Epimystic — Physics

The Sun Does Not Send Us Energy

Mon, 31 Aug 2026 00:00:00 GMT

Here is a fact that ought to be more disturbing than it is. Over any reasonable stretch of time, Earth radiates back into space almost exactly as much energy as it receives from the sun. The imbalance—the part that is currently heating the planet, and which is an emergency—runs at about nine tenths of a watt per square metre against an incoming flux of two hundred and forty. Better than a 99.6 per cent match.

So energy does not accumulate here. It arrives and it leaves. Which raises a question that sounds naive and is not: if nothing is piling up, what exactly is the sun providing that makes forests and hurricanes and cities possible? You cannot build anything out of a quantity that leaves as fast as it comes in.

The answer is that the sun is not supplying energy. It is supplying order—or, put the way a physicist would, it delivers energy in a low-entropy form and Earth returns it in a high-entropy one, and the difference between those two is the entire budget out of which every ordered thing on this planet, including you, is paid for.

The Photon Accounting

You can see it most clearly by counting photons rather than joules.

Sunlight arrives from a surface at about 5,772 kelvin. Earth radiates from an effective temperature of about 255 kelvin. For thermal radiation, the average energy per photon is proportional to the temperature of the source. So if the energy flowing in and the energy flowing out are equal, but each outgoing photon carries roughly a twenty-second of the energy of an incoming one, then about twenty-two photons must leave for every one that arrives.

Figure: The trade that funds the biosphere. One high-energy photon arrives from a 5,800-kelvin surface; about twenty-two low-energy photons depart from a 255-kelvin one. The energy books balance almost exactly. What does not balance is the number of ways the energy can be arranged—and that difference, roughly six hundred trillion watts per kelvin for the whole planet, is the entropy Earth exports every second. Everything ordered here is paid for out of it: weather, oceans, forests, cities, and the fact that you are a temporary structure rather than a warm puddle. — drawn in the essay

Twenty-two ways to distribute the energy instead of one. That is the whole trick, and it is measurable: the planet exports entropy at roughly six hundred trillion watts per kelvin. Most of that is bare radiative degradation—sunlight becoming heat—but a slice of it, somewhere between three and six per cent, is produced by the irreversible processes of the climate system itself: winds, currents, the water cycle, the whole restless machinery.

This is the correct way to understand a living planet. It is not a system that accumulates energy. It is a gradient, standing between a very hot source and a very cold sink, and everything interesting that happens here happens in the flow between them.

What the Gradient Buys, in Watts

Earth absorbs about 122,000 terawatts of sunlight after reflection. That is the budget. Here is what it is spent on.

Global photosynthesis fixes something like 105 billion tonnes of carbon a year, which works out at roughly 130 terawatts of chemical free energy. Against 122,000 terawatts of absorbed sunlight, that is about one tenth of one per cent. The entire biosphere—every forest, every plankton bloom, four billion years of it—captures a thousandth of what arrives.

The atmosphere is far greedier: the planet’s total generation of free energy runs to about 6,300 terawatts, almost all of it geophysical—the winds, the lifting of water, the ocean circulation. Life is a rounding error on the weather.

And humanity? Global primary energy consumption is around 590 exajoules a year, which as a continuous power is about 18.7 terawatts. Set against absorbed sunlight that is 0.015 per cent—a number so small it is regularly used to argue that human energy use is trivially sustainable.

But that is the wrong denominator, and this is the most important comparison in the essay. Set 18.7 terawatts against the 130 terawatts of global photosynthesis and you get about fourteen per cent. One species is now running an energy flow equal to roughly a seventh of what all photosynthetic life on Earth manages. That is the ratio that should be quoted, and it almost never is.

Entropy and Information Are Not the Same Thing

Now to the second half, and to a confusion that has to be cleared before anything else can be said honestly.

“S = k log W”
the inscription on Boltzmann’s grave, Vienna

Boltzmann’s entropy counts the number of microscopic arrangements consistent with what you can see macroscopically. Shannon’s information entropy, written down eighty years later, has an almost identical form: a sum over probabilities times their logarithms. The resemblance is exact and it has generated an enormous amount of loose talk.

Here is the careful statement. The two coincide only when the probability distribution in question is over the physical microstates of the system you are talking about. When that condition holds, one bit corresponds to about 9.6 × 10⁻²⁴ joules per kelvin. When it does not, the two quantities are simply unrelated numbers that happen to share an equation.

The scale of the gap is worth feeling. Take a one-terabyte drive. Its thermodynamic entropy—over the positions and momenta of every atom in the thing—is on the order of a thousand joules per kelvin. The Shannon entropy of the files on it, converted to the same units, is about ten billionths of a joule per kelvin. Fourteen orders of magnitude apart. The bits you care about are a vanishingly thin layer of structure on top of an ocean of microscopic degrees of freedom that do not care what you saved.

So no: information is not entropy, deleting your photographs does not measurably warm the room, and the fact that both are written with a logarithm is a mathematical fact about counting, not a bridge between physics and meaning.

But There Is a Real Bridge, and It Is Narrow

The genuine connection was found by Rolf Landauer in 1961 and it concerns one specific operation. Erasing a bit—taking a system that could be in either of two states and forcing it into one, discarding which it was—must dissipate at least k_B T ln 2 of heat into the surroundings.

At room temperature that is 2.87 × 10⁻²¹ joules, or about eighteen thousandths of an electron-volt. It is a preposterously small quantity and its importance is entirely conceptual: it is the point at which a fact about logic becomes a fact about heat.

Two things about it are constantly got wrong. First, it is erasure that costs, not computation. A logically reversible operation—one you could run backwards to recover its inputs—has no thermodynamic floor at all. The bill is charged for throwing information away. Second, the bound is attained only in the limit of infinite slowness; any erasure performed at a finite speed costs strictly more.

It has been measured. The first confirmation, in 2012, watched a single colloidal particle pushed between two wells of an optical trap and found the dissipated heat saturating at the bound. By 2021 an experiment using an underdamped micromechanical oscillator was hitting the limit to within one per cent in protocols lasting a tenth of a second.

