→ The arrow of time

The puzzle

Newton's laws, Maxwell's equations and quantum mechanics all work just as well run backwards. Film two billiard balls colliding and the reversed film looks fine. Yet a film of an egg breaking, played backwards, is obviously wrong. Where does the one-way-ness come from? Loschmidt raised this against Boltzmann in 1876. Established

Entropy is counting

Boltzmann's answer (1877): entropy counts how many microscopic arrangements look the same from outside — S = k ln W. A gas spread through a box can be arranged in vastly more ways than a gas crammed in one corner, so spreading is overwhelmingly likely. Un-spreading isn't forbidden; for 10²³ molecules it is absurdly improbable. Established

The catch: the past

Counting only gives an arrow if things started ordered. Everything traces back to the early universe being in an extraordinarily low-entropy state — the Past Hypothesis. Low in one part only: it was hot and in thermal balance, but spread almost perfectly evenly, which for gravity is the least-spent arrangement there is (see One entropy, two ledgers). Penrose estimated the odds of such a start by chance at 1 in 10 raised to the power 10¹²³. Why it began that way is unexplained: inflation, the Janus point, baby universes and cyclic models are all proposals. Contested This is hole H3.

Stars: where the ordered start gets used

A smooth early universe had one big store of order left: gas that gravity could gather. Gravity pulls it into stars, and a star is an engine. It fuses light elements into heavier ones — the carbon, oxygen and iron that planets and people are made of — and sends the energy out as sunlight. When it dies it scatters what it made, and the next stars and planets form from that. Established

Earth then takes in that sunlight and sends the same energy back out as about twenty times as many infrared photons. That trade — few, energetic photons in; many, cooler ones out — is the low entropy everything here runs on. See Stars forge the elements and Earth's energy budget.

Entropy climbs; complexity rises and falls

Low entropy isn't calm — it means plenty of free energy is still unspent: potential that can still make things happen. The early universe was a hot, fast-moving soup, but spread almost perfectly evenly, and for gravity evenness is the unspent state. Everything since has been gravity spending it. See Is entropy a thing? Established

Think of a river. Entropy is how far downstream you are: it only increases. Activity is how fast the water is dropping: the rapids. The universe's rapids are behind it — stars were born fastest about 10 billion years ago, "cosmic noon", and today at about a tenth of that rate. Ahead: small red dwarfs burning quietly for trillions of years, then embers. Established (the first stars being huge is predicted, not yet seen Contested)

And complexity lives in the middle. Pour cream into coffee: at first it sits on top — simple. At the end it's evenly mixed — simple again. In between come swirls and tendrils. Entropy rises throughout; complexity rises, then falls. Stars, planets and people are eddies in that current, existing only while energy flows downhill. Contested (the picture is widely used; how to measure complexity isn't settled)

See it: the complexity line in the Entropy box, the star-birth curve on the Cosmic timeline (ordinary time), stars as engines in Stars forge the elements, and Earth living off the flow in Earth's energy budget.

At the edge. Some physicists suspect gravity itself is a large-scale, statistical effect, like temperature — see Gravity as thermodynamics Contested. And some argue the lumpiness of the universe distorts how we read its expansion, perhaps enough to explain dark energy — see Timescape: clocks in voids Contested.

The other arrows

Several arrows point the same way. Radiation spreads out from sources, never converges onto them. Memory: records — photographs, fossils, memories — form in the direction entropy increases, which is why we remember the past, not the future. Cosmology: the universe is expanding. One more is tiny: the weak force treats past and future very slightly differently in a few particle decays — real, but far too weak to be the cause. Established for each arrow; how they're linked is Contested.

How we know

• The second law of thermodynamics — entropy of an isolated system doesn't decrease — has never been seen to fail at everyday scales.
• Small systems do show brief, predictable backward fluctuations (fluctuation theorems), exactly as the counting predicts.
• The microwave background shows the early universe was extremely smooth — the low-entropy start the Past Hypothesis needs.