What Is Space and Time?

A plain-language introduction for the curious reader. No physics or philosophy background is needed — only a willingness to look hard at two things you swim in every second of your life without ever noticing them.

The puzzle in 30 seconds

Space and time seem like the least mysterious things there are. Space is just the emptiness that things sit in; time is just the ticking that carries us from breakfast to bedtime. What could be simpler?

But start asking basic questions and the ground gives way. Is empty space a real thing — a giant invisible container that would still be "there" if you removed every atom in the universe? Or is "space" just a way of talking about how objects are arranged, so that with nothing in it there would be no space at all? Does time actually flow, like a river carrying the present moment forward — or is that feeling of flow a kind of illusion, and past, present, and future all equally real? And is the future already out there, fixed and waiting, or does it not yet exist?

These are not word games. Modern physics — Einstein's relativity above all — has genuinely surprising answers to some of them, and it has turned what looked like idle questions into some of the deepest problems in science. This page is a tour of the big ones.

Two things, three questions

Almost every puzzle about space and time is a version of one of three questions. (The technical section is organised around exactly these — see What Is the Philosophy of Space and Time?.)

• Are space and time real things, or just relationships? Is space a container, or only the pattern of distances between objects?
• Does time really pass? Is there a special moment called "now" that moves — or is that just how things look from inside?
• What decides the shape of space? Is it obvious and fixed (the geometry you learned in school), or could space be "curved," and how would we ever know? And underneath that: is space made of points, smooth and endlessly divisible — or does it come in smallest lumps?

Let's take them in turn. After that come the questions modern physics has added: what space is made of, whether anything really has a location, how many dimensions there are, why time runs one way and not the other, why space is getting bigger, and whether anything could visit its own past.

Question 1: Is empty space a thing?

Here is a debate that has run for over 300 years, between two of history's greatest minds.

Isaac Newton said: yes, space is a real, self-standing thing — an infinite, invisible stage on which the whole show of the universe plays out. Even a totally empty universe would still have space.

Gottfried Leibniz said: no, that is a fantasy. "Space" is just a convenient word for how things are laid out relative to each other — this cup is 20 cm from that plate. Take away all the objects and you haven't got an empty container; you've got nothing at all. (See Substantivalism and Relationism.)

Who's right? Newton had a killer piece of evidence: spin a bucket of water and the surface climbs the sides. Something is clearly, physically different about spinning versus not spinning — you can feel it on a merry-go-round. But different relative to what, if the bucket were alone in an empty universe? Newton said: relative to space itself. That suggests space is real after all. Leibniz's followers have been trying to answer the spinning bucket ever since. (See Newton's Bucket.)

The strange thing is that this ancient argument is still alive — Einstein's theory of gravity reopened it in a dramatic new form, because in that theory space and time turn out to bend, and something that bends starts to look a lot like a real, physical thing.

That reopening cuts both ways, and it is worth seeing how. On one side, the physicist Ernst Mach offered Leibniz's camp a comeback to the bucket: perhaps the water climbs the sides because it is spinning relative to all the other matter in the universe — the distant stars — rather than relative to space itself. Spin the heavens around a stationary bucket, on this view, and the water should still climb. It is a beautiful idea, it directly inspired Einstein, and whether his final theory actually delivers it is still disputed. (See Mach's Principle.)

On the other side, Einstein found an argument that seems to cut against space being a real thing — and it troubled him so much that it stalled his work for two years. Roughly: if spacetime were a genuine collection of points, you could take a solution of his equations and slide all the matter over a bit, leaving the underlying points where they were. You would get a second, different arrangement — different points doing different jobs — that no possible experiment could tell apart from the first. A theory that makes such undetectable distinctions looks like a theory with something wrong in it. This is the hole argument, and it remains the sharpest modern weapon against treating space as a self-standing container. (See The Hole Argument.)

A third answer: perhaps space is in us

Newton and Leibniz disagree about almost everything, but they share an assumption: that space is out there, and the only question is what kind of out-there thing it is. Immanuel Kant proposed something stranger, and it has never really gone away.

On Kant's view, space and time are neither substances nor relations between objects. They are the form of our experience — the apparatus the mind uses to lay out anything it encounters. We do not discover that things are arranged spatially and successively; we cannot take in anything at all except by arranging it that way. Space and time belong to the viewing, not to the view. Ask what the world is like in itself, with the human apparatus subtracted, and on this account you are not entitled to an answer.

A puzzle he pressed makes the idea less airy than it sounds. Consider your two hands. They are mirror images, and every internal measurement is identical — same distances between the same knuckles, same angles everywhere. Yet no amount of turning will let a left hand occupy the space a right hand just vacated; a left glove will not go on your right hand. Now imagine a universe containing nothing whatever except one hand. There are no other objects for it to stand in relations to — and yet, surely, it is determinately a left hand or a right one. What could that difference consist in? Not in the relations among its own parts, which are the same either way; and not in relations to other things, since there aren't any. Kant took this to show that handedness is a relation to space itself, and hence that space is not merely the arrangement of its contents — a direct hit on Leibniz. (See Handedness and Incongruent Counterparts.)

The sting in Kant's mature position is that it makes the Newton–Leibniz quarrel look misconceived: the two of them are arguing about the reality of a container that is, in the end, a feature of the observer. As we'll see, relativity destroyed the specific form of his theory. But the general suspicion — that some of the structure we find in space and time is contributed rather than found — is very much alive, and it is exactly what is at stake in the next question.

Question 2: Does time actually flow?

This is the one that keeps philosophers up at night.

Everyone feels time flowing. The present moment seems to move: this instant is here, then it's gone, swept into the past, while the future rushes toward us. The past feels fixed and the future feels open.

But here is a troubling question: how fast does time flow? "One second per second" — but that's not a speed at all; it's like saying a stationary car moves "one metre per metre." Ask how fast the present moves and you can't give a real answer. That makes some philosophers suspect that the "flow" of time isn't a feature of the world at all — it's a feature of us, of what it's like to be a conscious being with a growing pile of memories. (This is Kant's thought from the last section, aimed at time: the passing may be in the apparatus rather than in what the apparatus is looking at. You don't have to accept his whole system to find the suggestion hard to shake off.) (See Temporal Passage.)

This leads to one of the wildest ideas in modern thought: the block universe. On this view, past, present, and future all equally exist. The universe is like a completed film reel or a loaf of bread, laid out whole in four dimensions (three of space, one of time). There is no special moving "now" — every moment thinks it is "now," the way every place is "here" to whoever is standing there. Dinosaurs and your great-grandchildren are just as real as you; they're simply located elsewhere in time, the way Australia is real but not here. (See The Block Universe.)

It helps to have names for the options on the table, because there are really only three serious ones:

• Presentism — only the present moment exists. The past is gone and the future hasn't happened; reality is a single thin sliver that keeps being replaced. This is what almost everyone believes before they think about it.
• Eternalism (the block universe) — all moments exist equally. Nothing comes into or goes out of existence; "now" is just where you happen to be standing.
• The growing block — the past and present are real but the future is not. Reality accumulates: each moment is added to a block that gets steadily bigger, which honours both the fixity of the past and the openness of the future.