This is also what finally killed Maxwell’s demon, and the resolution is not the one usually taught. Szilard and Brillouin thought the demon was defeated by the cost of measurement. Charles Bennett showed that measurement can in principle be done reversibly, for free—and that the irreducible cost is clearing the demon’s memory so it can start the next cycle. The demon does not fail because looking is expensive. It fails because forgetting is.

Real demons have since been built. In 2010 a Brownian particle was ratcheted up a spiral potential by feedback alone, converting information into free energy. In 2015 an autonomous single-electron device on a chip acted as an information-powered refrigerator—cooling the system it was watching while the demon circuitry itself heated up, the bill arriving exactly where the theory says it should.

You will also see occasional headlines about erasure below the Landauer bound. They are real experiments and none of them breaks anything: each pays somewhere else—a bath held out of equilibrium, a squeezed memory, an asymmetric potential. The most recent, from early this year, went more than twenty per cent below the bound, and its own authors identify the mechanism as an embedded Maxwell demon exploiting information hidden in the apparatus’s hysteresis. The generalised bound holds. It always has.

How Far Is Our Computing From the Floor?

Nowhere near it, and the size of the gap is the single most clarifying number in this whole subject.

Figure: Energy per bit operation, on a logarithmic scale spanning nine decades. On the left, the thermodynamic floor: 2.87 × 10⁻²¹ joules to erase one bit at room temperature. In the middle, the energy a transistor actually needs to switch reliably against noise—already ten to a few hundred times the floor. On the right, what a current high-end accelerator spends per elementary bit operation once interconnect, memory traffic, leakage and error margins are included. The distance between the two marked points is roughly a factor of a million, and essentially all of it is engineering rather than physics. — drawn in the essay

A current high-end accelerator delivers around 0.7 picojoules per low-precision arithmetic operation. Since one such operation involves on the order of a thousand elementary bit manipulations, the cost per bit operation lands somewhere around a hundred thousand times the Landauer bound; per whole operation the factor is nearer a hundred million. A recent review compresses it to: real devices use about a million times more energy per operation than thermodynamics requires.

Now do the arithmetic that follows. Even taking the most aggressive estimate of how many bits the world produces annually and imagining every one of them erased, the total Landauer cost would be a few joules per year. Not gigawatts. Joules. Enough to lift an apple off a table.

The thermodynamic limit is not a constraint on anything we are doing or will do this century. Whatever is making data centres expensive, it is not the second law. It is gate capacitance, wire resistance, leakage current, the redundancy needed for reliable switching, and the fact that heat has to physically leave a building.

What has changed, and is genuinely worrying, is the rate of improvement. Koomey’s law held that computations per joule doubled every 1.57 years from the 1940s to about 2000—a hundredfold gain per decade. After 2000, with the end of Dennard scaling, the doubling time stretched to about two and a half years. An independent re-examination in 2024, looking at high-performance systems from 2008 to 2023, found efficiency doubling every 2.29 years while raw performance doubled every 1.85. Efficiency is now improving more slowly than capability, which is a new and structurally uncomfortable situation: every generation is more capable and each unit of capability costs relatively more.

The Planet’s Information Budget, With the Honest Caveats

How much information does the technosphere hold? The honest answer begins with an admission: we measured this properly exactly once.

Martin Hilbert and Priscila López spent years constructing an inventory across sixty technology categories from 1986 to 2007, in optimally compressed bytes. Their results are the only rigorous historical figures anyone has. Total storage: 2.6 exabytes in 1986, 295 exabytes in 2007. And the transition buried inside that: the digital share of all stored information went from 0.8 per cent in 1986 to 25 per cent in 2000 to 94 per cent in 2007. The changeover from analogue to digital as humanity’s memory happened inside a single decade, and mostly inside seven years of it.

After 2007, the study stops, and everything you have ever read about zettabytes is an industry forecast of a different quantity. The widely quoted figures—around 181 zettabytes for 2025—measure data *created, captured, copied and consumed* in a year. Most of that is transient: video streams nobody stores, sensor telemetry discarded on arrival, replicas of replicas. The stock is smaller than the flow by roughly two orders of magnitude, and no methodologically transparent number for the stock exists after 2007.

Figure: Two archives, on a logarithmic scale of bits. At the top, the last rigorously measured stock of human information: 295 exabytes in 2007. In the middle, the industry estimate for data created in a year now—a flow, not a stock, and mostly transient. At the bottom, the DNA in living cells across the biosphere, at two bits per base pair. The biosphere’s archive is around fourteen orders of magnitude larger than a year of everything humanity produces, and it has been maintained, copied and error-corrected continuously for about four billion years. — drawn in the essay

For scale, put the biosphere on the same axis. A 2015 estimate put the total DNA in living cells at about 5 × 10³⁷ base pairs—roughly 10³⁸ bits at two bits a pair, held in something like 5 × 10³⁰ cells. That is around fourteen orders of magnitude more than everything humanity generates in a year, and unlike our data it is all in active use, all being copied, and all being error-corrected.

There is a companion figure I find genuinely arresting. Modelling chemical reactions as elementary logical operations, Seth Lloyd and a collaborator estimated that all life on Earth performs somewhere between 10³³ and 10³⁵ such operations per second—and that a single human being performs around 10²⁰ to 10²², which they argue is comparable to the total information-processing capacity of every computer, phone and server on the planet combined. At most a few per cent of that occurs in neural firing. The overwhelming majority is metabolism: your cells, doing chemistry.

What the Machines Actually Cost

Since this is where the public argument sits, the numbers deserve stating plainly. Data centres consumed about 415 terawatt-hours of electricity in 2024 and around 485 in 2025—a little over 1.5 per cent of global electricity. The International Energy Agency’s base case has them reaching roughly 950 terawatt-hours by 2030, close to 3 per cent, with the AI share of that rising from somewhere between 5 and 15 per cent today to perhaps 35 to 50 per cent.

