Stop Drawing Me as a Little Ball

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.

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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.

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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.

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“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.