The Push of Nothing: A Force Inside the Void

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Take two metal plates and empty out everything between them: no air, no charge, no magnetic field. Bring them within a micron of each other and the plates begin to be pushed toward one another. In the middle of nothingness, what is pushing them?

Picture two metal plates. Flat as mirrors, facing one another. Both are electrically neutral, neither one is a magnet. Now pump out all the air between them; leave behind not a speck of dust, not a single molecule of gas. By textbook logic, these two plates have nothing whatsoever to say to each other. No charge, no current, no matter, and therefore no force. And yet, when you shrink the gap between them far enough, the plates begin to be drawn together. Something is pressing in on them. And the name of that something, at least as the story was first told, is nothingness itself.

The place where this idea was born was not a theoretical institute but an industrial laboratory. In nineteen forty-eight, Hendrik Casimir was working on an utterly ordinary problem at the research laboratory of the Dutch electronics company Philips: colloids. That is, the question of why very small particles suspended in a liquid sometimes stay dispersed and sometimes clump together and sink to the bottom. The company's interest in the question was not philosophical but commercial; half of its products depended on suspensions of exactly this kind. The force pulling the particles toward each other was already known: even in uncharged molecules, the distribution of charge inside shifts one way for an instant, then the other, and this momentary imbalance provokes a response in a neighbour, so the two attract.

When Casimir, together with his young colleague Dirk Polder, carried the calculation a little further, he found something strange. As the distance grew, the attraction died away faster than expected. The reason was simple but subtle: electromagnetic influence travels at the speed of light. By the time one molecule's message reaches its neighbour, the sending molecule has already moved on to some other state. When the reply comes back, the coordination has broken down. Because of this delay, the interaction between two atoms weakened not with the sixth power of the distance, but with the seventh.

What was truly unsettling, though, was the shape of the result. The expression that emerged was astonishingly clean; none of the messy details of the atom survived in it, only Planck's constant and the speed of light. Recounting it years later, Casimir said that this very cleanness had left him uneasy. During a walk with Niels Bohr, he described the matter. Bohr, as if muttering to himself, said that it must have something to do with zero point energy. That single sentence rebuilt the problem from the ground up.

Because according to quantum field theory, empty space is not empty. The electromagnetic field exists at every point in space, and every possible mode of vibration of that field, even at absolute zero, never comes fully to rest; an energy remains that cannot be reduced to zero. The vacuum is not the name of nothingness; it is the name of a field's lowest energy state. And that state trembles.

Casimir took the problem away from atoms and handed it directly to the field. Only certain wavelengths fit between two conducting plates; just like a guitar string fixed at both ends, only the vibrations that fit exactly can survive. Outside the plates there is no such restriction; every wavelength is free. So the variety of vibration inside is sparser than it is outside. The surplus pressing in from outside is greater than what pushes back from within, and the plates are dragged toward one another.

The numerical form of the result is just as spare: the force per unit area depends only on Planck's constant, on the speed of light, and on the fourth power of the distance between the plates. No material, no charge. That fourth power is what creates the real drama in this story. At a gap of one micrometre the force is so small that measuring it is next to impossible. Drop the gap to ten nanometres, that is, shorten the distance by a factor of one hundred, and the pressure rises by a factor of one hundred million, reaching the order of one atmosphere: the very air pressure bearing down on your shoulders at sea level. Nothingness, at the right scale, behaves like tonnes of weight.

Sailors had known of an observation resembling this effect for centuries: in a heavy swell, two ships lying side by side are drawn toward each other, because in the narrow stretch of water between the hulls the play of the waves is restricted, while the open sea outside is unbounded. The analogy is not perfect, but it puts the intuition in the right place.

Measurement, however, was a craft all its own. The first attempt came in nineteen fifty-eight, from Marcus Sparnaay, who worked in that same Philips laboratory. Using a spring balance he caught a force, and reported that what he had found did not contradict Casimir's prediction; but in practice the uncertainty of his measurement was one hundred percent. Holding two plates perfectly parallel, and cleaning off the stray charges that lingered on them, produced errors so enormous that they swamped the very force he was hunting. Real proof came forty years later. In nineteen ninety-seven, at the University of Washington, Steve Lamoreaux resorted to a trick that cut the parallelism problem out at the root: instead of a flat plate, he used a sphere, because the closest point between a sphere and a plane is single and well defined. With a torsion pendulum he measured across separations from zero point six to six micrometres, and found agreement with theory at the level of five percent. A year later, at the University of California's Riverside campus, Umar Mohideen and Anushree Roy used an atomic force microscope to push the measurement, over the range from zero point one to zero point nine micrometres, down to the one percent level. The debate was no longer about whether the force existed.