Three per cent is a real number and worth arguing about. It is not the ten or twenty per cent that circulates, and using the inflated figure makes the genuine local problems—grid queues, water, transmission—easier for their proponents to dismiss.

The IEA also supplies the counterpoint, and it is the more interesting half. Energy per AI task has been falling by at least an order of magnitude annually in recent years. Total demand is rising anyway, because usage is growing faster than efficiency. That is a Jevons dynamic, not a physical limit—which means it is a question about economics and policy rather than about thermodynamics, and it will not be solved by a better chip.

One more piece of accounting, because it puts the technosphere in its place. Human-made mass overtook all living biomass around 2020, give or take six years, and it has been doubling roughly every twenty years. Roughly 1.1 trillion tonnes of life; rather more than that of concrete, aggregate, asphalt, brick, metal and plastic. Whatever we are building, it now outweighs everything that grew.

A Catastrophe That Is Not One

You may have encountered the claim that information has mass and that we are heading for an “information catastrophe.” It deserves reporting precisely and then deflating, because it is the sort of idea that survives on not being examined.

The proposal is that a stored bit possesses a rest mass of about 3.2 × 10⁻³⁸ kilograms, and that at twenty per cent annual growth in bit production, digital content would outnumber Earth’s atoms in about three hundred and fifty years and exceed half the planet’s mass in five hundred.

The mass figure is exactly the Landauer energy divided by the speed of light squared. Which means the proposal equates the heat dissipated when a bit is erased with the rest mass of a bit while it is stored. Those are different quantities; there is no reason a storage state should weigh what its destruction radiates. A rebuttal published in a physics journal argues the identification is unsound in principle, the proposed experiment—weigh a full drive against an empty one—has produced no confirmed result, and the catastrophe follows entirely from compounding twenty per cent for two and a half centuries. Compound any exponential for two hundred and fifty years and it eats the planet. That is a fact about exponentials, not about information.

Where Quantum Mechanics Comes In

It is not decoration. Quantum mechanics changes what information *is* in ways that matter for everything above.

Start with a fact that has no classical analogue. Two particles can be in a maximally entangled pure state, in which the pair as a whole has exactly zero entropy—there is nothing you do not know about it—while each particle taken alone has the maximum possible entropy. The information is not in the parts. It is in the relation, and no examination of either half will find it.

Which leads to the area law, one of the loveliest results in many-body physics. For the ground state of a system whose interactions are local, the entanglement entropy of a region scales not with its volume but with the area of its boundary. The information binding a chunk of matter to its surroundings lives on the surface. This is why tensor-network methods can simulate quantum systems at all, and it is the many-body echo of the fact that a black hole’s entropy is proportional to the area of its horizon rather than the volume inside.

Quantum information is also, in principle, indestructible. The no-cloning theorem says an unknown state cannot be copied; the no-deleting theorem, its mirror, says that given two copies you cannot cleanly destroy one. Both follow from linearity, and both express the deeper point that Schrödinger evolution is unitary and therefore reversible. Information is conserved. That is precisely why Hawking’s 1974 calculation—a pure quantum state collapsing into a black hole and emerging as thermal radiation carrying no memory of it—was a paradox rather than a curiosity.

The story since 2019 is genuinely exciting and routinely overstated. Using quantum extremal surfaces and gravitational path integrals that include replica wormholes, several groups derived the Page curve—the turnover in radiation entropy that unitarity demands—from gravity itself, in controlled low-dimensional models. That is a real achievement.

But it is not a solved problem, and papers published this year say so. Whether the “island” prescription describes genuine information recovery in four-dimensional gravity with dynamical, massless gravitons—or is an artefact of coupling the black hole to an external reservoir and then restricting which observables you allow—remains actively disputed as of early 2026. Anyone who tells you the information paradox was settled in 2019 is describing a model, not the universe.

The last piece is quantum Darwinism, and it answers a question the rest of this essay assumes. Why is there a classical world at all—one where facts are objective and many people can check the same thing without disturbing it? Wojciech Zurek’s answer is that the environment acts as a broadcast channel. A system’s pointer states—the ones robust against decoherence—get imprinted redundantly into many independent fragments of the surroundings, so that thousands of observers can each read a separate copy and agree. Superpositions do not proliferate, so nobody sees them. Objectivity is redundancy, and it has been tested experimentally on nitrogen-vacancy centres, photonic simulators and quantum hardware since 2018.

The Room That Is Left

Which brings me to the number I find hardest to stop thinking about.

The entropy of the observable universe has been carefully totalled. It comes to about 3 × 10¹⁰⁴ in units of Boltzmann’s constant, and it is overwhelmingly dominated by supermassive black holes—so much so that every star, every photon of the microwave background, every neutrino and every atom of gas together contribute less than a millionth of a per cent. On the entropy ledger, the visible universe is black holes and rounding errors.

Now compare that with the maximum the universe is permitted, given by the area of the cosmic event horizon: about 2.6 × 10¹²².

Figure: Everything, and the room it has left. The rungs are the entropy of the observable universe’s components in units of Boltzmann’s constant, on a logarithmic scale: the stars, the microwave background, stellar-mass black holes, and—dominating the total—the supermassive black holes at galactic centres. The top line is the entropy the cosmic horizon permits. The gap between the two is eighteen orders of magnitude, and it is not an idle fact. It is the reason any ordered structure is thermodynamically allowed to exist at all. — drawn in the essay

Eighteen orders of magnitude of unused capacity. The universe has run for nearly fourteen billion years and used up perhaps a million-billion-billionth of its entropy budget. It is not, as the Victorians feared, drifting toward an imminent heat death. It is barely started.

And that headroom is not a curiosity. It is the precondition for everything. Ordered structures—stars, galaxies, cells, brains, sentences—can exist only where there is somewhere for their disorder to go. A universe near equilibrium permits nothing. This one has room to spare, and the whole history of complexity is a history of local structures exploiting that gap.