(See Presentism and Eternalism.) There is a related and even older split over whether passage itself is a real feature of the world — the A-theory — or whether the world contains only the fixed relations earlier than and later than, with our sense of flow supplied by us — the B-theory. In 1908 the philosopher J. M. E. McTaggart pushed this so far that he concluded time is unreal, arguing that passage requires every event to be future, then present, then past, which are incompatible properties. His argument is almost universally rejected and almost universally taught, because nobody agrees on exactly where it goes wrong. (See McTaggart's Argument and A-Theory and B-Theory.)

If all times are equally real, what are you?

The block universe forces an odd question about your own shape. You have spatial parts — a hand, a foot, a left half. Do you also have temporal parts?

On one view you do not: you are wholly present at every moment, the same complete object today as yesterday, passing through time as a whole. On the other, you are a four-dimensional object extended through time the way a road is extended through space — sometimes called a worm — and what is present today is a part of you, the way the near end of the road is part of the road. You-at-seven and you-now are different parts of one long thing.

The second picture sits naturally with the block universe, and it quietly solves a problem that has annoyed philosophers since Heraclitus: how can something change and yet remain the same thing? If you are a four-dimensional object, the answer is easy — a banana is green at one end of it and yellow at the other, exactly as a road is narrow at one end and wide at the other. No contradiction, just different parts with different properties.

The price is that you become something rather large and mostly elsewhere, of which the person reading this sentence is a thin slice. Whether that is a discovery about what you are, or a picture that has confused a life with a shape, is very much still argued about. (See Persistence Through Time.)

Why would anyone believe something so strange as the block universe? Because of Einstein.

The surprise that changed everything: "now" is not universal

The single most mind-bending discovery about time came from Einstein's special relativity in 1905, and it is this: whether two distant events happen "at the same time" depends on how you're moving.

Einstein did not decide this by taste. It follows, with almost no wriggle room, from one stubborn experimental fact: light always travels at the same speed, no matter how you are moving when you measure it. That should be impossible. Run toward a thrown ball and it comes at you faster; run away and it comes slower. Run toward a light beam at half the speed of light, and it still arrives at exactly the usual 299,792,458 metres per second — not one metre per second faster. Experimenters spent decades trying to catch light behaving normally and never could. Einstein's move was to stop treating this as a puzzle to be explained away and start treating it as a rule, then ask what else must be true if it holds. The answer turned out to be: nearly everything you believed about "at the same time" has to go.

In everyday life we assume there's a single, universal "now" ticking away everywhere at once — that this instant on Earth is the same instant on a distant galaxy. Relativity says: there isn't. Two people walking past each other at different speeds will genuinely disagree about which faraway events are happening "right now," and — this is the shocker — neither of them is wrong. There is no fact of the matter about a single, universe-wide present moment. (See Relativity and the Reality of Simultaneity.)

This is devastating for the cozy idea that time flows and only the present is real — because whose present? If different observers can't even agree on what "now" includes, maybe there is no special "now" out there at all. That's the road to the block universe, where all moments are equally real. Many physicists and philosophers think relativity more or less forces this picture on us. Others resist. The argument is still going. (This is the deepest reason the "block universe" is taken seriously and not just science fiction.)

Try it yourself: the train and the lightning

You don't have to take any of that on trust. Einstein's own thought experiment gets you there in about a minute, using nothing but the rule that light travels at a fixed speed.

Picture a train running down a track, and two bolts of lightning striking it — one at the front, one at the back. Alice stands on the platform, exactly halfway between the two scorch marks the bolts leave on the ground. The light from each strike races toward her, and because both flashes travel at the same speed over the same distance, they reach her eyes together. Alice concludes, correctly: those two strikes happened at the same time.

Now put Bob on the train, seated exactly halfway along it, and suppose he is level with Alice at the instant the bolts hit. The two flashes set off toward him — and while they are in transit, Bob is moving toward the front one and away from the rear one. So the front flash reaches him first.

Here is the whole argument. Bob cannot explain this away by saying the front flash travelled faster, because light doesn't do that; it goes at the fixed speed for him just as it does for Alice. He is midway between the strikes, both flashes covered the same distance at the same speed, and the front one arrived first. There is only one conclusion available to him: the front bolt struck earlier. For Alice, the strikes were simultaneous. For Bob, they weren't.

Now ask the fatal question: which of them is right? There is no answer. There is no experiment that makes the platform's opinion the true one, because the platform is no more "really at rest" than the train is — the Earth is hurtling around the Sun, the Sun around the galaxy, and nothing anywhere is standing still in any absolute sense. Both are simply reading off what "at the same time" means from where they sit. That's it: that's the relativity of simultaneity, and everything else — the slow clocks, the short rulers, the twins — is bookkeeping that follows from it.

So what replaces "now"? The light cone

If there is no universal present, has time descended into a free-for-all where nobody can say what happened before what? No — and the thing that saves it is one of the most elegant ideas in physics.

Because nothing can outrun light, every event has a definite reach. Imagine a flash going off where you are standing right now: it expands outward at the speed of light, and everything it can eventually touch is your future light cone — the set of events you could still influence. Run the same picture backwards and you get your past light cone: everything that could have sent a signal, a push, or a photon to you here and now. All of history that could possibly matter to you arrives through it.

About those events, everyone agrees. Every observer, however fast they're moving, agrees that your birth is in your past and tomorrow's breakfast is in your future, because those are connected to you by chains of cause and effect slower than light. What observers disagree about is the vast remaining region — events too far away to reach you in the time available, like something happening on a star a thousand light-years off, one second ago. Those events are in neither your past nor your future. They are simply elsewhere, and the order of them is what shifts depending on how you move.

So relativity does not abolish before and after. It abolishes before and after for events that could never have affected each other anyway. Causality survives intact; only the universal snapshot dies. That is the trade, and it is a much better bargain than it first sounds. (See Spacetime for the geometry behind this picture.)

Two more surprises: slow clocks and short rulers

That single discovery — no universal "now" — has two famous side effects you may have heard of.

Moving clocks run slow. If someone speeds past you, everything about them — their watch, their heartbeat, their ageing — ticks slower than yours. And they say exactly the same about you. It sounds like a contradiction, but it isn't, because the two of you no longer agree on what "at the same time" means. This is not a trick of the eye; it is real and measured every day. The satellites behind GPS orbit at about 14,000 km/h, which loses their onboard clocks around 7 millionths of a second per day — and since the system works by timing signals that travel at the speed of light, an uncorrected error that size would push your phone's position off by kilometres within a day. (Gravity does something even bigger to those same clocks, in the opposite direction; we'll come to it below.) Tiny particles called muons reach the ground from the upper atmosphere only because moving so fast stretches out their brief lives. And in the famous twin paradox, a twin who rockets away and comes back is genuinely younger than the one who stayed — not because either aged wrongly, but because they travelled different paths through spacetime, and the paths were not the same length in time.

That last point is worth pausing on, because the geometry runs backwards from the one you know. On a map, the straight line is the shortest route between two points, and any detour makes your journey longer. In spacetime it inverts: the twin who stays put takes the route of greatest elapsed time, and every detour through space is time lost. Speed, in a real sense, is something you pay for out of your own clock — which is why the traveller comes home young.

