☁️Chapter 1

Two mirrors, one sky

Start with the sky. The air above you has weight. At sea level it presses on every square centimetre of you, about a fingertip, with the weight of about 1.03 kilograms. That push is one atmosphere.

Now the mirrors. A perfect mirror reflects every kind of light completely, visible or not. No real material does that.

Take two of them, flat and parallel, with no charge, joined by a wire so they sit at the same voltage. Put them in an empty box at absolute zero, the coldest anything can be, and bring them ten nanometres apart.

They are squeezed together 1.28 times as hard as the air presses on you (this page's arithmetic). At 10.6 nanometres the squeeze would match the sky's exactly; at 10 nanometres it is 28% more.

Over a fingertip's area, that squeeze matches the weight of 1.33 kilograms. Two fingertip-sized perfect mirrors, ten nanometres apart, could hold up a kilogram bag of sugar with a third to spare.

"As hard as the sky" is only a comparison of two pushes. No air takes part: the squeeze is there in a vacuum, where the most precise experiments are done.

Now the catch. Real metals are poor mirrors for the waves that matter at this gap (chapter 4 explains why). Real gold plates ten nanometres apart feel about 0.14 to 0.19 atmospheres: roughly an eighth of the perfect squeeze, somewhere between a ninth and a seventh (this page's estimate). Aluminium does no better, at about 0.15 atmospheres. Real gold or aluminium plates reach one atmosphere only at about 5 to 6 nanometres (this page's estimate).

And nobody has measured two flat plates at ten nanometres. The ten-nanometre number is a calculation, from a theory that experiments have tested at wider gaps.

📏Chapter 2

Halve the gap, sixteen times the squeeze

The idea began with atoms. In 1948 Hendrik Casimir and Dirk Polder, at Philips in Eindhoven, worked out how two neutral atoms (atoms with no overall electric charge) attract each other when they are far enough apart that the time light takes to cross between them matters. Then Casimir asked the same of two perfect mirrors, and on 29 May 1948 he presented the answer.

His answer needs just three things: the gap, the speed of light, and Planck's constant, the number that sets the size of quantum effects. Nothing about the metal or the electron's charge. That's the sign of an ideal case, and real materials part company with it exactly where the squeeze is strongest (chapter 4).

The squeeze climbs steeply as the gap closes. Halve the gap and it grows sixteen times: two times two times two times two. So it also fades fast. At a micrometre, a thousand nanometres, the perfect-mirror squeeze is about a hundred million times weaker than the air's push. At 5 nanometres it is about 20 times stronger.

Two conditions are easy to miss. The mirrors must carry no charge and sit at the same voltage: a stray few hundredths of a volt adds an electric pull that, at gaps of a micrometre, can swamp the effect.

And the formula is for absolute zero, but at ten nanometres warmth changes nothing that matters.

Drag the gap and see how fast the squeeze climbs. Then switch to real gold 👇

Switch to real gold and it falls further behind the perfect mirrors as the gap shrinks: a little under half their squeeze at 100 nanometres, about an eighth at 10, and a sixteenth to a twelfth at 5 (this page's estimate).

🎸Chapter 3

The waves that fit

In quantum theory, light and every other electric and magnetic wave come in patterns called modes, each with its own wavelength, direction and alignment. Each mode behaves like a weight on a spring, and keeps a little energy even in its lowest state: its zero-point energy.

So even empty space has a smallest possible spread in its electric and magnetic fields, one that can't be removed. Measure the fields and the values scatter around zero, though nothing is moving and no particles appear and vanish (Nº 3 makes the same point).

Add up the zero-point energy of every mode and the total is infinite. What matters for the mirrors is only how the total changes when they are there.

Between two mirrors, a wave crossing the gap must fit it, with a still point at each mirror, like a note on a guitar string. Only some lengths fit across: twice the gap, the gap itself, two-thirds of it, half of it, and so on. Outside, every length fits.

Long waves aren't banished from the gap: one kind runs along it at any length. What the mirrors change is the count.

Now count. Inside, add up the energy of every wave that fits. For comparison, add up what the same stretch of empty space would hold without the mirrors. Both totals grow without limit the more waves you count, but their difference doesn't: it settles to the same small leftover once you count enough waves. The closer the mirrors, the lower that leftover, so they pull together.

One way to picture it, set out by Peter Milonni and colleagues in 1988: the waves outside push on the mirrors harder than the fewer waves inside. It's one picture, not the only one (chapter 12 has another).

Change the gap, then count the energy 👇

At a 10 nanometre gap the longest wave that fits across is 20 nanometres: extreme ultraviolet, far shorter than anything you can see. The ruler's mark shows where gold's free electrons give up, and that is the next chapter's story.