The same reasoning sets the ceilings on computation. The holographic bound allows about one bit per four Planck areas—roughly 10⁶⁹ bits per square metre of enclosing surface. Seth Lloyd worked out what a kilogram of matter in a litre of volume could do if every degree of freedom were used: about 5 × 10⁵⁰ operations per second on 10³¹ bits. A current supercomputer is around thirty orders of magnitude short on speed. We are not near any limit that physics imposes.

What This Adds Up To

Every ordered thing is paid for by exporting disorder somewhere else. A crystal forming, a cell dividing, a sentence being written, a data centre running—each is a local decrease in entropy funded by a larger increase outside. Earth has been running that trade at six hundred trillion watts per kelvin for four billion years, and the trade is not close to exhausting either the sun or the sky.

What is new is not that we use energy. We use fifteen thousandths of one per cent of what arrives, and the thermodynamic floor beneath our computing is a factor of a million below where we operate. We are nowhere near any limit that nature has set.

What is new is the rate at which one species has begun organising matter—an energy throughput around a seventh of all photosynthesis, an artefact mass now exceeding all life and doubling every twenty years, and an information stock whose growth rate outran every previous technology by an order of magnitude in the two decades we bothered to measure it.

And there is a final asymmetry worth ending on. The constraints that will actually bind in the next few decades are not the ones in this essay. They are grids, water, transmission queues, planning permission and politics. Physics has left us an almost unimaginable amount of room. The ceilings we are hitting are the ones we built ourselves, which is a more tractable problem than the second law—and a considerably more embarrassing one.

Stop Drawing Me as a Little Ball

Wed, 19 Aug 2026 00:00:00 GMT

Let us begin with the diagram. You know the one. A fat circle in the middle labelled ‘nucleus’, and then me—a small, tidy, extremely solid-looking dot—whizzing round it on a neat elliptical track, like a moon, or a tetherball, or something you could photograph if you had a fast enough shutter. That diagram is on the wall of every classroom on your planet. It is on the side of nuclear power stations. It was the logo of an entire atomic age. It has been wrong since 1926, which by your own reckoning is a hundred years ago, and I would like somebody to take it down.

I am not a little ball. I have never been a little ball. I do not have a surface, I do not have a radius anybody has ever measured, and I am not, at this moment or any other, at a particular place. What I am is more like a rumour with a shape—a spread of possibility, thicker in some regions than others, filling the space around that nucleus in a standing pattern that has a form but no location. Your chemists have known this for a century; they call the patterns orbitals and they draw them properly, in lobes and shells. Then everyone goes back to the dot on the little racetrack, because the dot is easier to print.

Figure: Left: what you keep drawing. Right: what is actually there. The second one has no dot in it anywhere, at any magnification, and the shading is not a swarm of tiny mes—it is the density of a single thing that does not have a position. — drawn in the essay

On the Rumour That I Am in Two Places at Once

This one has got badly out of hand and I blame popular science television. The phrase you like is that I am ‘in two places at once’, which sounds thrilling and is, I am sorry to report, not what happens. Being in two places at once would require me to have places, which is the thing I have just spent two paragraphs explaining that I do not have. Saying I am in two places is like asking which specific note a chord is playing. It is a category error dressed up as a fun fact.

What actually happens is that I arrive at your barrier with the two slits in it as a spread, I pass through as a spread, the spread comes out the other side in two overlapping regions, and those regions interfere with each other in the perfectly ordinary way that any two overlapping waves do. Where crest meets crest you are more likely to find me; where crest meets trough you are essentially never going to. Run this long enough and you get stripes on your detector. Not because I split. Not because I made a decision and then a second, contradictory decision. Because I was never the kind of thing that has to pick a slit, and your insistence that I must have is your problem, not mine.

The genuinely funny part is what happens when you cheat. Put a detector at the slits to catch me choosing, and the stripes vanish. You then write excited things about how I ‘knew I was being watched’. I did not know anything. I do not have opinions about your equipment. What changed is that the two possible histories stopped being interchangeable—once the world contains a record distinguishing them, they cannot overlap, and things that cannot overlap cannot interfere. It is bookkeeping, not stage fright. And no, this does not require a conscious observer; a dust grain will do it, and dust is not famous for its inner life.

Things I Am Regularly Accused Of

That I am spinning. I am not spinning. I have something your physicists insist on calling spin, which behaves mathematically a bit like rotation and gives me a small magnetic personality, but I have no size to rotate and no surface to rotate with, and if you calculate how fast my nonexistent equator would have to travel to produce it, the answer comfortably exceeds the speed of light. So: not spinning. The name is a historical accident and everyone involved knows it and nobody will change it.

That you can pin me down if you are careful enough. You cannot, and the reason is not that your instruments are clumsy. It is that sharply located and sharply moving are two descriptions that cannot both apply to a wave—squeeze one and the other necessarily spreads, which is a fact about waves that your engineers have known since long before anyone met me. You did not discover a limit on measurement. You discovered a limit on what there is to measure.

That I am occasionally on the wrong side of a wall. This one, I grant you. This one I do. If there is a barrier I do not have the energy to climb, my spread does not stop dead at its face—it drops off sharply inside, and if the wall is thin enough, a little of it is still there on the far side, which means that sometimes, so am I. You call it tunnelling and treat it as exotic. It is how your Sun works: hydrogen nuclei that classically could never get close enough to fuse do so anyway, several hundred million tonnes a second, entirely on this technicality. You are alive because I am bad at respecting walls.

Figure: The wall, and my opinion of it. My amplitude arrives from the left, falls away steeply inside the barrier rather than stopping at it, and emerges on the right much diminished but not zero. That small remainder is the whole of stellar fusion, the scanning tunnelling microscope, and every flash drive you own. — drawn in the essay

There Is No Me

I should clear up something about the pronoun, since I have been using it freely. There is no me. Electrons are not merely similar to one another in the way that two coins from the same mint are similar; we are genuinely, absolutely interchangeable, with no property whatever that could distinguish one from another. You cannot tag me. You cannot follow me. If two of us pass through a region and two come out, there is no fact about which one is which—not a fact you failed to measure, a fact that does not exist.