Moving rulers shrink. By the same token, a fast-moving object is measured as shorter, front to back, than when it sits still. Nothing is crushing it; it is the mirror image of the clock effect. Measuring a moving thing's length means catching where both its ends are at the same moment — and, once again, observers can't agree on what "the same moment" is.

We never notice any of this in ordinary life for one reason only: the effects are vanishingly small until you approach the speed of light. Near it they become enormous — and they are exactly the price of there being no universal "now." (See the relativity of simultaneity.)

Question 3: Can space be curved?

For 2,000 years, everyone assumed the geometry of space was the one Euclid wrote down: parallel lines never meet, the angles of a triangle add up to 180°, and so on. It seemed not just true but necessarily true — how could space be any other way? Kant made this the centrepiece of a whole philosophy: Euclid's geometry, he argued, isn't something we learn from the world, it's the framework our minds impose on any possible experience. We can no more perceive a non-Euclidean world than we can see a colour outside the spectrum. Geometry was therefore certain in advance, and guaranteed to apply.

But there was a splinter in the woodwork, and it had been there since antiquity. Euclid's fifth postulate — given a line and a point beside it, there is exactly one line through that point that never meets the first — is wordier and less self-evident than his other four, and for two millennia mathematicians tried to prove it from them. Every attempt failed, usually by smuggling in an equivalent assumption without noticing. (See The Parallel Postulate.)

The earthquake

In the early nineteenth century Gauss, Bolyai, and Lobachevsky independently worked out why every proof had failed: the postulate cannot be proved, because denying it doesn't lead to a contradiction. It leads to a different geometry — an entirely coherent one. Assume infinitely many parallels through the point and you get hyperbolic geometry, where triangles have angle sums less than 180°. Assume none and you get elliptic or spherical geometry, where they add up to more. (See The Discovery of Non-Euclidean Geometry.)

You already own an example of the second one. On a globe, the "straight lines" — the shortest routes, which is what airliners fly — are the great circles, and any two of them always meet: there are no parallels. Start at the North Pole, go down to the equator, turn 90°, go a quarter of the way round, turn 90°, and go back to the pole. You have drawn a triangle with three right angles: 270°. Euclid's geometry simply isn't true of a sphere's surface, and nothing about that is mystical.

But notice what that example quietly relied on: a triangle the size of a quarter of the planet. The angle sum is not a fixed alternative number — it depends on how big the triangle is. The amount by which it overshoots or falls short of 180° is proportional to the triangle's area. A triangle drawn on a football pitch is also on the surface of the Earth, and its angles also exceed 180° — by about a hundred-millionth of a degree, which no instrument will ever see. This is why the sphere feels flat when you walk on it, and it is the general rule: any small enough patch of a curved space is indistinguishable from a flat one. Curvature hides at small scales and only announces itself over large ones — which is both why it took so long to suspect, and why Einstein's theory can be as strange as it likes about black holes while your kitchen stays perfectly Euclidean.

What sealed it was consistency. Beltrami and Klein built models of the new geometries inside ordinary Euclidean geometry — the hyperbolic plane as the inside of a disc, with distances reckoned so the edge is infinitely far away. Anyone who could derive a contradiction from hyperbolic geometry could then derive one from Euclid's. The alternatives were not confused; they were exactly as sound as the original. Kant's necessity was gone. (See Independence of the Parallel Postulate and Hyperbolic Geometry.)

Something of Kant does survive the wreck, and it is worth separating from what doesn't. Dead: the claim that physical space is necessarily Euclidean and that we could not so much as conceive otherwise — mathematicians conceived otherwise, and then the universe obliged. Alive: the milder thought that a theory has to lay down a framework before it can test anything, a framework that is fixed in advance relative to that theory while remaining revisable when the theory is replaced. Reichenbach called this the relativised a priori, and it is now a standard way of keeping Kant's insight without his mistake. Arguably also alive: that we must represent things as spread out in space and strung out in time at all may well be a condition of having experience — even though which geometry that space has turns out to be none of our minds' business.

"Curved" doesn't mean "bent into something"

The usual sticking point: if space is curved, what is it curving into? A sphere is bent through the surrounding room — so doesn't curved space need a higher dimension to bend through?

It doesn't, and seeing why is the single most useful idea in this whole area. Gauss proved that curvature is intrinsic: it can be measured entirely from inside a surface, with no reference to any outside at all. Imagine an ant that can never leave the surface it lives on and has no notion of "up." It can still find out where it is. It draws a triangle and adds the angles: 180° means flat, more means sphere-like, less means saddle-like. Or it paces out a circle and compares the circumference to the radius — on a sphere it comes up short, on a saddle it runs long. Curvature is a fact about distances within the surface, not about how the surface sits in anything.

So when physicists say spacetime is curved, they are not saying it is draped through a fifth dimension. They are saying that if you measure carefully enough with rulers and clocks that never leave the universe, the answers won't be the ones Euclid predicted. There is no "outside" required, and none is claimed.

Geometry becomes an experimental science

Once alternatives exist, the question "which geometry does actual space have?" stops being a matter for the armchair and becomes a matter for instruments. Riemann — who generalised all of this to spaces whose curvature varies from place to place — said so explicitly in 1854: the geometry of physical space is a question for physics. Gauss is said to have already tried to check, surveying a huge triangle between three mountain peaks to see whether its angles came to 180°. They did, within the error of his instruments — and by the area rule above they were always going to: a triangle a few tens of kilometres across is nowhere near big enough for the curvature of space to show. Space is very close to flat around here, and you need starlight grazing the Sun, or the whole visible universe, before the question gets interesting. (See The Epistemology of Geometry.)

Why gravity, of all things, turned out to be geometry

Then Einstein discovered that our universe actually uses one of the alternatives. But why should gravity be the thing that reveals it? The answer starts with an oddity that had been sitting in plain sight since Galileo.

Gravity is the only force that treats everything identically. Drop a hammer and a feather in a vacuum and they fall together; an astronaut did exactly this on the Moon in 1971, and they hit the dust at the same moment. Every other force in nature is choosy — electricity moves charged things and ignores neutral ones, magnetism yanks iron and not copper, and how hard you're pushed depends on what you're made of. Gravity alone gives every object the same acceleration regardless of its mass, its material, or anything else about it. Newton could write this down but not explain it; in his theory it is a coincidence, requiring that the "mass" that resists being pushed happens to equal the "mass" that responds to gravity, for no particular reason.

Einstein turned the coincidence into a foundation. In 1907 he had what he later called the happiest thought of his life: a man falling freely does not feel his own weight. Step off a roof and, for the duration, gravity vanishes — not by being cancelled but by being genuinely absent from your experience. This is why astronauts float, which is worth pausing over, because the usual explanation is wrong: there is plenty of gravity in orbit, nearly as much as on the ground. They are weightless because they are falling, continuously, and missing the Earth. Turn the thought around and it works too: sealed in a windowless capsule, you could not tell whether the floor pressing your feet is the Earth beneath you or a rocket accelerating you through empty space. This is the equivalence principle, and it is the seed the whole theory grew from. (See The Equivalence Principle.)

