# IrreversibilityAndTime

On the tiniest length scales of matter, where atoms vibrate and photons of light shake electrons, there is no time. Or rather, there is no flow of time, no past or future. Every interaction is perfectly reversible; nothing wears out or breaks or unwinds or stops. (Footnote: we can talk about weak interactions, black holes, and CPT some other time; they don't change the answer.)

Imagine a game of billiards played on a frictionless table, with no pockets for the balls to fall into. After the first blow from the cue, the billiard balls never stop moving --- they bounce without losing energy off the cushions and collide with each other, ricocheting about forever. If we were to watch a movie of this rather boring situation, after it is well underway we would have no way to tell whether it were running forward or in reverse. Every encounter of a ball with an object would look exactly the same.

But on a microscopic level, this is precisely the situation of the world! Atoms bounce off one another, in an utterly reversible fashion; each individual collision looks perfectly legal if seen going backwards in time. Light is absorbed and emitted in the same symmetric way.

So how can there be any difference between past and future, if every single microscopic event is precisely reversible? Yet we know there is a difference: we remember the past but cannot (usually!) foresee the future; we and the artifacts we make age and break down, as does everything else we see, animal, vegetable, or mineral. How so?

The answer emerges from the fact that the world is built of many tiny parts. Turn from the boring ideal billiard game to a deck of cards. For starters, take a "deck" with only one card in it. No amount of shuffling will make any difference --- there are no "degrees of freedom" and no information content to the order of cards in a one-card deck. But add another card and now there are two possible configurations, one single bit of data. (We can imagine playing a simple, babylike game.) Add more cards, and the number of possibilities grows quickly --- so that with three cards there are six arrangements that we could shuffle the deck into, with four cards there are 24 orders, with five there are 120, and so forth.

A single-card deck shows no magic, and without close examination neither does a deck of two or three cards. No one would be startled to see, after a few shuffles, such a small set of cards randomly coming back to its original order. But consider a regular deck of 52 cards, for which the number of possible states is approximately 8 followed by 67 zeroes. Such a number is so large that if all the six billion people on Earth each shuffled a deck once a second, the chance of any one of those six billion decks returning to its original starting order during the age of the universe is utterly negligible. And yet, this is only a deck of 52 cards. How many more atoms are there in a droplet of water or the tiniest speck of dust? How many more arrangements could those atoms get themselves into?

That's the big secret of time: in a word, heat. Heat, the common everyday experience, the random vibrations of atoms and other tiny particles. Just as no plausible amount of shuffling can return a deck of 52 cards to its sorted order, similarly no amount of waiting for random vibrations of atoms can plausibly return a spilt puddle of milk to the cup that a child drops --- even though no law of Nature on the microscopic level forbids such a happening. The odds are too vastly stacked against it.

So we can tell past from future, by looking at how heat flows and chaos grows. Ordered things become increasingly random over time. Machines break; ink fades; stone wears away to dust; creatures age and die. We can create order only locally, at the expense of adding disorder elsewhere. It's a losing battle, but that's life.

Wednesday, July 21, 1999 at 21:11:38 (EDT) = 1999-07-21