The debate was about whose problem it was. Because by the nineteen nineties the Casimir force had stopped being a laboratory curiosity and had become an engineering obstacle.

Micromachines, carved into silicon wafers by chemical etching, had entered everyday life in those years. The accelerometers that trigger a car's airbag, the gyroscopes that know which way a phone has been turned, the arrays inside projectors made of millions of tiny mirrors each only a few micrometres across. They all shared one chronic ailment: once a moving part touched its neighbour, it never came back. It stuck. Some of the culprits were familiar: the capillary pull of the thin film of water left on the surface, stray electrostatic charges, short-range molecular attraction. But when the gaps dropped below one hundred nanometres, one more item joined the list, and this item grew as the fourth power of the distance.

Sticking was not the only problem. When you bring a spring-held part close to its neighbour, if the attractive force grows faster than the spring's restoring force, a point of instability is crossed and the part collapses irreversibly onto the opposing surface. From then on, anyone designing a micromachine had to enter a term from quantum field theory into their force budget.

In two thousand one, Ho Bun Chan and his colleagues, on a team that included Federico Capasso, turned this relationship around and put it on display. They built a tiny plate of polysilicon suspended from two thin torsion rods, and brought a metal-coated sphere close to it. As the sphere approached, the plate rotated, and the way the rotation angle depended on distance matched the Casimir calculation. The meaning was plain: the fluctuations of the vacuum were now moving a machine part. The effect could become part of the design.

The next question was unavoidable. If attraction glues parts together, could repulsion hold them apart in mid-air? A frictionless nanoscale bearing; gears that never touch one another.

Theory's first answers were tantalizing, but not something you could hold in your hand. In nineteen sixty-eight, Timothy Boyer calculated that a spherical shell of perfect conductor would be pushed outward rather than collapse inward; geometry, it turned out, could flip the sign. And in nineteen seventy-four he showed that placing a perfect magnetic mirror opposite a perfect electric mirror would give rise to repulsion. But no such material existed, and there still isn't one.

The realistic route ran through Evgeny Lifshitz's general theory of nineteen fifty-six. Lifshitz dropped Casimir's assumption of flawless mirrors and put in its place the real, frequency-dependent electrical response of the material; Casimir's clean formula was one idealized limit of this broader theory. A few years later, together with his colleagues, he derived the following condition: if you place a liquid between two solids, and the liquid's electromagnetic response falls right between those of the two solids over the relevant range of frequencies, the sign of the force reverses.

In two thousand nine, Jeremy Munday, Federico Capasso and Adrian Parsegian put this to the test. A gold sphere, a plate of silica, that is, silicon dioxide, and between the two a liquid called bromobenzene. Gold's response lay above that of bromobenzene, and bromobenzene's above that of silica. What made the measurement difficult was the fluid drag the sphere felt as it moved through the liquid; the team repeated the experiment at different approach speeds to strip out the drag force, which depends on speed. What remained was a force on the order of piconewtons, and it was repulsive. The sphere was being pushed away from the plate.

And this is exactly where the tension begins, because this victory has narrow limits. Repulsion requires a liquid; in dry vacuum the job is far harder. In two thousand six, Oded Kenneth and Israel Klich proved that in vacuum two bodies that are mirror images of each other will always attract, whatever they are made of. Which means the door was theoretically closed on the idea of pushing two identical parts apart in vacuum and holding them in mid-air.

The remaining road ran through asymmetry. In twenty nineteen, Rongkuo Zhao and his colleagues, in a study that Capasso also took part in, coated one of two gold surfaces with a thin layer of Teflon and immersed both of them in ethanol. The result was a hybrid behaviour: attraction at long range, repulsion at short range. Where the two curves crossed, a stable equilibrium point was born. The object hung suspended, at a gap on the order of a hundred nanometres, with no energy supplied from outside at all. A platform was proposed for contactless nanomachines and highly sensitive force detectors. To be honest, this is still a laboratory demonstration; not in a product, not on a production line.