Now the payoff. If a "force" can be made to disappear entirely just by choosing how you move, it was never really a force acting on things. Something that affects every object in exactly the same way isn't telling you about the objects at all — it's telling you about the arena they move in. That is the licence to stop describing gravity as a pull and start describing it as a shape: in general relativity, massive objects like the Sun bend the spacetime around them, and what we call gravity — the Earth orbiting the Sun, an apple falling — is just things following the straightest path available through a shape that is no longer flat. Nothing pulls the Earth; it is going as straight as it can. And the geometry isn't a backdrop chosen once and for all: it is a physical field, pushed around by matter and pushing back, with its own equations. Space and time warp, stretch, and ripple. (See General Relativity.)

Two loose ends tie this back to everything above. First, if gravity vanishes for anyone in free fall, what's left for the curvature to be? The answer is what you can't transform away: fall long enough in a big enough region and you notice that different parts of you are falling toward slightly different points, so you get stretched lengthwise and squeezed sideways. That unremovable stretching is curvature, and you have seen it — it is what raises the ocean tides. Second, Newton's gravity was instantaneous: move the Sun, and the Earth's orbit responds now, across a hundred and fifty million kilometres. After 1905 that was untenable, since it presupposes exactly the universe-wide "now" that relativity had just abolished. General relativity fixed it — a change in the gravitational field spreads outward at precisely the speed of light, no faster, which is why gravitational waves exist at all and why LIGO's black holes announced themselves on the same schedule as light would have.

Two details make the picture sharper than the usual rubber-sheet cartoon. First, even with no gravity at all, the geometry of spacetime was never Euclidean: combining a distance and a duration into a single spacetime interval involves a minus sign where Pythagoras would have a plus. That single sign is the whole of special relativity in geometric dress, and it's why the travelling twin comes home young — in this geometry a detour costs you time rather than adding to your journey. Second, the gravity you feel right now is almost entirely the curvature of time, not of space. Clocks run slower nearer the ground; the straightest path through a spacetime where time itself is warped is one that bends downward. The apple falls because time passes differently at its stalk and at the grass.

This has been measured, repeatedly, and the measurements are worth knowing because they turn a wild claim into a fact about the world.

Starlight bends. In May 1919, expeditions led by Arthur Eddington photographed stars near the edge of the Sun during a total eclipse, when the Sun's glare was blocked and they could be seen at all. The stars had shifted — their light was deflected as it passed the Sun by very nearly the amount the curving of spacetime predicts, and by twice what you'd get from treating light as an ordinary falling object. The results made Einstein world-famous overnight. Curvature also settled an old embarrassment: Mercury's orbit had long been known to drift by a tiny amount nobody could explain, and Einstein's equations gave the figure exactly. (See Tests of General Relativity.)

Clocks run slower lower down. Curved time has an effect you could in principle notice in your own house: a clock nearer the ground ticks more slowly than one on a high shelf, because gravity stretches time as well as space. It is a fantastically small effect, and it has been measured anyway — in 2010 physicists at NIST detected the difference between two atomic clocks raised just 33 centimetres apart. Your head really is ageing faster than your feet, by something on the order of a millionth of a second over a lifetime. This is also the larger of the two corrections GPS needs: being high above the Earth speeds those satellite clocks up by about 45 millionths of a second a day, which more than cancels the 7 they lose to their speed. The system is a working machine that would drift into uselessness within a day if either of Einstein's theories were wrong.

Spacetime ripples, and we have heard it. If spacetime can bend, it can also wobble — violent events should send waves of stretching and squeezing outward at the speed of light. In September 2015 the LIGO detectors caught one: two black holes, more than a billion light-years away, spiralling together and merging. The passing wave changed the length of a four-kilometre instrument by a fraction of the width of a proton. Spacetime is not a metaphor; it is something you can ring like a bell and listen to.

And where the curving runs away with itself, you get black holes — regions where spacetime is bent so steeply that no path leads back out, not even one travelled at the speed of light. They were long dismissed as a mathematical curiosity of the equations. In 2019 the Event Horizon Telescope published a picture of one.

So the shape of space isn't obvious, isn't fixed, and isn't decided by pure logic — it's a physical fact you have to go out and check. Two thousand years of certainty that Euclid's geometry had to be the geometry of the world turned out to be a habit of thought, not a discovery.

A catch: is the curvature a fact, or a choice?

One complication deserves its own paragraph, because it is the best objection in the neighbourhood. You never measure geometry nakedly. Every measurement of shape uses physical things — rulers, light beams, clocks — and those obey physical laws. So what an experiment tests is never the geometry alone; it is the geometry and the physics of your instruments, bundled together. Get an odd result and you have two ways out: say space is curved, or say space is flat and some force was quietly distorting your rulers.

Henri Poincaré made the point with a thought experiment. Imagine a disc-shaped world that gets colder toward the rim, in just such a way that everything shrinks as it moves outward — rulers, buildings, inhabitants alike. The residents would never notice their rulers shrinking, since everything shrinks together, and they would find the edge takes infinitely many steps to reach. Are they living in an infinite curved world, or a finite flat one full of a distorting force? Every observation comes out the same either way. Poincaré's verdict was that there is no fact being missed here: the choice is a convention, made for convenience, and he expected physicists would always keep Euclid and blame the forces. Reichenbach later made the trade precise — you can hold on to any geometry you like, provided you postulate a "universal force" that pushes on everything identically and so can never be detected. (See Conventionalism about Geometry.)

Physicists went the other way, and it is worth being clear about why, since it isn't because Poincaré was refuted. It's that the curved-space description earns its keep. Blaming an undetectable force means carrying a force whose only job is to hide a geometry — while Einstein's curvature, taken at face value, obeys equations that predicted things nobody had seen: light bending by a specific amount, Mercury's orbit drifting by a specific angle, waves at a specific speed. A convention that makes new correct predictions has stopped looking much like a convention. But the underlying worry — that fact and stipulation are harder to separate in physics than we'd like — has never fully gone away.

The other half of Question 3: what is space made of?

There's a question hiding underneath the last one. Before you ask which geometry space has, you should ask something more basic: is space made of points at all — infinitely many, packed infinitely closely — or does it come in smallest lumps, like pixels? Can you keep halving a distance forever?

The worry is 2,500 years old. Zeno of Elea pointed out that to walk across a room you must first reach the halfway mark; before that, the quarter mark; before that, the eighth. There is no first step to take, and there are infinitely many steps to get through. So how does anyone ever get anywhere? His companion puzzle: swift Achilles can never overtake a tortoise with a head start, because by the time he reaches where it was, it has crept a little further — and so on forever.

The standard answer is that infinitely many things can add up to a finite thing. The distances go 1/2 + 1/4 + 1/8 + … , and that sum is exactly 1 — not "nearly 1," not "1 if you're feeling generous," but 1. Zeno's hidden assumption was that infinitely many steps must take infinitely long; but the times shrink in the same proportion as the distances, and they too add up to a finite total. You cross the room in the ordinary number of seconds. Nailing this down rigorously is what the invention of calculus and, in the nineteenth century, the careful theory of limits was for. (See Zeno's Paradoxes and the Continuum.)

The bill for that answer: the real numbers

That resolution isn't free. It works by modelling space and time on the real numbers — the number line you met at school, including the fractions, and also the square root of 2, π, and everything else with an unending decimal expansion. Physics has taken this on board so completely that it's easy to forget it was a choice: in Newton's mechanics, in relativity, in quantum theory, spacetime is assumed to be a smooth continuum whose points are labelled by real numbers, infinitely divisible, with no smallest gap anywhere. (See The Real Numbers.)

