The Clock That Reads Nothing

The sun stood still over Gibeon for the better part of a day.

The story is in the book of Joshua. An army is winning a battle and running out of daylight, and the commander says out loud, in front of everyone, “Sun, stand thou still.” And it does. The sun hangs in the sky. The afternoon does not end when it should. The soldiers keep fighting under a sun that has stopped climbing and stopped falling, and by the time it finally moves again the enemy is broken and the day is won.

Set aside whether it happened. Hold onto the picture, because it hides a question that turns out to be one of the oldest and strangest questions anyone has asked, and most people think it has an obvious answer.

The sun has stopped. So has time stopped too?

What a clock is for

Almost everyone answers no, and answers fast. Of course time didn’t stop. The sun is just a big bright object in the sky. Time is something else, something bigger. Time is the thing that keeps going no matter what any object does. If the sun froze, the soldiers’ hearts would still beat, their thoughts would still run, the hourglass would still empty. Time would roll on underneath all of it, the way it always does.

This answer feels like bedrock, and it rests on a picture of time we all carry around. In that picture, time is a kind of river. It flows on its own, at its own steady rate, whether or not anyone is watching, whether or not anything is moving. It is the same river for you and for me and for a rock on the moon. And a clock, in this picture, is a measuring stick you dip into the river. The clock does not make time. It reads time, the way a ruler reads the length of a table. The table is already that long before you measure it; the ruler just tells you the number. In the same way, the hour is already passing before you check the clock; the clock just tells you which hour.

This is such a natural way to think that it feels less like an opinion and more like a plain fact about the world. Time is out there. Clocks read it. That’s all there is to say.

Isaac Newton said it too, and said it better than you or I could. In his Principia, the book that founded modern physics, he wrote:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external.

“Flows equably” means flows at a perfectly even rate. “Without relation to anything external” means it does not care about anything outside itself. Not the sun, not the stars, not you. Real time, on Newton’s view, is a river that would keep flowing at exactly the same rate even in an empty universe with nothing in it to move and no one in it to watch. The clocks we build are just our clumsy attempts to copy that river. Some copies run fast, some run slow, but the true time behind them is fixed and even and out there.

So the answer to the Gibeon question seems settled. The sun stopped. Time kept flowing. A clock in a soldier’s tent would have kept ticking off the real hours, because those hours belong to the river, not to the sun.

Now here is the trouble. The oldest careful thinking about time does not start where this picture starts. It starts by prying time loose from motion in a way that, once you see it, is very hard to un-see. And the man who did the prying is the same man who gave us the definition this whole idea is named after.

The counting hidden inside the clock

Look at what a clock actually does. A pendulum swings. A gear turns. Inside a wristwatch a tiny quartz crystal shakes back and forth, and a modern clock shakes tens of thousands of times a second. In every case the clock is doing one simple thing over and over: it is counting motions. Swing, swing, swing. Tick, tick, tick. When you read the clock, you are reading a count. So many swings since noon. So many ticks since you sat down.

The Greek philosopher Aristotle noticed this about two thousand three hundred years ago, and he built the most famous definition of time in history on top of it. In his Physics he asks what time is, and he first knocks down the easy answers. Time is not motion itself, he says, because motions can be fast or slow, but time cannot. “Fast” already means a lot of motion in a short time, and “slow” means a little motion in a long time. You need time already in your hand to say what fast and slow mean. So time can’t just be the motion. It has to be something else about the motion. Here is his answer, and it is worth reading slowly:

time is just this—number of motion in respect of before and after. Hence time is not movement, but only movement in so far as it admits of enumeration.

Unpack that. “Number of motion” means the count of the motion. “In respect of before and after” means you get the count by marking that this came before and that came after. And “movement in so far as it admits of enumeration” means: time is motion, but only the part of motion you can count. The swinging is not the time. The counting of the swings is the time.

He says it again even more plainly:

Time is not number with which we count, but the number of things which are counted.

Think of counting horses. There is the number “seven” you carry around in your head, and there is the seven-ness of these particular horses standing in front of you. Aristotle says time is the second kind. It is the count that belongs to the moving thing, the way seven belongs to the horses.

