbert’s sixth problem is not only in terms of axiomatizing the laws of physics, but also in terms of understanding the implications of these models [matemáticos]. We know that at the beyond, they end up fail. I think the modern motivation for the [sexto] Hilbert’s problem should be the understanding of what happens when these models break, ”he explained to Zaher haanione of the authors of the study of the University of Michigan.
The team is now interested in realizing what happens on the smallest and microscopic scale, when the most macroscopic fluid equations develop singularities – or, in other words, when their solutions cease to make sense.