And the real number line is a much stranger object than its tidy appearance suggests:

• Between any two points there is another — in fact infinitely many. No point has a "next" point. There is no such thing as two neighbouring positions in space.
• It is bigger than infinity. Cantor proved that the points in a one-centimetre segment cannot be put in a list, even an endless one — there are strictly more of them than there are whole numbers. And essentially all of them are unnameable: any scheme for describing numbers, in any language or notation, can only ever reach a listable few. A line contains uncountably many locations that nothing could ever pick out individually.
• Length is not the sum of the lengths of points. Each point has width zero. Put uncountably many of them side by side and you get a segment one centimetre long. That isn't a contradiction — mathematically, length is a property of sets of points rather than something accumulated point by point — but it should stop you saying "space is built out of points" too casually. Something extended is being assembled from ingredients with no extension.
• We can't even settle how many points there are. "Is there a size of infinity between the whole numbers and the points on a line?" is the continuum hypothesis, and it has been proved that our standard foundations of mathematics can neither prove nor disprove it. (See What Is Mathematical Logic?.)

There is also more than one rigorous way to build a continuum. The nineteenth century banished the infinitesimal — a quantity smaller than every positive number but not zero — as incoherent, and rebuilt calculus on limits instead. In the 1960s Abraham Robinson showed the infinitesimals had been slandered: you can have them, perfectly consistently, in a larger number system where each ordinary point is surrounded by a cloud of neighbours infinitely close to it. Both approaches give the same answers to ordinary questions, so nothing physical hangs on the choice — but it does mean "the continuum" is not a single unambiguous thing that space could straightforwardly turn out to be. (See Non-Standard Analysis.)

Is the world actually like that?

Here is the crucial split, and it's easy to miss. Resolving Zeno shows a continuum is possible — that infinite divisibility is coherent and motion through it makes sense. It does not show the world is one. That's a question for physics, and it is wide open.

The reasons to doubt it are serious. Trying to combine general relativity with quantum theory suggests a floor: the Planck length, around 10⁻³⁵ metres — as much smaller than a proton as a proton is smaller than a city — and the Planck time, the time light takes to cross it, below which the smooth picture is expected to stop making sense. Some leading approaches to quantum gravity build the graininess in deliberately — in loop quantum gravity, areas and volumes come in discrete quanta, so there's a smallest possible patch of surface the way there's a smallest possible electric charge; in causal set theory, the continuum is thrown out altogether in favour of a discrete scattering of events with nothing but a before-and-after ordering, out of which smooth spacetime is supposed to emerge at large scales. On these views the real number line is a marvellously good approximation to reality, not a description of it.

But discreteness has its own Zeno problem, and it's a sharp one. Zeno's fourth paradox, the Stadium, was aimed precisely at the idea of smallest units, and relativity adds a modern version: a fixed grid of space-atoms would be something you could move relative to, which would hand the universe exactly the preferred "at rest" frame that special relativity says doesn't exist — and the grid's spacing would contract for anyone moving through it. This is why causal set theory sprinkles its events randomly rather than lattice-fashion. Graininess that respects relativity is a demanding thing to build, not a free simplification.

And nobody has looked. The most powerful collider ever built probes down to about a ten-thousandth the width of a proton — still some ten million billion times too coarse to see anything happening at the Planck scale. At every scale we can actually measure, space and time behave as a flawless smooth continuum. So the question of whether that smoothness is a deep fact about the world or the most successful approximation in the history of science is, for now, settled by theoretical hunch rather than by experiment — which makes it one of the few genuinely ancient questions still standing more or less where Zeno left it.

Does anything have a location? Quantum mechanics and space

Everything so far has taken one thing for granted: that objects sit somewhere. Newton and Leibniz disagreed about what a place is, Einstein bent the arrangement of places out of shape, but nobody doubted that a thing has a position. Quantum mechanics doubts it.

An electron in an atom is not a tiny ball at some address we haven't yet looked up. On the standard reading it does not have a position between measurements — not "has one but we don't know it," but no fact of the matter until a measurement forces one. What it has instead is a wavefunction spread over a whole region, from which the odds of finding it here or there can be calculated. Look, and you get a definite location; stop looking, and the definiteness goes away again. (The companion page on quantum mechanics covers superposition, measurement, and uncertainty properly; what follows is only what they do to space and time.)

The asymmetry that should bother you

Here is the fact most worth carrying away from this section. In quantum mechanics, position is something you measure — an observable, usually without a definite value until you do. Time is not. Time enters the theory as a parameter: a label on the equation, an external clock ticking away in the background, the same for everybody. There is no "what time is it?" observable in the way there is a "where is it?" observable; you never find a particle in a superposition of two o'clock and half past.

So quantum mechanics treats space and time completely differently — and it does so at precisely the moment in history when relativity had finished welding them into a single four-dimensional object. Relativity says space and time are two aspects of one thing that different observers slice up differently. Quantum theory says one of them is a thing you measure and the other is a knob on the apparatus. That mismatch is not a technicality; it is a large part of why combining the two theories has defeated everyone for a century, and we will come back to what it does to time at the end of this page.

Where does the wavefunction live?

Now a question that sounds technical and isn't. For a single particle, the wavefunction is a wave spread over ordinary three-dimensional space, which is comfortable enough. For two particles it is not two waves in space. It is a single wave over a six-dimensional space — one dimension for each coordinate of each particle. For a hundred particles, three hundred dimensions; for the contents of a room, a number with no useful name.

Physicists call the arena of quantum states Hilbert space, and it is worth saying plainly what it is not: it is not a space you could walk around in, and its dimensions are not directions you could point. It is a space of possibilities, a bookkeeping arena in which each dimension records an independent way the system could be. Nothing in this section is about space in the sense the rest of this page has meant.

But that raises a genuinely spatial question. If the thing that carries all the physical information is a wave in a three-hundred-dimensional space, what is the standing of the ordinary three-dimensional space we appear to live in? Some philosophers bite the bullet — the high-dimensional arena is the real one, and familiar space is something like an appearance it generates. Others insist the wavefunction is a calculating device and the furniture of the world sits, as it always did, in three dimensions. The dispute is live and it is precisely a dispute about what space is. (See The Wavefunction.)

Does space still keep things apart?

The last casualty is the assumption that distance insulates. Prepare two particles together, send them light-years apart, and measure each. Their results are correlated — and John Bell proved in 1964 that the correlations are too strong to be explained by the particles having carried matching instructions from the start. Experiments have checked this to exhaustion, most decisively from the 1980s onward, and the instructions are not there. Whatever links the two outcomes is not a property packed at the source.

Two guardrails. Nothing is sent: you cannot use this to signal, because each result on its own looks like noise, and the correlation only appears when the two records are brought together and compared — by ordinary, slower-than-light means. Relativity's speed limit is intact. And the theorem doesn't force one specific conclusion; it forces a choice, and every remaining option gives up something we would rather keep.

Still, the flavour of the result is that spatial separation does not divide the world into independent pieces as cleanly as we assumed. Two things far apart can fail to have separate states at all. Space is still there, but one of the jobs we expected it to do — keeping distant things distinct and independent — it does not straightforwardly do. (See The Philosophy of Bell's Theorem.)