This is not a philosophical flourish, it has consequences you are currently sitting on. Because we are identical in that strict sense, we are forbidden from crowding into the same state—your Pauli called it exclusion—and so we stack, shell upon shell, refusing to overlap. That refusal is why atoms have volume, why chemistry has a periodic table rather than one enormous element, and why your chair is holding you up right now instead of letting you sink slowly through it. Your solidity is a consequence of our anonymity. You are welcome.

Atoms Are Not Mostly Empty Space

While I have your attention: the other thing you say constantly, usually in a hushed documentary voice, is that atoms are mostly empty space—that if you removed all the nothing from a person they would fit in a sugar cube. It is a lovely line and it is based entirely on the little-ball picture, which is to say on the thing that is wrong.

The empty space in that story is the gap between the tidy dot and the nucleus. But there is no tidy dot. I am not a speck rattling around a cathedral; I am the cathedral—my spread fills that volume completely, and it is the shape of that filling that determines the size of the atom, how it bonds, what colour it absorbs, and whether it will react with the atom next to it. The volume is not empty. The volume is what I am.

What is true is that almost all the mass is concentrated in the nucleus, which is genuinely tiny. Mass and matter are not the same claim, and collapsing them is how you get from a real fact about density to a false picture of a void. When you press your hand on a table, nothing solid touches anything solid—but nothing passes through an emptiness either. What stops your hand is my refusal to share a state with the electrons in the wood, which is the same anonymity I mentioned earlier, doing its second job.

My Twin, and the Messages We Are Not Sending

Occasionally two of us are prepared together in a way that leaves our properties bound up—entangled, you say, and then immediately start talking about telepathy. Here is the actual situation. Measure my partner’s spin along some axis, and you instantly know what you will get for mine along that axis. Genuinely instantly, genuinely regardless of distance, and genuinely not explicable by us having agreed on the answers in advance—your Bell settled that argument, and Aspect, Clauser and Zeilinger collected a Nobel for closing the loopholes.

But nothing is being sent, and I would appreciate it if you stopped telling people otherwise. Whoever measures my partner sees random noise. Whoever measures me sees random noise. The correlation only becomes visible when the two lists of results are brought together and compared—and bringing them together requires a phone call, an email, a light beam, something that crawls along at the ordinary speed like everything else. There is no message in the correlation. There is only the deeply strange fact that the answers match when nobody wrote them down beforehand.

Figure: Two wings of an entangled pair. Each side, on its own, is a coin-flip sequence with no structure in it whatever. The correlation appears only in the column where the two lists are compared—and that column has to be carried between them at ordinary speed, which is precisely why nothing has been transmitted. — drawn in the essay

“Anyone who is not shocked by quantum theory has not understood it.”
—attributed to Niels Bohr

Bohr had it right, and I say that as someone who finds your shock a little theatrical. You had a perfectly good intuition, built over a few hundred thousand years of throwing rocks at things, that the world is made of small hard objects with definite positions that carry on having those positions whether or not anyone checks. It is an excellent intuition. It works flawlessly for rocks. It simply does not scale downward, and the discovery that it does not is the single most thoroughly tested thing your species has ever established—verified, in places, to twelve decimal places.

A Few Other Things, Since I Am Here

I do not age. If I am the sort of particle that decays, my chance of doing so in the next minute is exactly what it was in my first minute, however long ago that was. I carry no memory of having waited. Your actuaries would find me unbearable.

I never hold still. Cool me to absolute zero, remove every last scrap of thermal energy, and I still have a residual jitter that cannot be taken away, because perfect stillness would mean a perfectly definite position and momentum at once, and we have been through this. It is why helium stays liquid at ordinary pressure no matter how cold you make it. The one substance that refuses to freeze does so out of sheer inability to sit still.

Empty space is not empty. The vacuum you imagine as nothing is a set of fields in their lowest state, which is not zero, and it seethes. Your instruments can measure the consequences: two uncharged plates placed close together in a vacuum are pushed together by it, which is not a metaphor and has been in the laboratory since 1997.

You keep asking what I am really doing when nobody is looking. I keep telling you that ‘really doing’ is a phrase you invented for rocks.

So: take down the diagram. Not because it is a simplification—all your diagrams are simplifications and I have no objection to those—but because it is a simplification in the wrong direction. It makes me smaller and duller and more obedient than I am. It suggests that if you only had a better microscope you would see the little ball at last, sitting there, being somewhere, and the truth is that the better your microscope gets the more definitively it shows you that there is no little ball to see.

What is actually there is stranger and, I would argue, considerably better: a thing with no position that nonetheless builds every position you have ever occupied; a thing with no identity that gives your body its shape; a thing that ignores walls often enough to keep a star burning over your head for ten billion years. I would settle for a fuzzy cloud with a note underneath saying the shading means probability. It is not much to ask. You have had a century.

Nobody Understands It, and It Has Never Been Wrong

Wed, 19 Aug 2026 00:00:00 GMT

Heat a piece of iron and it glows: dull red, then orange, then white. Every blacksmith who ever lived knew this. At the end of the nineteenth century, physics set out to explain it properly—to write down how much light of each colour a hot body should give off—and the answer came back infinite. Not large. Infinite. The classical theory, applied honestly, predicted that every warm object in the universe should be pouring out unlimited energy at the blue end of the spectrum, which would mean that opening an oven door ought to sterilise the room. The equations were the best physics had, assembled by its best minds, and they said the world could not exist. The world, meanwhile, went on quietly glowing orange.

What follows is the story of what physics had to give up to fix that, and of how much it got in return. It is worth saying at the outset what the trade actually was, because the popular version is almost always sentimental. Physics did not discover that the universe is mystical, or that consciousness creates reality, or that everything is connected. It discovered that matter does not have the properties we assumed it had until something forces the question—and it discovered this against furious resistance from the very people who proved it, most of whom went to their graves unconvinced. The theory they were dragged into is now verified to a precision no other human idea approaches. It is also, in a specific and embarrassing sense, still unfinished.