This sounds like a small, dry distinction. It is not. Because a count is a strange kind of thing to have in your universe. A pile of stones can sit there with no one around. But the number of the stones is not sitting there in the same way. The number shows up when something counts. And Aristotle, having defined time as a number, was honest enough to walk straight up to the edge of the cliff this puts him on:

Whether if soul did not exist time would exist or not, is a question that may fairly be asked; for if there cannot be some one to count there cannot be anything that can be counted, so that evidently there cannot be number.

Read that twice. He is asking: if there were no mind anywhere, no soul to do any counting, would there be time at all? And his own definition pushes him toward a shocking answer. No counter, no count. No count, no number. And time is a number. So no counter, maybe no time.

That is the first crack in the river. You walked in sure that time was the most out-there, mind-independent thing in the world, the one thing that would keep flowing in an empty universe. And the oldest careful definition of time, the one everything else is built on, says time might be exactly the kind of thing that needs a mind around to exist. Not the swinging. The counting. And counting is something minds do.

The master clock in the sky, and how it broke

There is an obvious way to shove that worry aside, and people reached for it early. Fine, you say. Maybe a count needs a counter. But we don’t need a human counter, because the universe counts for us. Look up. The sun rises and sets, rises and sets, dead regular. The stars wheel overhead and come back to the same place, night after night, year after year. The heavens are one gigantic clock, and it has been ticking off days and years since long before anyone was here to watch. That is the master clock. Every clock we build is just checked against it.

Aristotle himself saw why this idea is so tempting. Of all the motions in the world, the turning of the heavens is the steadiest and the best known, so it makes the natural yardstick. That is why, he says, people are so tempted to say time simply is the movement of the sphere of the sky. The old astronomers built their whole science on this. The Greek astronomer Ptolemy filled book after book with circles inside circles, all in the service of pinning down exactly where the sun and planets would be, so that the sky’s motion could be read like a dial. The heavens keep the time; we just read the heavens.

So the river is saved. It doesn’t need your mind after all. It needs the sky’s motion, and the sky is always moving.

Which brings us back to Gibeon, because there is one man who took that exact thought and broke it with that exact story.

Augustine of Hippo, writing his Confessions around the year 400, spends a long, restless stretch of that book circling the question of time, and he is famous for admitting how lost it leaves him:

What, then, is time? I know well enough what it is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled.

But he is not too baffled to demolish the master-clock idea. He brings up the sun standing still on purpose. If time were nothing but the motion of the heavenly bodies, he reasons, then when the sun stopped over Gibeon, time would have had to stop with it. But that is not what the story says. The battle went on. The soldiers kept swinging their swords through a whole extra stretch of afternoon. In Augustine’s words, the sun stood still, “but time continued to pass.” So time cannot be the sun’s motion, or any heavenly motion. He drives it home with a homelier example: imagine the sun freezes, but a potter’s wheel keeps spinning. We could still time the spins, still say this one took longer than that one. The clock in the sky is off; a clock on the ground still works. So the sky’s motion was never what time was.

Then Augustine asks the question that turns everything inward. If time is not out there in the sky, then where is it, and what are we measuring when we measure it? His answer:

It is in my own mind, then, that I measure time.

When a sound passes, he points out, you cannot measure it while it is past, because it is gone, and you cannot measure it while it is future, because it isn’t here yet, and the present has no length at all. So what are you measuring? Not the thing. You are measuring the impression the thing leaves in you, the stretch of it held in your attention and your memory. Past, present, and future, he says, are really three things happening in one place: “the present of past things is the memory; the present of present things is direct perception; and the present of future things is expectation.” Time is a kind of stretching of the soul.

Watch what just happened to the master clock. To save the river from Aristotle’s worry, we moved the counting out of our heads and up into the sky. Augustine has now moved it right back down, out of the sky and into the head. The place where time is measured is not the heavens. It’s you.