Now let us come to the uncomfortable question that lies beneath this whole story. Up to this point I have described everything as the pressure of the fluctuations of the vacuum. But do these experiments really prove that empty space carries energy?

In two thousand five, Robert Jaffe of the Massachusetts Institute of Technology took direct aim at this assumption. What he showed was this: the Casimir force can be derived from beginning to end without any mention whatsoever of zero point energy. In Lifshitz's framework the force arises from the fluctuation of the charges and the currents inside the plates; the quantum jitter of the electrons in the metal speaks, by way of retarded electromagnetic fields, with the jitter in the opposing plate. You are not obliged to attribute any energy to the empty space in between.

The criterion Jaffe offers is persuasive. The force depends on the fine structure constant, the number that tells you how strongly matter couples to light. When you turn that coupling down in thought, the force disappears; whereas the zero point energy of the vacuum would, by definition, go on sitting right there. What is more, the measurements too are sensitive to the material in a way that supports this: real metals become transparent at high frequencies, and in order to seat the experiment on the theory it is essential to account for the optical data of the material. Casimir's elegant formula, made up of only two fundamental constants, is an idealization that has never been observed directly in any laboratory.

Today the great majority of physicists see these two accounts not as contradictory, but as two languages writing the same physics into different ledgers; the calculations give the same number. But the sentence that this experiment proved the energy of the vacuum says more than the data permit. What the Casimir experiment measures is a difference: how the energy changes when you bring the plates closer together. About the absolute level it says not a single word.

The real open wound stands exactly there. If you set out to sum the zero point energies of the quantum fields up to any reasonable upper limit, what comes out is an energy density of unimaginable size for empty space. Since gravity responds to energy, at that density the universe ought long ago to have collapsed in upon itself or been torn to pieces. And yet the density of the dark energy that is accelerating the expansion of the universe is ridiculously small; on the order of one billionth of a joule per cubic metre. The chasm between the two numbers is quoted as lying somewhere between sixty and a hundred and twenty orders of magnitude, depending on which cutoff you choose, and it is spoken of as the worst theoretical prediction in physics. The Casimir effect does not heal this wound, because it measures differences, not the level.

Even so, the reality of quantum fluctuations is firmly supported from elsewhere. In nineteen forty-seven, Willis Lamb measured a minuscule splitting between two levels of the hydrogen atom that were expected to be equal in energy; that splitting was the direct signature of the electron interacting with the fluctuations of the field. And the tiny departure of the electron's magnetic moment from the value expected of it went on to become one of the most delicately tested predictions in all of physics.

The most striking result came in twenty eleven. Back in nineteen seventy, Gerald Moore had predicted that if you could shake a mirror with an acceleration approaching the speed of light, you could tear real photons out of the vacuum; the trouble was that no mirror can be rattled anywhere near that fast. A team in Sweden, instead of moving a mirror physically, changed the electrical boundary condition of a superconducting circuit billions of times a second. The effective mirror was oscillating at a speed on the order of a few percent of the speed of light. Out of the circuit, with no source placed inside it, came microwave photons. Light torn out of the vacuum.

The wrong conclusion to draw from this is already waiting, so it is worth saying plainly: this is not free energy. The Casimir force does work once, as the plates draw together, but in order to pull them apart again you have to give back exactly the same amount of work. The ledger closes. None of the contraptions that promise to draw limitless energy from the vacuum has any counterpart in physics.

The lesson that remains is quieter, but deeper. What the Casimir effect shows is that the vacuum is not a neutral stage upon which events take place; it is among the actors. Nothingness is not an absolute thing, but a state defined by its boundaries; when you change the boundary by bringing two plates closer together, you have also changed what the nothingness between them is. And this is no longer merely a debate about concepts. An engineer designing a device that works at gaps of tens of nanometres, having written gravity, friction and electrostatics into the force budget, is obliged to open one more line. On that line there is nothing. And nothing, at that scale, pushes back.

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