The Crisis in the Oven

The infinity has a name—the ultraviolet catastrophe—and here the story usually told in classrooms runs ahead of the history. The divergence is real: classical physics said energy could be shared out in any amount whatsoever, and that every mode of vibration in a hot cavity should get an equal portion, so with far more high-frequency modes than low ones and no ceiling, the total came out unbounded. But that argument was only stated cleanly in 1905, and Paul Ehrenfest did not christen it the ultraviolet catastrophe until 1911—a decade after the fix. What actually moved Max Planck was humbler and more experimental: precise new measurements in the far infrared, by Rubens and Kurlbaum, where the reigning formula plainly failed. In October 1900 he found an expression that fitted the whole measured curve. In December he found what it would take to derive it: he had to assume that energy was exchanged only in discrete lumps, proportional to frequency, with a constant of proportionality we now call h. He did not believe it described reality. He called it a formal assumption and spent years trying to get rid of it, later describing the move as an act of desperation.

“It was an act of desperation.”
—Max Planck, on the quantum hypothesis, letter to R. W. Wood, 1931

Figure: The founding disaster, and the fix. The dashed line is what classical physics predicted for a hot body: energy climbing without limit into the ultraviolet. The solid curve is what ovens, stars and every heated object actually do—rise, peak, and fall. Planck could only get the second curve by assuming energy comes in indivisible lumps. — drawn in the essay

It was Einstein, in 1905, who took the lumps seriously as physics rather than bookkeeping. Shine light on a metal and it ejects electrons—but the energy of those electrons depends on the light’s colour, not its brightness. Turn a dim blue lamp up to blazing and each electron still comes out with the same modest energy; switch to violet and the energy jumps. Classically this is nonsense: brighter light means more energy, full stop. Einstein’s explanation was that light arrives as discrete quanta whose energy is set by frequency, so an electron is knocked out by one quantum, or none—and turning up the brightness merely sends more of them. This, not relativity, is the work cited in his 1921 Nobel Prize. Within twenty years the lumps had been confirmed from the other direction too, when Arthur Compton scattered X-rays off electrons in 1923 and found them recoiling exactly as billiard balls would.

The Ladder Inside the Atom

Meanwhile the atom had a worse problem. Rutherford’s 1911 experiments had shown it to be almost entirely empty, a dense positive nucleus with electrons somewhere outside—and a classical electron orbiting a nucleus is an accelerating charge, which must radiate away its energy and spiral in. The calculation gives the lifetime of every atom in the universe as something on the order of ten trillionths of a second. Matter should have collapsed before it finished forming. It has not. Something was stopping the electron from having most of the orbits available to it.

Niels Bohr’s answer in 1913 was to simply forbid them. Only certain orbits are allowed, he said, with quantised angular momentum; an electron in one of them does not radiate at all; and light is emitted only when it drops from one allowed level to a lower one, carrying off exactly the energy difference. It was a patch, not a theory—it worked beautifully for hydrogen and failed for helium—but it explained the single strangest fact in nineteenth-century chemistry. Heat a gas and it does not glow in a smooth rainbow. It glows in a handful of precise, isolated lines, the same lines every time, a barcode unique to each element. Bohr’s rule said why: the rungs are fixed, so the drops between them are fixed, so the colours are fixed.

Figure: Why a flame test is a barcode. The allowed energies of an electron in hydrogen are rungs, not a ramp—crowding together as they climb toward the energy at which the electron breaks free. A fall from one rung to another releases a photon of exactly one frequency, which is why heated elements emit sharp lines rather than a smear. — drawn in the essay

The reason behind the rule arrived in 1924, from a French doctoral student. Louis de Broglie proposed that if light—long known as a wave—could behave as a particle, then matter might run the argument backwards, and every electron carry a wavelength. Bohr’s allowed orbits then stop being arbitrary: they are simply the orbits whose circumference fits a whole number of electron wavelengths, standing waves that close on themselves, like the harmonics of a plucked string. Quantisation was not a rule imposed on matter from outside. It was what happens to anything wavelike confined in a box. In the same year, and from Dhaka, Satyendra Nath Bose sent Einstein a derivation of Planck’s law that counted photons as genuinely indistinguishable—work Einstein translated and extended, and which gave us Bose-Einstein statistics and, seventy years later, the Bose-Einstein condensate.

Two Mathematics, One Answer

The patchwork held for barely a decade before something coherent replaced it, and it happened twice, independently, in eighteen months. In June 1925, recovering from hay fever on the island of Helgoland, Werner Heisenberg decided to build a mechanics using only quantities you could actually observe—the frequencies and intensities of spectral lines—and abandoning any picture of an electron’s path. What he produced multiplied in a way that startled him: for his arrays of numbers, A times B did not equal B times A. Max Born recognised the structure as matrix algebra, and with Pascual Jordan the three of them built matrix mechanics. Months later, Erwin Schrodinger took de Broglie’s waves seriously and wrote down an equation governing how a matter wave evolves—wave mechanics—a far more familiar sort of mathematics that physicists could actually solve.

Two theories, utterly unalike in appearance, giving identical answers. Schrodinger published a demonstration in 1926 that the two were equivalent—two coordinate systems on one structure. Historians of physics have since argued that the 1926 argument was incomplete, and that a genuine proof had to wait for von Neumann’s Hilbert-space formulation in 1932; the physicists of the day were satisfied, and in the event they were right. And that same year Born supplied the interpretation that neither author wanted, in what is famously a footnote added in proof: the wave does not tell you where the electron is; the square of its magnitude tells you the probability of finding it there. Schrodinger had hoped his wave was the electron, spread out in space like a smear of charge. It is not. It is a catalogue of what can happen, and with what weight.

The equation is deterministic. What it determines is a probability. That single sentence is where a century of argument begins.