This is not a fringe view held by one monk. The line runs straight through the next thousand years of careful thinkers. John Locke, building his whole theory of the mind in 1689, argues that we don’t even get the idea of time from watching things move. We get it from watching one thought follow another inside us. When that inner train of thoughts stops, as in dreamless sleep, our sense of duration stops too, and hours vanish with no trace. And Locke adds a needle that will matter enormously in a moment: you cannot actually prove that any two stretches of time are the same length. You believe the swings of a pendulum are equal, but as he puts it, two successive lengths of duration, “however measured, can never be demonstrated to be equal.” Every clock rests on an assumption that some motion is perfectly even, and that assumption can never be checked from the inside. George Berkeley, a generation later, went further still and said that time pulled apart from the succession of our own ideas is simply nothing at all. Even the psychologist William James, writing scientific psychology in 1890, found that our sense of the present is not a knife-edge but a small smear a few seconds wide, and that the same hour feels long or short depending on how full of memories it is.

So by now the confident river is in real trouble. The oldest definition says time is a count, and a count wants a counter. The move to make the sky the counter got smashed by a frozen sun. And a long line of careful people keep finding time not out in the world but inside the observer.

Newton draws the river back, and Kant redraws the map

This is exactly the point where Newton plants his flag, and we should give his answer its full strength, because it is not naive. Newton knew all of this. He had read the arguments that time lives in the mind. And he said, in effect: none of that touches the real thing. Yes, our clocks are made of moving parts. Yes, our sense of time is a mushy inner feeling. But behind all the sloppy copies stands the true original, “absolute, true, and mathematical time,” flowing “equably without relation to anything external.” The mind-measured time Augustine talked about is just the shadow. The river is the substance. Newton then went and built a physics on that river so powerful that it put men on a path to the moon three centuries later. When a theory works that well, you do not throw out its foundations lightly.

And notice: Newton’s absolute time answers Aristotle’s worry head-on. Does time need a counter? No, says Newton. It flows on its own, needing no mind and no motion, in a perfectly even stream. The river is real, and it is one river for the whole universe. That last part matters. Newton’s time is universal. There is a single true “now” that sweeps across all of space at once. Your now and my now and the now on a distant star are the same now, all riding the one river together. This is the picture you walked in with, now armored in the greatest physics ever written.

The German philosopher Immanuel Kant, a few decades later, tried to end the fight with a move so deep it is still argued about. He said both sides were half right and half wrong. Time is not out in the things, the way Newton wanted. But it is also not just a soft feeling you happen to have, a rough impression you could shake off. Time, Kant said, is the form your mind imposes on everything it experiences. It is built into the machinery of the observer, before any particular experience arrives:

Time is nothing but the form of our internal intuition.

You cannot experience anything at all except as coming before or after or during something else. You can imagine empty time with nothing in it, Kant points out, but you cannot imagine an experience with no time in it. So time is not a thing you find in the world; it is the shape of the window you look through. That is why he can say time is “a condition a priori of all phenomena whatsoever” — a rule the mind brings to the world rather than a fact it reads off the world.

Sit with where Kant leaves the argument, because it is a genuinely strange place. Time is both maximally necessary and maximally tied to the observer. You could never lose it, never think it away, and yet it belongs to the shape of your mind, not to the things themselves. The river you were so sure was out there might really be the current of your own looking.

But Kant is still doing philosophy. He is telling you how time must work given how experience must work. You could nod along and then object: fine, that’s a clever story about the mind, but out there in the physical world, surely Newton is right and there is one true universal time, whether or not our minds distort it. Surely the physics, at least, keeps the river.

That is the objection. It held for over a hundred years. Then a patent clerk in Bern took it apart with a train and a flash of lightning.

Einstein, and the count that the motion changes

Albert Einstein’s argument, in his own popular book on relativity, starts with the plainest question you can ask. Two bolts of lightning strike a long stretch of railway, one far up the line, one far down. You say they struck at the same time. What does that even mean?

