Efforts to Ground Physics in Math Are Opening the Secrets of Time– www.wired.com

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Now, three mathematicians have finally provided such a result. Their work not only represents a major advance in Hilbert’s program, but also taps into questions about the irreversible nature of time.

“It’s a beautiful work,” said Gregory Falkovich, a physicist at the Weizmann Institute of Science. “A tour de force.”

Under the Mesoscope

Consider a gas whose particles are very spread out. There are many ways a physicist might model it.

At a microscopic level, the gas is composed of individual molecules that act like billiard balls, moving through space according to Isaac Newton’s 350-year-old laws of motion. This model of the gas’s behavior is called the hard-sphere particle system.

Now zoom out a bit. At this new “mesoscopic” scale, your field of vision encompasses too many molecules to individually track. Instead, you’ll model the gas using an equation that the physicists James Clerk Maxwell and Ludwig Boltzmann developed in the late 19th century. Called the Boltzmann equation, it describes the likely behavior of the gas’s molecules, telling you how many particles you can expect to find at different locations moving at different speeds. This model of the gas lets physicists study how air moves at small scales—for instance, how it might flow around a space shuttle.