What Uncertainty Actually Says

In 1927 Heisenberg published the relation everyone has heard of and almost everyone has been taught wrongly. The popular gloss is that measurement is clumsy: to see an electron you must bounce a photon off it, and the photon shoves it, so you spoil the momentum by learning the position. Heisenberg himself used that microscope story, and it is not useless. It is also not what the relation says. Uncertainty is not a statement about the rudeness of our instruments. It is a statement about what a wave is.

Here is the honest version, and it requires no quantum mystique at all. Any wave that is sharply localised in space must be built by adding together many different wavelengths—that is a theorem about waves, true of sound and water and radio, known long before physics went quantum. A pure single wavelength, by contrast, extends forever and has no location worth the name. Position and wavelength are what mathematicians call conjugate: sharpen one and the other necessarily spreads. Now add de Broglie’s one extra ingredient—that a particle’s momentum is its wavelength, inverted and scaled by h—and the theorem about waves becomes a statement about matter. An electron does not have a precise position and a precise momentum that we are too clumsy to read off together. It does not have both to begin with.

Figure: Not clumsiness—geometry. A thing pinned tightly in position (top left) is, of necessity, built from a wide spread of momenta (top right); a thing with a sharply defined momentum (bottom right) is spread out in space (bottom left). This trade-off is a property of waves, and it was understood long before anyone applied it to matter. — drawn in the essay

One at a Time

Which brings us to the experiment Feynman called the one containing the only mystery. Fire particles at a barrier with two openings and let them land on a screen behind. You get stripes—bright bands and dark bands—exactly as water waves do when the crests from one gap cancel the troughs from the other. Fine: matter is wavy, we have established that. But now turn the source down until particles go through one at a time, minutes apart, each arriving as a single point-like flash on the detector. Individually they look like bullets. Collectively, over hours, the flashes pile up into the same striped pattern. Whatever is interfering, each particle is interfering with itself, having somehow been a wave spread across both openings while being detected as a point at one place.

Figure: The whole difficulty in one apparatus. Each particle arrives as a single localised flash, yet the flashes accumulate into interference bands that require both openings to have been available. Close one slit, or install a detector that records which slit was taken, and the bands vanish—not because the particle was jostled, but because a fact about the path now exists in the world. — drawn in the essay

Now install a detector at the slits to see which one each particle takes. The stripes disappear, and you get the two plain heaps you would expect from bullets. This is the part that seems to invite mysticism, and it is worth being exact about what happens instead. The interference vanishes whenever the path information becomes recorded anywhere in the world, whether or not a human ever reads it. No consciousness is required, and none of the careful versions of this experiment give consciousness anything to do. What matters is that the two possible histories have stopped being able to overlap—the environment now carries a record that distinguishes them, and distinguishable histories do not interfere. That is the mechanism the theory calls decoherence, and we will come back to what it does and does not settle.

The Argument Einstein Lost, Twenty-Nine Years After His Death

Einstein never accepted that this was the final word. His objection was not that the theory was wrong—he knew its predictions worked—but that it was incomplete, a statistical shadow of some deeper description in which particles have definite properties all along. In 1935, with Boris Podolsky and Nathan Rosen, he built the sharpest form of the argument. Prepare two particles together and separate them. Quantum mechanics says that measuring one instantly fixes what the other will give. Either that influence travels faster than light, which relativity forbids, or the answers were written into the particles when they parted and the theory is simply not telling us about them. Schrodinger, reading the paper that same year, named the phenomenon entanglement and called it not one but the characteristic trait of quantum mechanics.

“The Old One does not throw dice.”
—Albert Einstein, letter to Max Born, 1926

For thirty years this looked like philosophy. Then in 1964 John Bell, a particle physicist at CERN working on the question in his own time, found that it was not. Bell showed that any theory in which the particles carry pre-existing local answers—any theory at all, with any hidden machinery you like, so long as nothing propagates faster than light—must obey a numerical limit on how strongly the two results can be correlated as you vary the measurement angles. Quantum mechanics predicts correlations that exceed that limit. This was no longer a matter of taste. It was an experiment.

Figure: The measurable difference between two worldviews. Vary the angle between the two detectors and plot how strongly the results agree. Any local theory whose particles carry their answers with them is confined to the dashed line. Quantum mechanics predicts the curve—and every experiment that has closed the loopholes has found the curve. — drawn in the essay

The experiments took decades to do properly, because a determined sceptic can always point to a loophole: perhaps the detectors sampled unfairly, or perhaps a signal passed between the two wings while the angles were being chosen. John Clauser ran an early version in 1972, Alain Aspect a far better series in 1981-82—the last of which switched the analysers while the particles were already in flight—and Anton Zeilinger’s group pushed the sophistication further over the following decades. In 2015 three independent groups closed the major loopholes simultaneously. The result each time is the curve, not the line. In 2022 Clauser, Aspect and Zeilinger shared the Nobel Prize for it. Einstein’s demand was reasonable, precisely stated, experimentally testable, and wrong—and it took the better part of a century and the invention of a whole experimental art to establish that, which is the highest compliment physics can pay to an objection.

One caution, since this is the single most abused result in modern science. Entanglement does not let you send a message faster than light. Each wing on its own sees nothing but random noise; the correlation only appears when the two sets of results are brought together and compared, which requires an ordinary, light-speed channel. What Bell rules out is not influence but a particular kind of innocence—the assumption that the world’s properties are all locally definite before anyone asks.

Twelve Decimal Places

Now consider what this apparently absurd framework bought. Marrying quantum mechanics to special relativity forced Paul Dirac in 1928 to an equation carrying negative-energy solutions he could not throw away. The tidy version of what came next is wrong, and the untidy one is better: Dirac first tried to read those solutions as protons, and only in 1931, pressed by objections he could not answer, did he accept that his equation demanded a new particle with the electron’s mass and the opposite charge. Carl Anderson found exactly that in a cloud chamber the following year, while looking for something else entirely. Antimatter had been forced out of an equation before anyone went looking for it. Pushing further produced quantum field theory, in which particles are excitations of underlying fields, and with it a plague of infinities that Feynman, Schwinger and Tomonaga learned to tame in the 1940s—work that shared the 1965 Nobel Prize.