🥇Chapter 4

Why real gold falls short

A metal works as a mirror because its free electrons, the ones not tied to any atom, move with an incoming wave and set up a wave of their own that cancels it. But they can only keep up with waves that are long enough. Gold's free electrons can follow waves longer than about 138 nanometres; aluminium's, longer than about 84.

At a 10 nanometre gap, every wave that fits across is 20 nanometres long or shorter. No metal is a good mirror for those, so real gold feels only a fraction of the perfect squeeze.

That 138 nanometres is where gold's free electrons give up, not where gold stops being shiny. Gold already soaks up much of the green, blue and violet light that falls on it, which is why it looks yellow (Nº 11). You might expect that to weaken the squeeze. It doesn't: the electrons doing the soaking-up are tied to gold's atoms, and for this squeeze they add to the pull.

The theory for real materials came from Evgeny Lifshitz in 1956.

It shows that the Casimir force and the familiar van der Waals stickiness between neutral things are one force, seen from two ends, and ten nanometres sits close to where one turns into the other.

This page used Lifshitz's theory for its real-gold estimate at 10 nanometres: between a ninth and a seventh of the perfect squeeze. It's a range partly because the inputs are uncertain, and partly because gold films differ from one another (the same films turn up in Nº 11).

Real surfaces cause trouble too. A gold film is bumpy, so even a "10 nanometre gap" is barely defined, and at 5 to 6 nanometres the bumps matter as much as the gap itself.

🔬Chapter 5

Measuring a push this small

Casimir predicted the force; he didn't measure it.

1. 1958a first test

   In 1958 Marcus Sparnaay tried with flat metal plates. His results "do not contradict" the prediction, he wrote, but the uncertainty was about as big as the force itself. It was a first test of whether the pull was there and roughly the right size, too rough to test the formula.

2. 1997about 5%, later revised

   A measurement good to a few per cent took almost forty more years. In 1997 Steve Lamoreaux used a twisting pendulum, a balance hung on a fine fibre, to measure the pull between a lens and a flat, both coated with gold. Between 0.6 and 6 micrometres he reported agreement with theory to about 5%. That comparison was later revised, by Lamoreaux himself and by others.

3. Notice the lens. Almost every precise experiment since has used a curved surface, usually a ball, against a flat, because a ball has one clear closest point (chapter 6 says why flat plates are so hard). Theory then turns the ball's pull into the squeeze between plates.

4. 1998about 1%

   In 1998 Umar Mohideen and Anushree Roy fixed a coated plastic ball, about a fifth of a millimetre across, to the springboard of an atomic force microscope, a microscopic beam whose bending measures tiny forces. Between a tenth and nine-tenths of a micrometre their data matched theory, to within about 1% of the force at the closest gap.

5. 2007an error as small as 0.2%

   Then came tiny machines. Ricardo Decca and colleagues held a gold-coated ball above a little plate rocking on two rods. By 2007 their measurement's error was as small as 0.2%, at gaps of about 160 nanometres. That is the size of their uncertainty, not a match with every theory.

Every one of these was done at a tenth of a micrometre or more. There is still a puzzle about how to treat a metal's electrons at micrometre gaps. It does not change the ten-nanometre number.

🧱Chapter 6

Why two flat plates are so hard

Casimir's formula is for two flat plates. So why not measure two flat plates? Because they have to stay parallel to a tiny fraction of the gap across their whole width. Tilt one by a whisker and, with a squeeze that climbs so steeply, the nearer edge does almost all the pulling.

A few teams have managed it. In 2002 Giacomo Bressi and colleagues measured two parallel plates coated with chromium, from half a micrometre to 3 micrometres, and pinned down the size of the squeeze to about 15%: as far as we can find, the first time flat plates were measured precisely enough to check how big the formula says the squeeze should be.

Closer gaps have needed curves. In 2008 Peter van Zwol and colleagues measured a gold ball against a gold plate from 200 nanometres down to about 12. Closer than 100 nanometres, their data matched theory to about 10%, once gold's measured response to light and the bumpiness of the surfaces were included. That's a ball and a plate, though, and real gold, not perfect mirrors.

One new result sits right in this territory. In 2026 a group at Aalto University in Finland reported a strong force between superconducting aluminium plates (cooled until electricity flows through them with no resistance at all), whose size is compatible with the Casimir force, at gaps that their own model puts at about 15 nanometres. Those gaps are the team's estimate, not a measurement.

💧Chapter 7

Can it push?

Not between two plates of the same stuff. In 2006 Oded Kenneth and Israel Klich proved that two bodies that are mirror images of each other, made of the same material, always attract.

Change the ingredients and it can turn round. Put a liquid in the gap between two different materials, and if the liquid's response to light lies between the two solids', the force pushes.

In 2009 Jeremy Munday, Federico Capasso and Adrian Parsegian showed it. They put a gold-coated ball and a plate of silica, the stuff of glass, in a liquid called bromobenzene. Below about 40 nanometres the two pushed each other away, gently. Gold against gold, in the same liquid, still pulled.