Put the three together and a suspicion forms that Newton and Leibniz never had to face. Their argument was about whether space is a substance or a system of relations. Quantum mechanics suggests a third worry: perhaps the world isn't fundamentally in space at all, and three-dimensional space is something that emerges — a good approximation at our scale to a reality organised on quite different lines. That is exactly the suspicion the quantum-gravity programmes at the end of the last section were built to chase down.

How many dimensions are there?

One more thing we have taken for granted throughout: that space has three dimensions. Left–right, forward–back, up–down, and that's the lot. Why three?

It is not a truth of logic. Mathematicians describe spaces of four, or eleven, or infinitely many dimensions without the slightest difficulty, exactly as they described curved geometries — and, as with curvature, consistency on paper says nothing about which one the world uses. So the number is a fact about our universe, and facts about the universe are supposed to have explanations.

There is at least a partial one, and it is a good deal more interesting than "because." In 1917 Paul Ehrenfest noticed that the strength of gravity and electricity depends on how many dimensions they spread out into: in three dimensions the force falls off with the square of the distance, in four with the cube, and so on. That detail turns out to be load-bearing. Only with the inverse-square law do you get stable orbits — in four or more spatial dimensions, planets either spiral into their sun or drift off at the smallest nudge, and the same argument applies to electrons around a nucleus, so you get no atoms either. In fewer than three, the possible structures are too impoverished to do anything interesting. Three dimensions may be the only setting in which the sort of thing that asks this question can exist — which is either a deep explanation or a way of changing the subject, depending on your appetite for such reasoning. Something similar goes for time: with two time dimensions, the equations of physics stop having well-posed solutions, so nothing could reliably predict anything. (See Dimensionality and the Structure of Space.)

Hiding a dimension

But if the number were larger, would we notice? Not necessarily — and the trick for hiding one is a hundred years old.

Look at a garden hose from across the field and it is a line: one dimension, position along the hose. Walk up to it, and an ant on its surface has a second direction available, around the circumference. The dimension was always there; it was just too small to register at a distance. Now do that to space itself: a fourth spatial direction, curled into a circle so small that nothing we can do gets any purchase on it.

In 1919 Theodor Kaluza tried it, and something remarkable happened. He wrote down Einstein's theory of gravity in five dimensions instead of four and found that it fell apart into two pieces: ordinary four-dimensional gravity, plus Maxwell's equations for electricity and magnetism. Two forces that had nothing to do with each other became one thing seen from a higher vantage point, and the price was a single hidden dimension. Oskar Klein later supplied the reason it stays hidden — it is rolled up at a fantastically small scale. The scheme didn't survive contact with the rest of physics, but the idea it planted did: extra dimensions can buy you unification.

A warning before going further. This has nothing to do with the curvature of Question 3. Curved spacetime, as we saw, needs no higher dimension to bend through — its curvature is measurable entirely from within. The dimensions here are extra places to go, posited for independent reasons; nobody is claiming that space needs somewhere to warp into.

Ten dimensions, and a catch

String theory takes the idea as far as it will go. Its proposal is that the fundamental objects are not points but tiny vibrating strings, with each mode of vibration appearing to us as a different kind of particle — the difference between an electron and a photon being something like the difference between two notes. It is a beautiful thought, and it comes with a bill: the mathematics is only consistent if spacetime has ten dimensions (nine of space, one of time), or eleven in its later form. The six we don't see are compactified — folded up, Kaluza-style, into an intricate shape at every point of ordinary space.

And then the payoff, which is the most extreme version of this page's recurring theme. On this picture the shape of the folded-up dimensions determines which particles exist and what their masses and charges are. Physics would be geometry, all the way down: not just gravity, as Einstein showed, but everything.

The catch is severe and worth stating plainly. Nobody has found a way to work out which shape is ours. The number of ways to fold six dimensions is often quoted as around 10⁵⁰⁰, each giving a different universe with different physics, and the theory offers no principle for picking. There is no experimental evidence for strings, no prediction anyone has managed to test and fail, and after decades of effort critics argue that a framework which can accommodate almost any outcome is not doing the job we ask of physical theories. Defenders reply that the mathematics has been too fruitful to be an accident. It is the sharpest live dispute about what should count as physics at all. (See Quantum Gravity.)

Not every version is beyond testing, though. In braneworld models the extra dimensions aren't tiny at all — they may be quite large, with everything we're made of stuck to a three-dimensional sheet, a "brane," like paint on a wall. Only gravity would spread into the extra room, which would explain something otherwise baffling: gravity is weaker than electromagnetism by a factor of about 10³⁶, a one followed by thirty-six zeros, and perhaps it seems feeble because most of it is leaking somewhere we can't go. That is checkable. If gravity spreads into extra dimensions, the inverse-square law must fail once you measure below their size. Delicate tabletop experiments have now tested it down to distances of a few tens of micrometres, and the LHC has looked for particles absconding into the bulk. Nothing so far — which has ruled out a good deal of the parameter space, exactly as a real test should.

Or perhaps there are fewer

The strangest modern possibility runs the other way. Black hole physics turned up a clue that nobody has fully digested: a black hole's entropy — roughly, the amount of information it hides — is proportional to the area of its horizon, not to the volume inside it. Information about a three-dimensional region seems to be stored on a two-dimensional surface, at one bit per tiny patch of area. That is not how volumes normally work.

This is the seed of the holographic principle: the suspicion that a gravitational universe in some number of dimensions can be exactly and completely described by a theory without gravity living on its boundary, one dimension lower. Where that has been made precise, the two descriptions are equally valid — neither is the "real" one. If something like it is true of our world, then the number of dimensions is not a bedrock fact at all but a feature of the description you happen to be using, and one of the dimensions you think you are standing in is a kind of projection. (See Black Hole Thermodynamics.)

Between the extra dimensions we might not be able to see and the dimensions that might not be there in the first place, "how many directions are there?" has gone the way of every other question on this page: from something too obvious to ask, to something nobody can currently answer.

Why can't you unbreak a cup?

Now for the question about time that everybody has actually noticed. A cup falls and shatters; the pieces never leap back together. Milk stirred into coffee never unstirs. People age in one direction. You remember yesterday and not tomorrow. Time, whatever else it is, has an arrow.

Here is the shock: nothing in the fundamental laws puts it there. Newton's mechanics, Maxwell's electromagnetism, Einstein's relativity — run any of them backwards and they work exactly as well. Film two billiard balls colliding, play it in reverse, and a physicist watching cannot object: every bounce obeys the same equations either way. But film a cup shattering, play it in reverse, and everyone in the room knows. Yet the cup is nothing but a very large number of particles, each obeying laws that don't care which way time goes. Where does the arrow come from?

Entropy, and why it isn't quite the answer

The standard reply is entropy, and it is half right. There are enormously more ways for the pieces of a cup to be scattered than to be assembled, more ways for milk to be dispersed than concentrated, more ways for a room's air to be mixed than sorted. Nothing forbids the tidy arrangements; they are simply outnumbered so catastrophically that a system shuffling among possibilities will, with overwhelming probability, be found in a messy one. The second law of thermodynamics is not a prohibition but a statement of odds — odds so lopsided that they look like a prohibition.

