Ludwig Boltzmann · Entropy
Why does time run only one way?
That time, that place
Newton's laws have no direction in time. Run a film of colliding billiard balls backwards and nothing looks physically wrong.
Yet coffee never reheats itself and a broken cup never reassembles. The individual laws have no arrow; the whole does. Why?
Why this question
Boltzmann's answer was probability. Think of the air in a room. All the molecules could, by chance, gather in one corner — no law forbids it.
But there are only a handful of such arrangements, and an unimaginable number of spread-out ones.
So nature goes to the spread-out side. Not because a force pushes it there, but because there are overwhelmingly more ways to be there.
What was found
Entropy counts those ways. Less 'disorder' than 'how many arrangements produce this state'.
The arrow of time comes from here: the past is the side with fewer ways, the future the side with more. Entropy is the only quantity in physics that tells you which way time runs.
Boltzmann fought long for this, at a time when leading figures denied that atoms were real at all. He took his own life in 1906. The existence of atoms was confirmed experimentally shortly afterwards. His gravestone carries the entropy formula.
Physics could not say why time runs one way
Gas properties computed from molecular statistics matched measurement
Entropy carried into information, and on to Shannon