The Quanta Podcast Audio Edition: Epic Effort to Ground Physics in Math Opens Up the Secrets of Time
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Feb 19, 2026 Mathematicians prove how individual particle collisions build up fluid behavior and why time seems to flow one way. The work completes a long-sought link from Newtonian particles to Boltzmann and then to Navier-Stokes. Innovative counting of collision patterns and wave-inspired decompositions make rare recollisions negligible. The result illuminates the mathematical roots of irreversibility and points toward broader extensions.
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Hilbert's Program Sets The Goal
- David Hilbert challenged mathematicians to axiomatize physics and link different physical models rigorously.
- This set the stage for proving that microscopic laws can imply mesoscopic and macroscopic equations.
Three Scales Describe Gases
- Physicists use Newtonian particle models, the Boltzmann equation, and Navier-Stokes to describe gases at micro, meso, and macro scales.
- Mathematicians sought rigorous derivations showing each scale follows from the previous one.
Rare Recollisions Are Crucial
- Boltzmann's derivation required an assumption that particles act nearly independently with rare recollisions.
- Previous proofs like Lanford's only held for extremely short times because recollisions become hard to rule out later.