But now notice the flaw, which took a long time to be taken seriously. The counting argument makes no reference to the direction of time, so it works just as well backwards: given a half-mixed cup of coffee now, the same reasoning says it was probably more mixed a minute ago. That is spectacularly false. Applied to the past, the argument that explains everything predicts nothing right.

The past hypothesis

So the asymmetry cannot come from the dynamics or from the counting. It has to be put in by hand, as a fact about how things started: the universe began in a state of extraordinarily low entropy, and everything has been running down ever since. Philosophers call this the past hypothesis, and it is doing more work than any other single assumption in this area — every asymmetry in your life is a downstream consequence of it.

Two things make it uncomfortable. First, low entropy at the Big Bang is not obviously what you'd expect: the early universe looks smooth and featureless, which for ordinary gases would mean high entropy, but under gravity smoothness is the unlikely, low-entropy state, since gravitating matter wants to clump. Second, nobody knows why the universe started that way. The explanation of time's arrow bottoms out in a boundary condition that is itself unexplained, which is not so much an answer as a very precise relocation of the question. (See The Arrow of Time and The Thermodynamic Arrow.)

Why you remember the past and not the future

The strangest part is that this reaches all the way into your head. A memory, a photograph, a footprint, a fossil — every record is a bit of order that was left behind, and leaving order behind requires having started from something more ordered still. Records of the past are possible for exactly the reason the past is low-entropy; records of the future are not, for exactly the reason it isn't.

Which suggests that the felt difference between a fixed past and an open future — the very thing that makes passage seem so obvious, and that Question 2 tried and failed to find in the physics — may not be a feature of time at all. It may be a feature of living in the aftermath of an unusually tidy beginning.

Why is space getting bigger?

Something has been missing from this page. We have asked whether space is real, what shape it is, and what curves it — but not what it is doing. It turns out to be doing something dramatic.

In 1929 Edwin Hubble established that distant galaxies are receding from us, and that the further away one is, the faster it goes. The natural reading is that we are at the centre of a great explosion, everything flying away from us. That reading is wrong, and the correct one is stranger.

Space itself is expanding. The galaxies are not travelling through space away from each other; the space between them is growing. Picture a raisin loaf rising in the oven: no raisin is moving through the dough, yet every raisin gets further from every other, and from the point of view of any one raisin, the distant ones recede fastest. Or take a balloon with dots inked on it and inflate it — the dots stay put on the rubber and separate anyway.

That analogy pays off immediately. Where did the Big Bang happen? Everywhere. It was not an explosion at a place in space; it was a condition of the whole of space, which was then much denser. There is no centre to point at and no edge to find; every observer anywhere sees the same recession in every direction, exactly as we do. And a second surprise: sufficiently distant galaxies recede faster than light, which is entirely permitted, because they are not moving through space. Relativity's speed limit governs things travelling in spacetime; it says nothing about how fast spacetime may stretch.

What we can see, and what there is

Because light takes time to arrive and the universe has a finite age, there is a horizon: a distance beyond which nothing has yet had time to reach us. That is the observable universe, about 46 billion light-years in radius — larger than 13.8 billion, the age in years, precisely because the intervening space has grown while the light was in transit. The horizon is not an edge of space. It is an edge of news.

Worse, or at least sadder: the expansion is speeding up, so galaxies are drifting past that horizon permanently. Astronomers in the far future will find a much emptier sky and much less evidence about how any of it began.

Is space finite or infinite, then? Measurements of the geometry come out flat to within a small fraction of a percent — but flatness does not settle it. A flat space can still be finite if it wraps around, like the screen of an old arcade game where flying off the right edge brings you back on the left. If it does, the same patch of sky should appear twice in the oldest light; people have searched for the repeats and found none, which pushes any wrap-around out beyond the horizon. So the honest answer is that we don't know, and may not be able to. (See Dimensionality and the Structure of Space.)

Did time have a beginning?

Run the expansion backwards and everything grows denser and hotter until, about 13.8 billion years ago, the equations report an infinity — which is how a theory says it has stopped applying. Whether that moment was the first moment, or whether time continued through it into something else, is exactly what our current physics cannot tell us.

If it was the first, the obvious question — what came before? — may be malformed. Saint Augustine got there 1,600 years early, answering that God made the world with time rather than in it, so there was no earlier when. Kant turned the difficulty into his first antinomy, arguing that both answers are provable: the world must have had a beginning, since otherwise an infinite stretch of history would have had to be completed to arrive at today; and the world cannot have had a beginning, since a first moment would need an empty time before it, with nothing to explain why things started then rather than sooner. Two sound-looking proofs of contradictory conclusions was, for Kant, evidence that time is not a feature of reality itself but of how reality appears to us. (See Time, Cosmology, and the Beginning.)

Could you visit your own past?

One direction of time travel is not merely possible but routine. Move fast, come back, and less time will have passed for you than for everyone else — you have travelled into their future. The astronaut Sergei Krikalev, who spent over two years in orbit, is a fraction of a second younger than he would have been on the ground. It is a real effect, measured constantly, and it is only a question of engineering how far you take it.

Going the other way is the hard problem, and the surprise is that our best theory of space and time does not forbid it.

Gödel's universe

In 1949 the logician Kurt Gödel gave Einstein a birthday present: a solution to the equations of general relativity describing a universe that rotates. In it, the rotation drags the light cones around so far that a sufficiently determined traveller, always moving forward through their own local time, can arrive back at their own past. Not a fantasy or an approximation — an exact solution of the field equations, sitting there in the theory.

Our universe is not that one; it doesn't rotate measurably and it does expand. But Gödel's point was never astronomical. If the laws governing our world permit worlds where time loops, then time cannot be, of its nature, the sort of thing that flows uniformly from past to future — a lapsing that is essential to time itself cannot be optional in some universes. Gödel drew a conclusion in the spirit of Kant and of the block universe: the passage we experience is our contribution, not the world's. (See Time Travel.)

The grandfather paradox, defused

Everyone's objection: go back and prevent your own birth, and you get a contradiction, so time travel must be impossible.

The standard reply is more interesting than either "it's impossible" or "you'd create a new timeline." It is that the past is not something you can change, because there is only one past and you were already in it. If you travel back, whatever you do there is part of the history that led to your setting off. You may try to shoot your grandfather; the gun jams, or you miss, or the man you shoot turns out not to be him. Not because a mysterious force protects history, but because the only sequences of events that exist are the consistent ones. You are free to act; you are not free to make what happened not have happened.

This is unsettling in a specific way: it means you could find yourself unable to do something perfectly ordinary — like fire a working gun at a stationary target — for no local reason whatsoever.

Why physicists remain sceptical

None of which makes a time machine likely. Every known scheme for building one requires matter with negative energy density, in quantities and configurations nobody knows how to obtain, and Stephen Hawking's chronology protection conjecture proposes that quantum effects blow up violently around any would-be loop and destroy it before it can form. The conjecture is unproven — it would take the missing theory of quantum gravity to settle — but it captures the general suspicion that nature has a way of forbidding this that we haven't found yet.

The reason it matters here isn't the machine. It is that a hundred years of trying has not produced a proof that the past is closed. Whatever makes the future feel open and the past feel fixed, our best physics has not so far been willing to certify it.

And then time goes missing

One last result, and it is the strangest on this page.

