matter
"Matter" begins as tiny billiard balls in a box and ends as something far stranger: a wave that leaks through walls, a crowd whose only observable is its statistics, and a collection of particles so identical that mislabelling them corrupts the physics. This thread follows the substance itself — from the quantum grain of a single particle, through the statistics of a gas, to the point where the classical picture of matter's heat breaks and demands quanta.
Units touched PU-202 · PU-203 Adjacent threads waves · chance · energy Stations 4
The stations
Transmission through a rectangular barrier
First, matter stops being a little ball. A particle is a wave, and its amplitude bleeds through a wall it classically cannot surmount — tunnelling. Whatever matter is, it is not solid in the everyday sense.
The Maxwell–Boltzmann speed distribution
Now take a mole of it. You cannot track each particle, so matter becomes a distribution: a temperature-set spread of speeds. The individual dissolves into a curve, and that curve is what you measure.
Sackur–Tetrode entropy & the Gibbs paradox
Count the states of that gas and the entropy comes out wrong — until you concede the particles are genuinely indistinguishable. Matter's constituents have no identities to swap; the paradox is the proof.
Equipartition, and the failure that demanded quanta
The classical account of matter's heat — ½kT per degree of freedom — works for warm gases and then collapses for solids and cold. That failure is where matter is finally forced to be quantum all the way down.