Ten years later Rongkuo Zhao and colleagues balanced a pull against a push: a tiny gold flake in ethanol, a kind of alcohol, settled at a steady height over a coated gold surface.

Both pushes happened in a liquid. Neither is levitation in air, and neither has anything to do with gravity.

In empty space, nobody has made the force push between ordinary plates. Theory allows it only with unusual ingredients, such as a perfectly magnetic plate or metal objects in special shapes, and so far those are ideas on paper.

🧲Chapter 8

Micromachines that snap shut

Micromachines, or MEMS, are mechanical parts made at the scale of micrometres: beams, plates and combs on soft springs. When their surfaces come within a few hundred nanometres of each other, the Casimir and van der Waals pull can drag a part on a soft spring into contact and hold it there. Engineers call that kind of sticking stiction. The Casimir pull is one cause; water films, trapped charges and the stickiness of surfaces in contact are others.

Here's how the snap works.

1. Hang a small plate on a spring above a fixed plate.
2. As the pull drags it closer, the spring pulls back harder,
3. but the Casimir pull grows far faster.
4. For perfect mirrors, once the plate has been pulled in by a fifth of its gap, the spring can't win any more, and the plate snaps shut.

The snapping gap is stubborn. Take a perfect-mirror plate a tenth of a millimetre square, on a spring that pulls back with one newton (about the weight of an apple) for every metre it is stretched. It snaps shut if it starts closer than 174 nanometres (this page's arithmetic). Make the spring ten times stiffer and that gap only falls to 110 nanometres; ten times softer, and it only rises to 275.

Real gold pulls more weakly, so the same plate snaps only below about 150 nanometres (this page's estimate). Across the figure's settings, real gold's snapping gap is about 4 to 5% smaller than perfect mirrors' at the widest gaps, and over a fifth smaller below 70 nanometres (this page's estimate, which if anything makes the gap shrink a little too much).

The force has moved a real micromachine, too: in 2001 Ho Bun Chan and colleagues at Bell Labs used the pull of a gold-coated ball to tilt a plate half a millimetre across.

Once a part has snapped, it stays stuck: freeing it takes work. Bring the plate closer and watch the spring's line miss the curve 👇

💡Chapter 9

Shake a mirror, make light

So far the mirrors have sat still. In 1970 Gerald Moore showed that a mirror whose position changes fast enough turns that unremovable spread in the fields (chapter 3) into real photons, particles of light. It's called the dynamical Casimir effect.

The photons come in pairs. Each photon has a frequency, how many times a second its wave wiggles, and the two frequencies in a pair add up to the shaking frequency. They are commonest near half of it.

The catch is speed: the number of photons grows with the square of the mirror's speed, and no real mirror can be shaken fast enough to make many.

Shake a metal mirror two billion times a second through a swing of one nanometre either way: in this page's simplest model (one face of the mirror, no box of mirrors around it), you'd wait about 40 days for a single pair. A published estimate for such a mirror, with different assumptions, says about a photon a day.

a wait of about40daysfor a single pair (this page's simplest model: one face of the mirror, a one-nanometre swing either way)

The way round is to move something that isn't a lump of matter. In 2011 Christopher Wilson and colleagues at Chalmers University of Technology in Sweden put a SQUID, a tiny superconducting loop whose electrical behaviour depends on the magnetic field through it, at the end of a superconducting line that guides microwaves.

Changing that field about 11 billion times a second moved the point where the microwaves bounced back, to and fro, like a mirror. The team estimates that this electrical mirror's effective speed approached about 5% of the speed of light. Nothing material moved.

At 50 thousandths of a degree above absolute zero, heat photons are few, though in an ideal wire they would still roughly match the new ones. There they saw photons around half the shaking frequency, linked in the way that marks pairs. There were 1,000 to 2,000 times more than an ideal wire would make, which the team puts down to stray resonances, unwanted ringing in the wiring.

A team in Finland saw the effect too, in 2013. As far as we can find, no mechanically moving mirror had made these photons as of October 2026.

And the light isn't free.

Whatever does the shaking pays for every pair: the vacuum supplies the spread, the shaking supplies the energy.

Shake it 👇

🕳️Chapter 10

Less than nothing?

Between perfect mirrors, the energy in the gap is lower than outside, by the same amount at every point. At 10 nanometres the gap holds about 43,000 joules less per cubic metre than the empty space outside (this page's arithmetic, for perfect mirrors; a joule is about the energy it takes to lift an apple by a metre).

That's what "negative energy" means here: less than empty space. The mirrors' own energy is vastly larger, so the total stays hugely positive, and nothing here is negative mass.