Recall the mismatch from the quantum section: quantum theory treats time as an external parameter, a clock on the wall that ticks the same for everyone, while general relativity treats it as part of the very thing being solved for. When physicists try to quantise gravity — to apply the quantum rules to spacetime itself — that conflict has to be resolved, and the resolution is brutal. The central equation comes out with no time in it at all. The state of the universe does not evolve; it simply is. Physicists call this the frozen formalism, and the difficulty of making sense of it is called the problem of time.

Nobody thinks this means nothing ever happens, so the interesting work is in explaining why we seem to be in a world where things do. The most attractive suggestion is that time is relational all the way down: there is no cosmic clock, but the universe contains subsystems that are correlated, and any part of it that keeps a record of another part will find that the correlations line up exactly as they would if there were a flow. Time, on this view, is not something the universe moves through — it is something an insider infers from the way its pieces are arranged. A static whole, containing observers who cannot help experiencing history.

If that has a familiar ring, it should. The block universe reached almost the same conclusion from philosophy and relativity alone, a century earlier, without any of this machinery. Quantum gravity may be arriving at the same destination by a very different road — one on which time is not merely unmoving, but not fundamental at all. (See The Problem of Time.)

A different question: time as it is lived

Step back, because there is a tradition that would say this whole page has been answering the second question first.

Everything above treats time as something out in the world, to be measured, mapped, and if necessary eliminated. Another line of thought — running through Augustine, and taken up in the twentieth century by Husserl, Bergson, and Heidegger — starts from the other end. Not what is time? but: what is it to be temporal? What is time like for the kind of creature that has one?

The opening observation is that lived time is nothing like a row of instants. You do not hear a sequence of separate tones; you hear a melody, in which the note just gone is still somehow present and the next is already leaning in. Husserl called those the retention and protention built into every moment of awareness, and concluded that the present we actually inhabit has thickness — it is not the knife-edge instant that physics uses. Whatever the "now" in the equations is, nobody has ever experienced one. (See Temporal Passage and the Experience of Time.)

Bergson takes on Einstein, and loses

Henri Bergson pushed this into a confrontation. Real time, he argued, is durée — an indivisible flowing known from the inside, and the moment you lay it out as a line with positions along it you have converted time into space and mislaid the very thing you meant to describe. In April 1922, at a meeting in Paris, he put this to Einstein directly: the clock effects of relativity concern readings on instruments, not the single real duration in which we all live.

Einstein's reply was flat and famous — there is the time of the psychologist and the time of the physicist, and the time of the philosophers does not exist. It was a rout. Bergson's specific claims about relativity turned out to be mistaken, and his standing among scientists never recovered.

But it is worth being precise about what was settled. Einstein showed that lived duration is not a rival physics — not that it is unimportant, and not that there is nothing there. Bergson's error was to enter his insight in a competition it was never equipped to win.

Heidegger's inversion

Heidegger's Being and Time (1927) makes the bolder move: it treats the physicists' time as the derived thing. The picture of time as an endless uniform sequence of now-points is, on his account, an abstraction we reach by stripping away how time is actually encountered — and we mistake the residue for the original.

What gets stripped away is that we do not sit in time the way a stone sits in a river. To be the kind of being we are is to be stretched out: always taking up a past we did not choose, occupied with a present, and pressing into a future. And the whole structure takes its shape from having an end. A life is finite, the future one presses toward is one that runs out, and that is what makes any moment matter more than any other. Clock time — the indifferent sequence in which one instant is exactly as good as the next — is precisely what is left once you have removed everything that made it someone's.

The same book does it for space, and here it lands directly on Question 1. Nearness in lived space, Heidegger notes, is not distance in metres: the spectacles on your nose are further away than the picture across the room you are looking at, and the person you are talking to on the phone is nearer than the wall behind you. The space you actually inhabit is organised by concern and use. That is a relationism of a wholly different kind from Leibniz's — the relations are ones of significance, not of distance. (See The Question of Being.)

Is this a rival to relativity?

Almost certainly not, and the errors are available in both directions.

When a physicist says the flow of time is an illusion, the claim is that no term in the equations answers to it. That leaves completely untouched the question of what it is to live something that has a shape, a direction, and an ending — which is a question, and not a confused version of the physics one. Equally, when a phenomenologist says the physicists' time is a derived abstraction, that is not a discovery that clocks are wrong, and it predicts nothing. Bergson came to grief by running the two together; the opposite mistake is to conclude that because physics found no passage, there was nothing there to be explained.

Question 2 left open the possibility that the flow of time is "a feature of us." This is the tradition that took that seriously and went to look — not to explain the feeling away, but to describe what it is a feeling of.

A few more rabbit holes

Once you pull on these threads, wonderful puzzles tumble out:

• How do we even measure time and space? There is no master clock or master ruler hanging in the universe. A second is officially defined as so many billion vibrations of a caesium atom, and since 1983 a metre is defined as the distance light travels in a tiny sliver of a second. So we now measure distance in terms of time — space and time are knitted together even in the definitions of our everyday units. (See Space and Time in Special Relativity.)
• Is anything really at rest? Relativity says no: there is no experiment that reveals who is truly standing still, which is why Alice on the platform had no privilege over Bob on the train. And yet — the faint afterglow of the Big Bang fills all of space, and there is exactly one state of motion in which it looks the same in every direction. By that standard we are moving at about 370 kilometres per second, and the direction is known. This does not smuggle Newton's absolute space back in: it is a fact about the contents of the universe, not the stage, and it restores neither a universal "now" nor a preferred physics. But it does mean the universe supplies a natural frame to keep time in, even though it is under no obligation to.

Why it matters

You might think none of this touches daily life — but the ideas are quietly enormous. If the block universe is right, then in some sense every moment of your life is permanently part of the world's furniture rather than something that gets erased as it passes — a thought some people find consoling and others find airless, and which no amount of physics will settle for you. If "now" is not universal, then our deepest intuition about time is simply mistaken. If the arrow of time traces to a boundary condition on the early universe, then even the difference between a settled past and an open future is a local accident of when we happen to live. And the fact that plain thinking about space and time could be overturned by experiment is one of the great lessons of science: even the things that seem most obvious, most built-in, most impossible-to-doubt, can turn out to work in ways no one imagined.

Space and time are the stage on which everything else happens. It turns out the stage has a plot of its own.

Where to go next

For the philosophical treatment — the arguments laid out properly, with their objections and replies — start at What Is the Philosophy of Space and Time?. The three questions above map onto Substantivalism and Relationism, The Nature of Time, and Space and Geometry.

For the physics itself, with the equations, the technical Physics section begins with the Postulates of Special Relativity — the two short assumptions from which every surprise on this page follows — and builds through Spacetime to General Relativity and the Einstein field equations. Quantum Gravity surveys the programmes competing to finish the job.

If the continuum was the part that caught you, the mathematics behind it is in The Real Numbers and, for the infinitesimal road not taken, Non-Standard Analysis. If it was the geometry, the Geometry section starts from Euclid's axioms and works through the parallel postulate to the non-Euclidean geometries and curvature; the machinery Einstein needed is developed in Differential Geometry.

And for another deep question given the same plain-language treatment, see What Is Free Will? — which turns out to share a border with this one, since whether the future is already out there is exactly what a block universe seems to settle.