He walks you through it. Put an observer exactly halfway between the two strike points, standing beside the tracks. If the light from both strikes reaches her at the same instant, then, we agree, they were simultaneous. Fine. Now run a train down the track, fast, and put a second observer at the middle of the train, so that at the moment of the strikes she is right next to the first observer. Here is the catch. The train is moving toward one flash and away from the other. So the light from the front strike reaches the train-observer a hair sooner, and the light from the rear strike a hair later. She sees them at different moments. For her, the two strikes were not simultaneous.

Neither observer made a mistake. There is no third, correct answer sitting behind them. The two lightning bolts are simultaneous for the woman by the tracks and not simultaneous for the woman on the train, and that is the end of the story. Einstein states the conclusion flat out:

Every reference-body has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Read that against Newton. Newton said there is one true time for the whole universe, one master “now” for everyone. Einstein says there is no such thing. Ask “what time is it, really, everywhere at once,” and the universe has no answer, because “now” is not a single sheet that lies across all of space. Two people moving relative to each other will honestly disagree about which faraway events are happening at the same moment, and both are right. The philosopher Alfred North Whitehead, writing about the same discovery, put the loss in one line: in the new physics, he said, “there is no such unique present instant.”

And it gets more physical than disagreement about faraway lightning. A clock in motion, Einstein shows, actually runs slow compared to one at rest — not because it’s broken, but because that is what time itself does. “As a consequence of its motion the clock goes more slowly than when at rest.” Two clocks, started together and set moving differently, will read different amounts of elapsed time when they meet again. Not different guesses about the same true time. Different actual times.

Now circle all the way back to Aristotle. He said time is the number of motion. Two thousand three hundred years later, Einstein shows that the motion changes the number. How much time passes between two events depends on how you moved between them. The very motion that time is the count of reaches back and alters the count. The count is real, but there is not one count. There is yours, and there is mine, and if we have moved differently, they do not match, and nothing in the universe is standing behind us keeping the one true tally.

You do not have to take this on faith. You are almost certainly carrying the proof in your pocket. The satellites that run the map on your phone each hold an atomic clock, and those clocks are racing along their orbits and sitting up in weaker gravity, so by the rules Einstein wrote down they tick at a slightly different rate than the clocks on the ground. The difference is tiny, a few tens of millionths of a second a day. But your phone finds your position by comparing the timing of signals from several satellites, and even that much timing error becomes miles of error on the ground within a day. So the engineers build the correction in. Every working navigation system on Earth runs on the daily, practical admission that there is no single universal time. Newton’s one true river is not just philosophically shaky. If you trusted it, you would drive into a lake.

Back to Gibeon

Return to the sun frozen over the battlefield, and the question we started with. The sun has stopped. Has time stopped too?

Augustine’s answer was already unsettling. No, he said, time didn’t stop, because time was never the sun’s motion in the first place; it was being measured somewhere else, in the soldiers, in the mind. That alone should have shaken loose the idea that time is a river out there that clocks simply read.

Einstein’s answer is stranger, and it runs the other way. It is not just that time kept passing when the sun stopped. It is that even while the sun moves, there is no single time for it to keep. There is the sun’s time, and the soldier’s time, and the time of a man watching from a hill, and if any of them move differently, their clocks part ways and never fully agree again, and no cosmic clock overhead is keeping the true count that theirs are copies of. The master clock in the sky was the first thing to fall, back with Augustine. The last thing to fall, with Einstein, was the idea that there is a master clock anywhere at all.

So look one more time at the clock on your wall, the humble thing you were so sure just reads the time. It is counting motions, the way Aristotle said. It needs the counting, the way a number needs a counter. It does not agree, down to the last fraction, with a clock that has traveled differently, the way Einstein showed. And there is no universal time hiding behind it for it to be right or wrong about, because Newton’s one true river turned out not to be there.

The clock on the wall is not reading the time off the universe. It is keeping a count. A real count, an honest count, the one that governs your life and your appointments and your age. But it is yours, tied to where you are and how you move, and the universe is not keeping the same one behind your back.

You walked in certain that time was the one thing in the world that had nothing to do with you. It may turn out to be the thing most bound up with exactly where you stand.