Real metals are messier. In 2002 V. Sopova and Larry Ford worked out the energy in the gap for one common, simple model of a metal. In it, the energy in a 10 nanometre gap between real plates isn't below the outside at all: it's above it, everywhere in the gap. The centre only dips below once the gap is wider than about 1.3 micrometres for aluminium (their figure), or about 2.2 for gold (this page's arithmetic from their formula).

The pull still comes from a lowered energy: the energy of the whole arrangement drops as the plates come together.

Mirrors aren't the only way below the vacuum. Squeezed light, whose noise has been pushed below the vacuum's in one respect at the cost of more in another, dips below it too, and in 2017 a team saw it happen. Quantum theory limits how deep and how long such a travelling dip can be; the one between mirrors stays put only because the mirrors are there.

Nobody has measured the energy in the gap, let alone weighed it: every experiment measures a force. A balance called Archimedes, completed in a Sardinian mine in March 2025, aims to find out whether vacuum energy has weight; as far as we can find, it had not reported a result as of October 2026.

🌌Chapter 11

The biggest mismatch

The universe's expansion is speeding up (Nº 1). The simplest explanation is a steady energy in empty space itself, called dark energy. It is tiny: about half a billionth of a joule in every cubic metre.

Now the big one. Add up the zero-point energy of every wave the vacuum could hold, and stop only where gravity's own quantum effects should take over, at an energy called the Planck energy. The total overshoots dark energy by a factor of around 10¹²⁰: a one with 120 zeros after it. The exact power depends on where you stop counting, from about 10¹¹⁸ to 10¹²³.

overshoot, around10¹²⁰a one with 120 zeros after it: the naive total against dark energy, a rough guess, not a prediction

Yakov Zel'dovich raised the mismatch in the late 1960s, and Steven Weinberg's 1989 review is the classic account of what's called the cosmological constant problem. The total is a naive estimate, not the prediction of any worked-out theory, so the fairest name for it is the largest mismatch between a rough guess and a measurement.

Can the Casimir effect help? No. It measures a difference, the energy inside the gap against the energy outside, in which the infinite parts cancel. The cosmological constant problem is about the total, the very part that cancels, and about whether it weighs anything. A Casimir experiment, however precise, measures neither. The energy missing between mirrors is not dark energy.

Turn both dials 👇

🤔Chapter 12

Is empty space really full?

So does the Casimir effect show that empty space is full of energy?

Many physicists cite it as evidence that the vacuum's energy is real: Casimir worked the force out from a change in zero-point energy, and the force is measured. Weinberg's 1989 review spoke of "the reality of zero-point energies".

In 2005 Robert Jaffe argued that this doesn't follow. The same force, he showed, can be worked out with no vacuum energy at all, as a pull between the charges and currents in the two plates: the same van der Waals stickiness as in chapter 4, seen at a longer range. Julian Schwinger and colleagues had worked Casimir forces out this way in 1978.

Jaffe's clue was the one from chapter 4: weaken the grip between electrons and light, and real plates stop pulling. To Jaffe, a force that vanishes when the charges are switched off is hard to call a property of empty space alone. In the waves picture, the same thing simply means the plates no longer change the waves.

Both descriptions give the same number. Every experiment measures the force, so no experiment can tell them apart.

Either way, empty space isn't empty in the everyday sense: the unremovable spread in its fields stays.

This page's view. The force is certain: measured to about 1% between a ball and a flat, and predicted by Lifshitz's theory, apart from that puzzle about metals at micrometre gaps. The story told about it, waves outside pushing harder or charges in the plates pulling together, is a choice of bookkeeping: the same sum, arranged differently. And neither story says how much the vacuum weighs.

🎯Chapter 13

Ten nanometres, again

Here's the thread. Perfect mirrors ten nanometres apart, at absolute zero, are squeezed 1.28 times as hard as the air presses on you. The waves that matter at that gap are too short for any metal to reflect well, so real gold feels roughly an eighth of it. The force is well measured at a tenth of a micrometre and more. It can push in a liquid and snap a micromachine shut, and a mirror moved fast enough makes light.

So the ten-nanometre number is not what real plates feel, and it isn't a measurement. It isn't proof that the vacuum is full of energy, and it isn't dark energy.

Nor is it free energy. Bringing perfect plates from far apart to ten nanometres gives out at most a tiny amount of energy, about 0.00043 joules per square metre, and only once; pulling them apart costs it all back.

Where things stand, as of 25 October 2026:

• newthe Finnish report of a strong force between superconducting plates is new;
• openthe puzzle about metals at micrometre gaps is still open;
• not yetas far as we can find, no mechanically moving mirror has made these photons;
• not yetand, as far as we can find, the balance in Sardinia hasn't yet said whether vacuum energy weighs anything.

Let's add it all up. 🏷️

Ten nanometres is where perfect mirrors would be squeezed as hard as the sky, and where real ones are already poor mirrors.