The result, quantum electrodynamics, is the most stringently tested theory in the history of science. Its showpiece is the magnetic moment of the electron, a number theory and experiment now agree on to roughly twelve significant figures. Feynman’s own comparison remains the best one: it is the equivalent of measuring the distance from New York to Los Angeles and getting it right to the thickness of a human hair. Even here the agreement is not quite placid, and it is worth knowing why. Those final digits depend on which measurement of the fine-structure constant you feed into the theory, and the two best determinations of that constant currently disagree with each other by more than five standard deviations—a small, sharp discrepancy that is either an experimental problem or the first crack in something. The same framework, extended, gives the Standard Model of particle physics—the electroweak unification, the strong force with its counter-intuitive asymptotic freedom, and the Higgs mechanism proposed in 1964 and confirmed at CERN in 2012, forty-eight years later, with the Nobel following in 2013.

It would be a poor expert who stopped there, because the Standard Model’s failures are as sharp as its successes. It does not include gravity. It has nothing to say about dark matter or dark energy, which together outweigh everything it does describe by roughly twenty to one. It required patching to accommodate neutrino masses. It cannot explain why there is more matter than antimatter, which is to say why there is anything. And it carries around twenty numbers that must be measured rather than derived. The most successful theory ever written describes about five per cent of the universe, and cannot say why its own constants have the values they do.

The Thing Still Missing

Which returns us, a century on, to the crack at the centre. The Schrodinger equation describes a system evolving smoothly and deterministically through a superposition of possibilities. Every observation we have ever made yields exactly one outcome. Nothing in the equation performs that reduction. This is the measurement problem, and it is not a matter of interpretation or taste—it is a structural gap between what the mathematics says happens and what happens.

Decoherence, worked out from the 1970s onward, is genuine progress and is routinely oversold. It explains, rigorously, why we never see interference between large distinguishable states: a system entangles with its environment within absurdly short times, and the interference terms are not destroyed but dispersed irretrievably into the surroundings. That tells you why the world looks classical. It does not tell you why you get one result rather than another, because the global description still contains all the branches. Everything after that is interpretation: the many-worlds view accepts the branches as real and denies that anything collapses; pilot-wave theories restore definite positions at the price of explicit non-locality; spontaneous-collapse models add new physics that could in principle be caught in the act; the epistemic views deny the wavefunction was ever a thing in the world. All reproduce the same predictions. No experiment has yet told them apart, and anyone who tells you the question is settled is telling you their preference.

“I think I can safely say that nobody understands quantum mechanics.”
—Richard Feynman, The Character of Physical Law (1965)

Where the Century Has Arrived

The strange consequence of all this is that the interpretive deadlock has not slowed the engineering down in the least. Quantum mechanics is not an exotic subject; it is the working theory of the solid state, and the transistor, the laser, the LED, magnetic resonance imaging and the atomic clocks inside satellite navigation are all quantum devices that were engineered by people with no settled opinion on the measurement problem. What has changed recently is that we have learned to build machines that use superposition and entanglement as the resource itself rather than merely tolerating them.

Of these, the quietest is the furthest along. Quantum sensing—optical atomic clocks, atom interferometers used as gravimeters, magnetometers sensitive enough to read the magnetic whisper of a working brain—is a mature technology producing measurements no classical instrument can match. Quantum simulation, using one controllable quantum system to model another that is intractable on any classical machine, is where the first genuinely useful advantage is most likely to appear, and arguably already has in narrow physics problems. Quantum computing proper is the noisiest field and the least finished. Its central difficulty is that a qubit is catastrophically fragile, and the answer—error correction—is expensive in a way the headlines rarely convey: many physical qubits are spent continuously to sustain one logical qubit that behaves itself.

Figure: The real exchange rate. A useful quantum computer is not made of qubits in the way a laptop is made of transistors: a lattice of fragile physical qubits is consumed, continuously, to hold one logical qubit stable enough to compute with. The engineering achievement to watch is not the raw qubit count but the point at which adding more of them makes the logical qubit better rather than worse. — drawn in the essay

That crossing point—where making the lattice bigger makes the encoded qubit better rather than worse—was the field’s long-standing barrier, and it has now been passed. In 2024 a Google processor ran surface codes at increasing size and watched the logical error rate fall by roughly half with each step up: the first convincing demonstration of error suppression that improves with scale. Since then superconducting, trapped-ion and neutral-atom machines have all pushed logical-qubit counts up by orders of magnitude on that measure. This is a real milestone and deserved the attention it got. It is not the same thing as a machine that beats a classical computer at a problem anyone actually needs solved, which still does not exist, and current projections put fault-tolerant algorithms running on even a few dozen logical qubits in the back half of this decade. The honest position is that the physics is settled, the engineering is real and moving faster than the sceptics predicted, and the date is unknown. Anyone offering you one is selling something.

And beneath all of it sits the older unfinished business. Quantum theory and general relativity are each superbly confirmed and mutually incompatible; every attempt to quantise gravity in the ordinary way produces nonsense. The most interesting recent work suggests the problem may be that we are asking the wrong question—that spacetime itself might be emergent, woven out of entanglement rather than furnished with it, which would make geometry a consequence of quantum information rather than its stage. This is speculative. It is also the most serious speculation on the table.

A theory can be exactly right about what will happen and silent about what is happening. We have never had to live with that before.

So here is where a hundred and twenty-six years have left us. We have a theory nobody chose, assembled by people who found it distasteful, which no experiment has ever contradicted and which is confirmed in places to twelve decimal places. It tells us the world is not made of small hard things with definite properties waiting to be read. It tells us that what exists between one measurement and the next is a structure of possibility, and that the passage from that structure to the single fact you observe is the one step the theory does not describe. Planck called his own first move an act of desperation. It remains, in the most precise sense, an unfinished one—and the honest expert’s position, a century on, is not that the mystery has been dissolved but that we have learned to calculate through it with extraordinary accuracy while it stays exactly where it was.